GPT-1900
Collection
Pre-1900 LLMs for physics reasoning. RL models are physics-only; use the SFT model for general chat. Tune temperature (0.6-0.7). • 11 items • Updated • 4
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temporary relief ; and had tried every kind of remedy, that the regular and irregular practitioner had advised, to no purpose. She attributed the origin of her complaint to the severity of her accouchement, thirty years previous.
Having directed her to attend to the state of her digestive organs, I commenced the employment of Electricity on the 3d of of September, 1816, by insulation and vibration, directed to the affected parts, and so soon as the 7th of the month, though otherwise not better, she felt less pain in the back. She continued the application occasionally till the 30th, during which time, she gradually got better. She now waited to observe the effects produced, but not finding herself quite relieved, came to me again on the 16tli of October, and continued the Electricity for some days, when she reported herself to be quite free from every symptom of the complaint. She had also improved much in her general health, which no doubt had been greatly impaired by the malady, from which she declared.
she had not been even one day free, for the space of thirty years.
Though I have not met with many cases of this kind, in which I have been unsuccessful, I must candidly say, that I have been often disappointed, in the cure of this dreadful disorder. One reason of this failure, may perhaps be found in the opinion entertained of its being only a local a ffection, and the treatment required merely topical. Whereas, if the nerves themselves be affected only by sympathy, and a morbid change in the brain, occasions the disorder, very little can be expected from any local excitant. The division of the nerve, which has often proved useless, clearly indicates, that nothing short of a constitutional treatment, can cure the disease. I beg here to refer the intelligent reader, to an admirable work of Dr. Armstrong’s, on this most important subject, see his Practical Illustrations on Typhus Fevers, &c. 3d Edition, page 442. This book is deservedly held in the highest estimation by medical men.
Hypochondria -- Melancholy.
CASE 28. -- A young gentleman of fortune, who, when young, had been placed at a public seminary, where unfortunately he was seduced by his associates to the practice of a vice, as fatal to his peace of mind, as injurious to his health. This laid the foundation for a nervous disorder, which proved to him a source of protracted suffering. His mental powers became impaired, especially his memory. But, what was worst of all, \\\^ fancy dwelt for ever on imaginary evils, while increasing timidity and gloom, led him to banish himself from all society. His health daily declined, w hile a depression of spirits, and a fretfulness of temper, concurred to render him truly miserable.
In process of time, by a salutary change of habits, he partially recovered, and having become studious, and of a religious turn of thinking, he became the subject of a new kind of suffering. The terrors of future punishment now continually haunted
his fancy, enervated his powers, and embittered his existence. Under the pressure of these feelings he was ready to sink, when a ray of hope entered his mind, and so far dissipated despair, that for a while he felt somewhat recovered. Subsequent events, however, arising from family affliction, again, and again, brought him into a state of extreme nervous despondency . He frequently supposed himself so ill, as to be on the point of death, when a postman’s rap at the door, wmuld instantly banish the delusion. The disappointment of anticipated pleasure, filled him with rage, or overwhelmed him with grief. With all these perturbations of mind, he felt the whole train of dyspeptic affections, which, from their severity, led him at last to suspect, that he laboured under a disordered state of the nervous system.
The spell was now broken -- he commenced a course of treatment under a medical friend of mine, who prescribed diet more than medicine. He was then recom- |
If the. window shutter of an apartment be perfectly closed, an eye there turns upon an absolute blank: it perceives nothing. If a ray of the sun be then admitted, and made to fall upon any object, that object becomes bright, and afiects the eye as if it
MAKES BODIES VISIBLE. 127
were itself luminous. It returns a part of the light which.falls upon it, and it is visible in all directions, proving that it scat-, ters the received light all around. This scattered light, again, falling on other objects, and reflected from and among them until absorbed, like echo repeated many times and lost between perpendicular rocks, makes all of them also visible, although in a less degree, and the whole apartment is said to be lighted. If the sun's ray be made to fall upon a thing which from its nature reflects much of the light, as a sheet of white paper, the apartment will be well lighted: -- if, on the contrary, it be received on black velvet, which returns hardly any light, the apartment will remain dark; -- ^and, again, if received on a polished mirror, which returns nearly the whole light, but in one direction only, and therefore throws it upon some other single object, the efiect will be according to the nature of that object^ and nearly as if the ray had fallen directly upon it
Now, all bodies on earth, and very remarkably the ihass of atmosphere surrounding the earth, 'retain and difitise among themselves for a time the light received directly from the sun, and by so doing, maintain that milder radiance so agreeable to the sight, which renders objects visible when the sun's direct ray does not fall upon them. But for this fact, indeed, all bodies shadowed from the sun, whether by intervening clouds or by any other more opaque masses on earth, would be perfectly black or dark; that is, totally invisible. And without an atmosphere, the sun would appear a red hot orb in a black sky. On lofty summits, where half the atmosphere is below the level, the direct rays of the sun are painfully intense, and the sky is of darkest blue.
A shadow is the name given to the comparative darkness of places or objects, prevented by intervening obstacles from receiving the direct rays of some luminous body shining on the things around. The apparent darkness of a shadow, however, is not proportioned to its real darkness, but to the intensity of the surrounding lights. A landscape may be very bright, even when the sun is veiled by clouds, and then little or no shadow is perceived; but, as soon as the clouds pass away, deep shadows are cast behind every projecting object Yet the objects
128 LiGaT.
and places then appearing so dark, are, in reality, more illuminated than before the shadow existed; for they are receiving, and again scattering new light from all the mare intensely illuminated objects around them. A finger held between a candle and the wall, casts a shadow of a certain intensity; if another candle be then placed in the same line from the wall, the shadow will appear doubly dark, although, in fact, more light will be reaching the eye from it than before. If the candles be separated laterally, so as to produce two shadows of the finger, but which coincide or overlap in one part, that part will be of double darkness, as compared with the remainders. The most accurate mode of comparing lights is to place them at different distances from a screen or wall, so as to makeiliem at the same time throw equally dark shadows; and then, according to the law of decreasing intensity explained above, to calculate the intensities of the sources of light by the difference of their distances from the wall. The eye judges very easily of the equal intensity of compared shadows. |
earth, or other proper fubftance, be kept in a clofe vefTel, whereto the Nat.Hist. air has no accels, for as long a time as has been obferv'd fufiicient tx) w/''-^^'^'^ impregnate the like fubftance, or a portion of the fame matter that was iQcluded, it may help to remove our fcruples ; for if the body that was kept clofe, have either gain'd fait at all, or very much lefs in praportion to its bulk, than that which was kept expofed, we may thence learn, what is to be afcribed to the air in the production of nitre, or other faliiie concretions. And having oblerved none of thefe bodies, that would fofoon, and fo manifeftly even to the eye, difclofe a faline fubftance, as the blackifh vitriol-ore before mentioned j I judged this a very fit fubjeft, wherewith to try what maturation, or time, the air being lecluded, woii'd do in this cafe. Accordingly, having taken fome fragments of it, which we carefully freed from the -adhering vitriolic efflorefcence, we put of different fees of them into two conveniently Ihap'd glafTes, which being hermetically fealed, were order'd to be kept in fit places ^ by which means 'twas expelled, that even, without opening the glafTes, we iliould be able eafily to fee, by the changed colour of the fuperficial parts, whether any vitriolic efflorefcence was produced j but thro' the negligence, or miftake, of thofe to whom the care was recommended, the experiment was never brought to an iffue. Tho' after fome time I perceivM, that notwithftanding the glafs had been fo clofely ftopp'd, there plaiiily appeared on the outfide of the mafs, fome grains of an efflorefcence •, whofe colour, between blue and green, argued it to be of a vitriolic nrture. But although, till the fuccefs of fome fuch trial be known, 1 dare not confidently pronounce about the production or regeneration of falts, in bodies that have been robb'd of them, and afcribe it wholly to the air ; yet when I confider the feveral great effefts of the air upon feveral other bodies, I think it not raih to conjeCture, in the mean time, that the operations of the air may have a confiderable ihare in thefe phenomena i and fb, that there may be latent qualities in the air ; thefe qualities being underftood in concretOj together with the fiibftances, or corporeal effluvia, wherein they refide. And of fuch aerial qualities, taken in this fenfe, 1 fhall now proceed to mention Ibme other inftances.
The difficulty we find in keeping flame and fire alive, tho' bu: for AvUslfnk' a little time, without air, renders it fiifpicious, that there may be dil-y^f"^^^* '** perfed thro' the reft of the atmofphere, fome odd fubftance, either of*'''' a folar, aflral, or other foreign nature j on account whereof the air is fo uecefTary to the fubfiflance of flame. And this neceflity I have found to be more confiderable, and lefs dependent upon the manifeft attributes of the air, than is ufually obferv'd ij for by trials purpofely made, it has appear'd, that a fmall flame of a lamp, tho' fed perhaps with a fubtile, thin oil, wou'd in a large elafs-receiver expire for want of air, in a far lefs time than one wou'd believe. And it will not much leffen the difficulty to alledge, that either the grofs fuliginous fmoke in a clofe veflel flifled the fttme, or that the prefiiire of the air is requifite to
Vot. III. M impel
82 Hidden Qualities |
s a loose cottony mass, of a fine canary colour h poten cold. It is supposed thar
386 CADMIUM, COPPER.
other oxides of zinc exist, but they have not yet been studied.
Oxide of zine is precipitated when in solution by long boiling with great excess of carbonate of potash, or it may be precipitated, first, as sulphuret of zine by hydrosulphuret of ammonia, and then, after digesting with strong hydrochloric acid, to separate the sulphur, it may be precipitated by carbonate of potash ; from peroxide of iron, it may be separated by caustic ammonia, which precipitates the former but not the latter, unless it greatly preponderates.
Cadmium: Cd: Eq: 696. This metal is found in small quantities, in ores of zinc, from which it is separated by sulphuretted hydrogen. It is white, like tin; very ductile and malleable. It fuses considerably under a red heat, and is nearly as volatile as mercury. metal of no importance,
Copper: Cu; Eq: 395:7. This most valuable and extensively diffused metal is found native and crystallized, but the ore from which it is extracted for purposes of commerce, is copper pyrites, a double sulphuret of copper and iron, Much skill and experience is required in reducing this ore, for, as neither copper nor iron are volatile, it is necessary to oxidate and convert the iron into a fusible slag by roasting the ore in contact with siliceous matter, and then by repeated caleinations and additions of small portions of sand, gradually to expel the sulphur and the remainder of the iron. Much copper is obtained by throwing fragments of old iron into reservoirs in which the drninage water of copper mines is collected. This water holds much sulphate of copper in solution.
‘The general characters of copper are well known, Tt ranks in hardness next to iron, and is one of the most malleable of the metals. Itis incapable of decomposing water, except at a bright ved heat. At ordinary temperatures, if air be exeluded, the generality of the acids are without action on copper, but its oxidation is promoted in a remarkable manner when air has access to it; under these circumstances, the feeblest acids act upon it, and hence it is, that the metal has oceasion-
COPPER--OXIDES--TusTs FOR-- 387
ally found its way into culinary preparations with fatal effects, the soluble salts of copper being highly poisonous,
Copper forms with oxygen, suboxide, Cu,O, and protoxide, CaO. The suboxide of copper exists in nature, constituting ruby copper ore: artiticially, it may be prepared by igniting five parts of black oxide with four of copper filings, er by fusing three parts of subchloride of copper,* and two of dry carbonate of soda. Itis a reddish-brown powder, and as it resisis the action of air and moisture much better than the metal itself, it is usual to convert the surface of the vessels of copper into suboxide, or bronze them as it is termed. ‘This is effected by covering them with a paste of red oxide of iron, which, when heated, is reduced to protoxide, and by digesting in a boiling solution of acetate of copper, the vessels are freed from the protoxide of iron and cleaned.
Protoxide of copper, which is the base of the ordinary salts of copper, is best prepared by the ignition of the nitrate. It is remarkable for the facility with which it is reduced, at a low red heat, by carbon and hydrogen, a property which renders it exceedingly useful in the analysis of organic substances, as will be seen in the next lecture. |
173. Soilroad Brakes, -- During the uniform motion of a railroad car the tangential action between the track and each wheel IB small. Tluis, in Example 1, just cited, if ten ears of eight wheels each make up the train, eacli car weighing 20 tons, the backwai-d tangential action of the rails upon each wheel is only 25 lbs. When the brakes are applied to stop the train this action is much inci'eased, and is the only agency by which the rails can retard the train, directly or indirectly: directly, when the pressure of the brakes is so great as to preTcnt the wheels from turning, thereby causing them to "skid" (i.e., slide) on the rails; ■indi?rct7i/, -when tlie briJce-presenre is of such a value as still to ]wrniit perfect roiling of the wheel, in which case the rubbing (and heatiTig) occurs between the brake and wheel, and the tangential action of tlie rail has a value equal to or lees than the friction of rest. In the first case, then (skidding), the retarding influence of the raile is thefriotian ofinotion between rail and wheel ; in the second, a force which may be made as great as t\\e friction of rest between rail and wheel. Hence, aside from the fact that skidding produces objectionable flat places on the wlieel-tread, the brakes are more effective if so applied that skidding is impending, but not actually produced ; for the friction of rest is usually greater than that of actual slipping (§ IflO). This has been proved experimentally in England. The i-elarding effect of axle and rolling friction has been neglected in the above theory.
ExaTnple 1. -- A twenty-ton ear with an initial velocity of 80 feet per second (nearly a mile a minute) is to be stopped on a level within 1000 feet; required the necessary friction on each of the eight wheels.
Supposing the wheels not to skid, the friction will occur
FRICTION. 191
between the brakes and wheels, and is overcome through the (relative) distance 1000 feet. Eq. (XVI.), § 142, gives (foot- Ib.-second system)
- 8i^X 1000 = - ^ ^J(8^)*.
from which F { = friction at circumference of each wheel) = 496 lbs.
Kcamjple 2. -- Suppose skidding to be impending in the foregoing, and tlie coefficient of friction of rest (i.e., impending slipping) between rail and wheel to be/* =0.20. In what distance will the car be stopped ?
Example 3. -- Suppose the car in Example 1 to be on an upgrade of 60 feet to the mile. (In applying eq. (XVI.) here, the weight 20 tons will enter as a resistance.)
Example 4. -- In Example 3, consider all four resistances, viz., gravity, rolling friction, and brake and axle frictions, the distance being 1000 ft., and F the unknown quantity.
174. Estimation of Engine and Machinery Friction. -- According to Professor Cotterill, a. convenient way of estimating the work lost in friction in a steam-engine and machinery driven by it is the following :
Let p^ = mean effective steam-pressure per unit of area of
piston, and conceive this composed of three portions, viz., p^ = the necessary pressure to drive the engine alone unloaded, at the proper speed ; jp'„ = pressure necessary to overcome the resistance caused
by the useful work of the machines ; epf^ = pressure necessary to overcome the friction of the machinery, and that of the engine over and above its friction when unloaded. This is about \h% of p>^ (i.e., e = 0.15), except in large engines, and then rather less. That is, by formula, F being the piston-area and I the length of stroke, the work per stroke is thus distributed :
MECHANICS OF ENGINEERING.
in marine engines 2 lbs. or more per
p, is " from 1 to 1 J, c eqnare incli." |
rapid deviatian, for pre&Bures exceeding that limit. For woods, the limit h somewhat higher ; but, within this limits the results are mo re irregular than in the case of metals.
preci
170* Amount op the constant Proportion of THE Friction to the Pressure in different
% Substances.
An extensive table of the results which have been obtained on this subject will be found in the Appendii* The following may be mentioned aa general conclusions : 1 st. That the ratio of the friction to the pressure in all hard metals is, for pressures less than \'2 lbs- on the square inch, nearli/ ike same* For all metah, thtfrirtion is very little different from (me sixth of the presgure,
2d. The friction of the soft metals is greater than tbat of the hard oncf^.
3d* Tiie same relation obtains in respect to the friction of the soft woods and the hard ones- Thus two surfaces of yellow deal being pressed together, exhibited a fnction equal to more than one third the pressure, whilst the friction of two surfaces of red teak was scarcely more than one ninth of the pressure * These were the two extreme ratios in the case of woods*
Whether the fibres of the two surfaces of wood be parallel or perpendicular^ materially affects the amount of friction, and whether they be wet or dry.
Thus, when one surface of oak was pressed upon another, the fibres being parallel, the ratio of the Iction to the pressure was from -60 to '65 * whr^n
ILLUSTRATIONS Of MECHANlCi-
the surfaces were eo placad ia cDntact that their fibres were perpendumlan tbe ratio sank to -Si ; and when, the fibres remaining thus perpendicular, the surfaces were weiied it rose again to -71. It ii a practical faet of some importance, that the friction of surfaces of wood upon one another is thus sci considerably increased bj wetting them.
171 • The Amount of Friction is independist
OF THE Extent of the Surface pressed, pao-
VIDIO THE WHOLE AmOUNT OF THE PRESSURE REMA1H THE SAME, AlID THAT THE SuBSTANCK
OP THE Surface pressed is the same.
This is an important property of friction, which has heen established by numerous experiments. By increasing the surface which supports the pressure, you dinunish the amount of pressure upoa every point of it, and you thus so diminish the friction upon every point, that although there are more points which rub, their aggregate amount <rf friction is only the same as before.
Thus, in one of the experiments of Mr. Renni% a piece of cast iron, when laid upon its Jku side» which had a surface of 44 square inches^ and loaded, so as to press upon another surface of castirout with a force of 14 lbs., required a iorce Slbe* 4 oz- to make it slide ; wiien placed upon its ed^e^ which had a surface only of 6 J square inches, and subjected to the same pressure, 2 lbs. 2oz., were found sufficient to move it* The friction, in the one case^ waa then $4 ounces, and in the other^ 36.
172, The Faiction of a Boot when in a Statb of continuous motion, bears a constant e.axio to the p»es5ua£ upon it, which is the sam^, whatever bf ay be the velogitf or THE Motion,
^Thig fact results from the experimfinta of M* Morin, made in the years 1831, 1832, at Metz, on a very extensive scale, and under the saijction of the French government. |
Shadow and Penumbra. -- An opaque screen placed before aluminous bundle prevents it from passing. From this results a shadow^ which fills the whole space which would have been occupied by the intercepted bundle. If, for instance, the hand is held in the rays of the sun at a little distance from a wall, the shadow of the hand is seen on the walL In proportion as the hand is moved away from the wall the outline of the shadow is less clearly defined. This is because the sun is not a luminous jpoint^ but a disc of sensible diameter, every point of which produces a shadow. The true shadow or wmbra of the hand is that part of the shadow from which no portion of the solar disc is visible ; and the jpenwmbra the ill-defined border which surrounds the lunbra.
If a sunbeam be allowed to enter a darkened chamber through a small square hole, or one of any other shape, a screen placed very near the hole receives an image of it on a shadowed ground ; but if the screen be moved back, the image of the hole disappears in the peniunbra, and a perfectly roimd image of the sun takes its place. , Images produced by small openings.-- Effects of DifEtection. -- ^Every luminous ray which meets an obstacle to its course forms an image there, and illuminates it. It is just the same with any union of rays. A luminous object-- a candle-flame, for example -- may be considered as made up of an infinity of luminous points, each of which sends a pencil of rays to our eye, so that an image of the flame is formed therein. Similarly, any external object -- a church, for example (fig. 2) -- ^may be considered as formed of an infinity of luminous points, each of which sends rays to all objects surrounding it. In fact, if we place ourselves facing the church in a darkened room having a small hole bored in the direction of the building through the window-shutter, we shall see an image of the church formed in an inverted position
PHOTOGRAPHIC OPTICS.
upon a screen opposite the hole. For th© rays emanating from the top of the steeple pass through the hole and light
np the screen with their own colour ; those emanating from the wall do the same ; and so on with the rest of the building : thus an inverted image of If the hole in the
Fig. 2.
the church is formed on the opposite screen, shutter were very large, then each spot in the screen opposite would receive light from a great number of different and distant points of the object outside, all the images thus formed would overlap each other, and the image would be an illdefined one. The smaller, therefore, the hole is, the sharper but fainter is the image ; and conversely, the larger it is, the worse defined but brighter is the image. The size of the image evidently depends upon the distance of the church, from the hole, or of the screen which receives the image from the hole.
When the external object possesses very great Imninosity, and when the opening into the dark chamber is very minute, as, for example, when the image of the sun is received into the chamber through a thin sheet of copper pierced with a fine pinhole, the image is perceived to be not sharply marked out, but surrounded by a series of coloured rings which confuse its outline. This phenomenon has received the nameof diffraction of lights
Opaque, translucent, and transparent bodies. -- A body is opaque if it arrests the passage of rays which strike it; tramparent if it allows them to pass freely. There are no bodies either absolutely opaque or absolutely transparent. Opaque bodies when reduced to sufficiently thin laminaa always transmit some of the light which strikes them ; and transparent bodies in great thickness arrest part of the light
PRELIMINARY IDEAS. 7 |
It is customary, during the hysteric fit or paroxysm, to bleed the patient. In strong persons of a plethoric habit, and where the pulse is full, this may be proper; but in weak and delicate constitutions, or where the disease has been of long standing, or arises from inanition, it is not safe. The best course in such cases is to rouse the patient by strong smells, as burnt feathers, asafoetida, or spirits of hartshorn, held to the nose. Hot bricks may also be applied to the soles of the feet ; and the legs, arms, and belly, may be strongly rubbed with a warm cloth. Hut the best application is to put the feet and legs into warm water. This is peculiarly proper when the fits precede the flow of the menses. In cases of costiveness, a laxative clyster with asafoetida will be proper ; and, as soon as the ])aticnt can swallow, two table-spoonfuls ol a solution of asafoetida, or of some cordial julep, may be given.*
The radical cure of this disorder will be best ati tempted at a time when the palietit is most free
* When hysteric fits arc occasioned by sympathy they may be cured by exciting an opposite passion This is said to have been the case ot a whole schoo. of young ladies in Holland, who were all cured b.i being told that the lirst who was seized should bi burnt to death. Hut this method of cure, to m knowledge, will not always succeed. I woul therefore advise, that young ladies who are sub ject to hysteric fils should not be sent to boarding schools, as the disease may be cauglil by imilaliot I have known imiducss itself brought on by sym pathy.
OF HYSTERIC AFFECTIONS. 293
rom the fits. It ivill be greatly promoted by a proer attention to diet. A milk and vegetable diet, r'hen duly persi.stcd in, will often perform a cure. If owever the patient has been accustomed to a more enerous diet, it will not be .safe to leave it off all t once, but by degrees. The most proper drink i water, withasmall quantity of spirits. A cool ry air is the best. Coltl bathing, and every thing lat braces the nerves and invigorates the system, beneficial; but lying too long in bed, or whatver relaxes the body, is hurtful. It is of the reatest importance to have the mind kept checril and easy, and, if possible, to have it always □gaged in some agreeable and interesting pursuit. The proper medicines are those which strengthen le alimentary canal and the whole nervous sys- ;m, as the preparations of iron, the Peruvian ork, and other bitters. Twenty drops of the lixir of vitriol, in a cup of the infusion of the bark, lay be taken twice or thrice a-day. The bark and on may likewise be taken in substance, provided le stomach can bear them ; but they are generally 1 too small do.scs to have any effect. The chalyeate waters generally prove beneficial in this dis- ■der.
If the stomach is loaded with phlegm, vomits ill be of use; but they should not be too strong, 3r frequently repeated, as they tend to relax and eaken the stomach. If there be a tendency to • stiveness, it mu.st be removed, either by diet, or r taking an opening pill as often us it shall be xind necessary.
To lessen the irritnbility of the system, antispasodic medicines will be of use. 'I'lie best antis[)usodic medicines are musk, opium, and castor, ''hen opium disagrees with the stomach, it may ther be applied externally, or given in clysters, irutor has in some cases !)cen found to procure Dep where opium failed; for which reason Dr. ’'hytt advises, that they should be joined together likewise recoiumends the anti-hysteric plaster
291 UVrOClIONDRIAC affectiovs.
to be applied to tlie abdomen ; but. though autispasmodics and aiiodjiies are universally recominended,'yet all the extraordinary cures that I ever knew in hysteric cases were performed by means of tonic and corroborating medicines. |
485. The first law of motion may be stated thus. If no force act upon a body, it will, if at rest, remain for ever at rest ; or if in motion, it will continue for ever to move with a uniform velocity. We know this law to be true, and yet no one has ever seen it to be true for the simple reason that we cannot realise the condition which it requires. We cannot place a body in the condition of being unacted upon by any forces. But we may convince ourselves of the truth of the law by some such reasoning as the following. If a stone be thrown along the road, it soon comes to rest. The body leaves the hand with a certain initial velocity and is not further acted upon by it. Hence, if no other force acted on the stone, we should expect, if the first law be true, that it would continue to run on for ever with the original velocity at the moment of leaving the hand. But other forces do act upon the stone ; the attraction of the earth pulls it down ; and, when it begins to bound and roll upon the ground, friction comes into operation, deprives the stone of its velocity, and brings it to rest. But let the stone be thrown upon a surface of smooth ice; when it begins to slide, the force of gravity is counteracted by the reaction of the ice : there is no other force acting upon the stone except friction, which is small. Hence we find that the stone will run on for a considerable distance. It requires but little effort of the imagination to suppose a lake whose
[LECT.
surface is an infinite plane, perfectly smooth, and that the stone is perfectly smooth also. In such a case as this the first law of motion amounts to the assertion that the stone would never stop.
486. We may, in the lecture room, see the truth of this law verified to a certain extent by Atwood's machine (Fig. 66). This machine has been devised for the purpose of investigating the laws of motion by actual experiment. It consists principally of a pulley c, mounted so that its axle rests upon two pairs of wheels, as shown in the figure ; it being the object of this contrivance to enable the wheel to revolve with the utmost freedom. A pair of equal weights A, B, are attached by a silken thread, which passes over the pulley; each of the weights is counterbalanced by the other : so that when the two are in motion, we may consider either as a body
XV.] THE EXPERIMENT OF GALILEO. 233
not acted upon by any forces, and it . will be found that it moves uniformly, as far as the size of the apparatus will permit.
487. If we try to conceive a body free in space, and not acted upon by any force, it is more natural to suppose that such a body, when once started, should go on moving uniformly for ever, than that its velocity should be altered. The true proof of the first law of motion is, that all consequences properly deduced from it, in combination with other principles, are found to be verified. Astronomy presents us with the best examples. The calculation of the time of an eclipse is based upon laws which in themselves assume the first law of motion ; hence, when we invariably find that an eclipse occurs precisely at the moment for which it has been predicted, we have a splendid proof of the sublime truth which the first law of motion expresses.
THE EXPERIMENT OF GALILEO FROM THE TOWER OF PISA.
488. The contrast between heavy bodies and light bodies is so marked that without trial we hardly believe that a heavy body and a light body will fall from the same height in the same time. That they do so Galileo proved by dropping a heavy ball and a light ball together from the top of the Leaning Tower at Pisa. They were found to reach the ground simultaneously. We shall repeat this experiment on a scale sufficiently reduced to correspond with the dimensions of the lecture room.
489. The apparatus used is shown in Fig. 67. It consists of a stout framework supporting a pulley H at a height of about 20 feet above the ground. This pulley carries a rope; one end of the rope is attached to a |
Tbat tbe angles of intersection of valleys and streams are acute above and obtuse below, and tbat two streams invariably meet pn precisely tbe same level, are positions to wbi^b tbere are nar merous exceptions.
OLservations. -- We are fully disposed to give Mr. Farey all tbe merit tbat is justly due to his indefatigable personal researcbes, to thank him for tbe many practical facts and observations be bas already stated, and to bope tbat be will still add many more ta tbe general stock before his labours attain tbeir termination. Ig, wbat relates to practical matters and personal experience, bis communipations are generally correct and valuable ; and as far as tbey have been conflned to a simple statement of facts, have usually been perused by us with approbation and confidence : but with regard to his assigned cause of the present geological appear-; ances on the surface of this terrestrial globe, we bave never yet been able to mark its place in the scale of <jreation, or to view it in any other light than that of a phantom of bis .awa ioia* gtnation.
TRemarh tm SarrofO*s tkclid, by Mr. Sahti, SOS
It IS a well-known principle in nature, that the attraction of bodies, at a finite distance from each other, is reciprocal, proportional to their masses, and inversely as the squares of their distances. Mr. Farey supposes *' the probable period to be verj long, during which a satellite revolved in a continually .decreasing orbit, and affected the stupendous operations on the strata, previous to its fall into and assimilation with the compound mass of* the terraqueous globe/* If the period was very long and the orbit <:outinually decreasing, the distance between our globe and its approaching celestial visitant, when the action of gravity was first reversed at the surface of the earth, must have been considerable j ?ind the ratio between the terrestrial radius and this distance, far from being small. But as attraction is directly as the mass and inversely as the square of the distance, the mass of the satellite must evidently have been immensely great when compared with that of the earth : hence (according to Mr. Farey) we have a larg^ body revolving about a smaller -- a circumstance which cannot take place according to the present laws of nature. Mr. Farey's language above quoted also implies an approach of the satellite towards the earth 5 and though their approximation to each other would be mutual, the less body pr quantity of matter would past through the greater space in the same time 5 and therefore th© earth may be said, with more propriety, to have approached the. satellite. Besides, he who can conceive two immense solid bodies nearly of a spherical form (and we have no reason to suppose that ^ the satellite was of any other form) , falling into, and becoming assimilated with each other, so as to constitute a compound mass of nearly the same figure, must possess a very extraordinary couception, and probably a sufficient degree o^ credulity to believe, that each of two contrary propositions may be true. Absurd as these ponclusions may appear to which Mr. Farey's supposition naturally conducts us, equally so are the results of philosophic speculations in general, whenever the reins of judgment are abandoneif to the capricious power of imagination, or the dim veil of prejudice permitted to envelope the man.
Remarks on some of the Definitions and 4^ioms in Barrow'^^ Euclid. By WiM.?AM Saint, JS^y. -- Phil. Journ, No. 105.
In these remarks, Mr. Saint obviates the objections that have teen urged against Barrow's 6th and 7th Definitions as wanting the word integral ^ and shews them to be agreeable with the 0uthor*s definition of number and part. Definition 8th and 9th are objected to, as a number may be found which answers them both. The 15th definition appears to want the words less one* Pefiuitioi^ 23d^ ai(;oms Jth, Sih, and Qthj, Mr. 3* thinks obiec*
066 Captain Baits Imprapement on Anckors, i^c. |
viation differs. The achromatism^d^effected generally for two colors, preferably for those whichQ^k complementary. Owing to the irrationality of dispersion, ^heremaining colors are not accu¬ rately united, and the resul^T effect is still somewhat colored,, giving rise to a secondarj%$gprniin, in which the fixed lines may be inverted, depending u^ff^he relative dispersive powers of the two media.
357. Resuming E^s. (295) and (296), Art. 266, and supposing
the incidence sbprupon a thin prism, we have, taking the angles
for the sinep-o-) , _ „ x
< p = fi(pr , (406)
<P„ = ll4>„ (407)
.'Q
• • J.aK.
■$y
RELATING TO SOUND AND LIGHT.
23S
From the first two, we have
which, when substituted in the last, gives
d = (ji -- 1) a. (411)
Therefore, the deviation by a thin prism, with nearly normal in¬ cidence, is equal to the excess of the refractive index over unity,, multiplied by the refracting angle of the prism.
The deviation by two such prisms is
d2 = (ji -- 1) a + (pr -- 1) a , (412)
and for any number, 6n = E (p -- 1) «. (413)
If the two prisms be turned so as to have their angles in oppo¬ site directions, we have
and if 62 = 0, we must have as a condition,
p'-l
a'
p -- 1
Considering p and pr to apply in sii line H, and then to the red ray or Yu& H
^ <4I5)
n to the violet ray or
e have
The condition that till these rays is
o°- -
Sr
a .
Vv -- ^
rence of deviation should be zero for
selv
Therefore ^tfleAwo prisms will be achromatized for red and vio¬ let when A^^atio of the coefficients of dispersion of the media is inversely a^Che ratio of the refracting angles of the prisms.
ELEMENTS OF WAVE MOTION.
358. The following table gives the values of the refractive indices from which these coefficients can be obtained, for water, •crown and flint glass :
Table of Refractive Indices.
Refracting Sub¬ stances.
B.
Vr
C.
Vo
D.
E.
Il9
F.
Vb
G.
Vi
H.
Vv
Water . .
Crown Glass, No. 13 -
Flint Glass, No. 13 .
359. Achromatism of Lenses . Fora given radiant dis¬ tance /, we have for the focal distance of red rays, by Eq. (314), Art. 2 76, deviated by two lenses.
fr
r" -- (Vr 1) (r p/) + (Vr 1) {^rn r/r/) +
whence, when //' = /,", we have after reduction.
P. -- P r
P'v ~ /4
I _ L
•" j^er
The first lens being suppos^d^determined upon, r and r' are known, and r” is usually takei^tone equal to rr, as the two lenses are generally in contact throtminut ; r"' is then the only unknown quantity in the above equ^Eraf and can readily be computed.
The first members Js^Sqs. (418) and (421) being the same, we have o
whenciNve see that the problems of achromatism for lenses become
RELATING TO SOUND AND LIGHT.
those of prisms of the same material. Dividing both members of
Eq. (421) by - - ^ , we have
f1 g -- 1
Vv -- Vr
Vg-
H'v -- H',
V.-l)(p-pn)
Therefore an achromatic combination of two lenses for red and yiolet can be formed, when the ratio of the dispersive powers of the media is negative and directly as the principal focal distances of the lenses. For an achromatic objective, the negative lens must have the greater power in order that a real focus may exist. The focal lengths of the lenses can readily be found from the preceding table for an achromatic combination composed of crown and flint glass lenses.
360. To find the chromatic aberration of a lens, and the diam¬ eter of the least chromatic circle, we have for the red and violet focal distances,
yr, = (-.-1) (f-pj + yi
Subtracting the first from the second, we ha^Q
_L_Jl -(/S&P 1)
Multiply the second member by
v426)
, and substitute in the first
member //'* for //'//', ancLm^p results after substituting D and F9 for tlie dispersive po^F ana principal focal distance respectively, - (V
Ctf, f„ ... pfr
- Jr Jv -- Fo
S;
361. In Figure (85) we have approximately,
.'Q
ELEMENTS OF WAVE MOTION.
whence
rv _ Lr + Lv _ ff_ _ //\ ab AB AL a 9 |
not pafs oat. Therefore in refpeCt of thofe rays, which are reflected, we may call gp the arc of reflection, and may fay that this arc of reflection encreafes, as the diftance of the incident ray from the axis sa encreafes, till we come to the ray sd , the arc of reflection is gn for the ray sb, it is go for the ray sc, and gp for the ray sd. But after this, as the diftance of the incident ray from the axis sa encreafes, the arc of reflection decreafes 5 for og lefs than pg is the arc of reflection for the ray se, and ng is the arc of reflection for the ray sf.
From hence it is obvious, that fome one ray, which falls above sd, may be reflected from the fame point with fome other ray, which falls be¬ low sd. Thus for inftance the ray sb will be reflected from the point n, and the ray r/'will be reflected from the fame point j and confequently, when the reflected rays nr, nq are refraCted as they pafs out of the drop at r, and q , they will be parallel, by what has been (hewn in the for¬ mer part of this propofition. But fince the intermediate rays, which en¬ ter the drop between sf and sb, are not reflected from the fame point n, thefe two rays alone will be parallel to one another, when they come out of the drop ; and the intermediate rays will not be parallel to them. And . confequently thefe rays rv , qt , though they are parallel, after they emerge at r and q, will not be contiguous, and for that reafon will not be elfectual, by propofttion 314. The ray sd is reflected from p, which has been fhewn to be the limit of the arc of reflection 5 luch rays, as fall juft above sd and juft below sd, will be reflected from nearly the fame point/, as ap¬ pears from what has been already fhewn. Thefe rays therefore, will be parallel, becaufe they are reflected from the fame point p, and they will likewife be contiguous, becaufe they all of them enter the drop at one and the fame place very near to d. Confequently fuch rays, as enter the drop at d and are reflected from p the limit of the arc of reflection, will be effectual, by propofttion 314, fince when they emerge at the fore part of the drop between a and y they will be both parallel and contiguous.
If we can make out hereafter that the rain bow is produced, by the rays of the fun, which are thus reflected from drops of rain, as they fall whilft the fun fhines upon them, this propofttion may ferve to fhew us that this appearance is not produced by any rays, that fall upon any part and are reflected from any part of thofe drops : fince this appearance can¬ not be produced by any rays but thofe, which are effectual ; and effec¬ tual rays muft always enter each drop at one certain place in the fore-part of it, and muft: likewife be reflected from one certain place in the hinder furface,
486 A SYSTEM OF
316. When rays , that are effectual, emerge from a drop of rain after one reflection and two refractions ; thofe , which are mofl refrangible , will, at their emerjion , make a lefs angle with the incident rays , than thofe do , which are leaf refra?igible : and by this means the rays of diffe¬ rent colours will be feparated from one a?iother. |
*~M T~T0 M Sources of Error. The same as in the preceding experiment.
EXPERIMENTS IN HEAT 280
iparatus. The same as in the preceding experiment, the exception of the boiler and dipper, which are not ed.
inipulation. Determine the water -equivalent of the imeter, stirrer, and thermometer, as in previous experi- :, if it is not known already. (If the water-equivalent calorimeter of the same material was found in the pre- 3 experiment, calculate the water-equivalent in this exnent from a comparison of the masses of the two.) ace the smaller calorimeter in the larger, as in the pres experiment, and exercise all the precautions menkl. Fill the smaller nickel-plated calorimeter a little 3 than half-full of turpentine. Weigh the calorimeter its contents and deduce the mass (M) of turpentine. this pour what you estimate to be a mass of hot water it equal to one -half of the mass of the turpentine. temperature (t0°) of the water should be about 80° C, should be noted, together with the temperature (T0°) 16 turpentine, just before the water is poured in. The tare should be kept so thoroughly stirred that, when lighest temperature (T°) is read.it is uniform through- (It may happen that two or three minutes elapse wre the highest point is reached.) Deduce the mass of water added by weighing the calorimeter with the tained mixture immediately after T° has been read, noting the combined mass of the calorimeter and turttine. Correct all observed temperatures for the errors the thermometers used. Repeat three times in all.
A MAXCAL OF RXPERMEN'TS re PHYSICS
ILLUSTRATION
*= 54.78 grama."
m = 28.18 "
(, = 97.8° C.
T ■ :4».8°C.
r.=au°c.
Jf= 60.21 grama. '
«, = 97.6° C.
r =5i.o" a
r,= 90.8°C.
M -- S7.S1 grams.
M 80.03 "
U = 97 8° C.
r = 6e.50c.
r,=80.i°c.
Jkf=52 34gramB.
m =26.88 "
f, = 97.4° C.
7 = 52.0° C.
r^swc. j
* = 58 88 grama. "*
m =82.58 "
t, = B8.8" C.
T = 62.9°C.
T,= 19.8°0.
Mean, 0.401
Queatlotia and Problems. 1. Explain in detail the derivation of the above format* ft 3. Describe a meLhoil for the ileterrmuntimj of specific h
wbicli there is no need for a correction due to the
equivalent of the calorimeter or tt
EXPERIMENT 51
Object To determine the "melting-point" of paraffine. See " Physics," Art. 187.)
General Theory. When a solid is heated, its temperature "ises gradually until it begins to melt (or vaporize), and while the solid is changing into the liquid state the temperature either remains constant or changes at an abnormal rate. All crystals and most pure substances keep their temperature unchanged while the process of fusion is in progress, provided the mixture of solid and liquid is well *tirred. For such substances the fusion- or melting-point is the temperature at which the solid and liquid are in equilibrium together. (See Experiment 44.) Obviously, such substances, as they pass from the liquid into the solid state, begin to solidify at the "fusion temperature/'
However, when waxes and certain other bodies which become "pasty" -- such as plumbers' solder -- begin to melt, the temperature does not remain constant, but continues to change during the entire process until they are liquefied completely ; and if they are cooled when in the liquid state the temperature at which they begin to solidify is not that at which they previously began to melt. The average of these two temperatures is definite for any one substance, however ; and this is called the fusion-point.
To determine this temperature for paraffine, therefore, it is simply necessary to observe the temperature at which it begins to melt and that at which it begins to solidify after having been melted. (Naphthaline has been recommended as a suitable substance to use in this experiment in place of paraffine. It has a definite melting-point, but its odor
292 A MANUAL OF EXPERIMENTS IN PHYSICS
when melting is most disagreeable, and so it should be melted under a hood.) <
Sources of Error. |
* Gunpowder containing oxygen in its composition, may be fired in vacuo ; though the explosion will be much less audible 1 ban in tlw open air. " Ed.
Miscellaneous Experiments. 71
As sound is propagated by pulses of air, it is not audible under an exhausted receiver. For if a bell be struck in vacuo, we are insensible of any vibratory effect, but as the air is admitted, the sound is augmented in proportion ; so that, if the density of the air in the receiver were increased beyond that of the atmosphere, the sound^of a bell would be more forcibly heard in such a situation than when it is struck in the open air.
The time of descent of light and heavy bodies in vacuo is always the same. For the difference of time which we observe in the open air proceeds from the resistance of the medium through which they descend; but as this is nearly removed in an exhausted receiver, a feather will fall with the same velocity as a guinea.
Bodies which balance each other in the open air, lose their equilibrium in vacuo. If a piece of cork and a piece of lead, which balance each other in air, be weighed again under an exhausted receiver, the end that suspends the cork will descend, for when both these bodies are weighed in air, they lose the weight of an equal bulk of the air, consequently the cork loses more weight than the lead; but when they are placed under an exhausted receiver, what the cork lost by its magnitude in the open air it now gains in vacuo; and as the bulk of the lead is much less than the bulk of the cork, the weight of the cork in vacuo will exceed the weight of the lead as much as their respective bulks of air exceed each other in weight.
The rise of vapour and smoke is caused by the density of the air; for if smoke, or vapour, be placed under an unexhausted receiver, it will rise and darken the interior; but as the air is exhausted the smoke descends, and at length leaves the vessel quite clear. This serves to show that the air is lightest in moist and hazy weather, for then the density of the atmosphere is not sufficient to support the humidity it
72 Miscellaneous Experiments.
contains; therefore the weight of the vapour overpowers the resistance, and it descends in aqueous particles. Winged animals are incapable of flight in vacuo. If a butterfly be suspended by its horns, from a thread in the middle of the receiver, before it is exhausted the insect will fly with apparent ease from one side to the other ; but when the air is withdrawn, it hangs perpendicularly, and, notwithstanding its efforts, it is unable to change its position.
Breathing, which is the principle action of life, arises from the compression and elasticity of air.
The air which we breathe is compressed by the act of inspiration, and the vital principle of our being is supported by the wholesome particles that we inhale, whilst those which are corrupted by our lungs and unfit for the purpose of animal life are discharged in the act of expiration.
When animals are placed under a receiver and precluded from the common air they soon lose their life; though this effect is not immediate, but in proportion to the nature of the animal and the quantity of pure air left in the receiver. Some animals, such as a toad or a snake, will exist for a considerable time; but when the remaining air is completely corrupted the animal dies.
The quantity of wholesome common air which is necessary for a man's existence is about one gallon a minute : this destroys the vital quality of about 23 hogsheads in 24 hours. A burning candle will consume nearly the same quantity in the same time. In- haling air which is deprived of its oxygen by passing through fire, or a heated tube, causes immediate death. Animals placed under a receiver, which is supplied with burnt air, expire instantly.
As the existence of the animal body depends on a proper supply of fresh air, some idea of its operation in the lungs may be formed by the following experiment
Miscellaneous Experiments. 73 |
426. When we have determined the longitude of the nodes of a planet at epochs widely distant from each other, and refer the origin of these longitudes to the same point of the ecliptic, allowance being roade for the precession "of the equinoxes, we find
yaiure of the Planetary OrbiU. 271
that the nod^s are not strictly fixed. They have all a retrograde motion in the ecliptic ; but these motions are very slow, and belong to the class called secular. The inclinations of the orbits to each other and to the ecliptic, undergo, in like manner, slight variations*
The retrogradation of the nodes of the planets is analogous to that of the nodes of the moon. It is, as we shall see hereafter, a necessary consequence of universal attraction. The same may be said of the changes in the inclination. That analysis by which we ascertain the cause, enables us to calculate the effects.
427. The inclination of the several planetary orbits to the ecliptic, together with the position of their nodes, and the secular variations of these elements, will be given in the next section*
Mature of the Planetary Orbits, -- Kepler^s Laws*
428. The position of the plane of the orbit being determined, it remains to ascertain the law of the planet's motion, and the figure described by it.
Both these particulars would be known if we could assign for each instant the length of the radius vector drawn from the planet to the sun, and the angle formed by this radius with a fixed straight line drawn in the plane of the orbit, and passing through the centre of the sun. It was by this method that we traced from observation the figure of the solar orbit.
The first element to be determined is the duration of a complete sidereal revolution of the planet. The most simple and direct method of finding this, is to observe the interval that elapses between two consecutive passages through the same node. As the plane of the ecliptic gradually changes its position by laws already investigated, allowance must be made for this change during the interval in question, that is, the observations must be reduced to a fixed ecliptic. This is done by a simple interpolation, the motion of the planet near its nodes being known.
But it is natural to expect in the planetary motions perturbations analogous to those already recognised in the motions of the sun and moon. Hence, in order to diminish their effect as much as possible, we find it necessary to determine the mean motion
272 lyieory of the Planets.
from observations which embrace a great number of revolutions In this way the periodical inequalities are several times compensated during the interval, and the error which remains in the de- ^nitive result is rendered insensible, hj being distributed through so long an interval of time. The method is the same which we used in fixing with so much precision the length of the mean year, independently of the periodical inequalities of the sun's motion. |
arm on which the power or counterpoise is placed, is variable, so that the same power is thus made to balance different weights; this is the design of the weigher in moving the counterpoise backward and for ward, a figure, at the notch in which the Fig. 44. counterpoise in a given case may
rest, showing the weight which it balances.
In the scissors, the intelligent student will readily determine what is to be considered the power, what the weight, and what the fulcrum.
produced by means of a lever, do the extremities of the arms move in straight lines ? In the use of machines, how does the space passed over by the power compare with that passed over by the weight ? 117. What examples of the lever are mentioned ? What is the common balance ? In the common steelyards, why is the power or counterpoise made so as to move from place to place ? How is the weight the counterpoise balances in a particular case, shown ? Do scissors act on the principle of the lever ? What is to be considered the power, what the weight, and what the fulcrum ?
MECHANICS. 59
The torsion balance, which has been referred to (§ 36) as furnishing the necessary means of determining the difference in the weight of a body at the equator and at the poles, consists of a coiled spring usually enclosed in a metallic case. One end of it is attached to a fixed support, and the body to be weighed is suspended from the other ; and its weight is shown by the distance to which it extends the spring. Consequently, if a body weighs more at or near one of the poles of the earth than at the equator, it must extend the spring further at the former place than at the latter. By means of a balance of this kind, made with great care, and transported from the equator to a high latitude, it is said that the increased weight of bodies in places towards the poles has been made plainly sensible.
The description of this balance is introduced here, so as to be in connection with the remarks on the common balance, and not because it is in any manner in the mode of its action connected with the lever.
118. The second kind of lever is distinguished by having the power at one extremity, and the fulcrum at the other, with the weight between them.
In figure 45, which represents a lever of the second kind, the power
¥~ ' • II ^p""" ' is to the weight as the distance
jrjLy- from the fulcrum F to the point
^ where the power is applied is to
the distance from the fulcrum to
the point to which the weight is attached ; that is, the power is to the weight as F X is to F P.
An example of the use of this kind of lever is seen in the case of two men carrying a burden on a pole between them, one of whom may be considered the fulcrum and the other the power. It is evident the burden may be so suspended between them that any given portion of its weight may faH upon either one of them. As other examples of this kind of lever, common nutcrackers, chipping-knives, and treadles to lathes may be mentioned.
1 19. The third kind of lever is that in which the fulcrum is at one extremity, and the weight or resistance at the other, while the power is applied between them.
f. 118. How is the second kind of lever distinguished ? In figure 45, what is the ratio of the power to the weight ? What examples of the use of this kind of lever are mentioned ? If two men are carrying a weight on a pole between them, how must it be placed so that each shall sustain just one half of it? 119. What is the third kind of lever? In the use of this kind of lever, which must be greatest, the power or the weight ? Is the object of the lever always to gain power ? When a man raises a ladder against the side of a building, what is to be considered the power, weight and fulcrum ? Is he obliged, in raising it, to lift more than its weight ? In the use of this kind of lever, does the weight or power move through the
60 NATURAL PHILOSOPHY. |
grooved wheels. The central wheel of the set near the west wall is round grooved, and the other two, which can be set either 6 or 4 inches apart, have flat-bottomed grooves. The purposes which tliese wheels serve are numerous and important. In the first place the middle ones are employed to reduce the friction of the lid, as has already been explained. In one of the cathetometer operations the lead balls and the tops of their supporting pieces have to be observed in order to find the levels of their centres when they are hanging out of sight inside the apparatus. At the same time the lid must be raised, and held out of the way ; but it cannot conveniently be removed altogether. To accomplish this, steel bands are passed over the flat-g]'ooved pulhes, and are each of them pinned to the ball holder at one end and hooked to an exactly equal counter-weight at the other. The balls can then be raised, and will remain hanging at any level at which they may be left. Two cords are hooked on to the eyes of the pillars R R of the lid, and after passing round the outermost puUies above, converge, and then, becoming single, pass over the central pulley next the west wall. There, a weight exactly equal to the lid, serves to counterbalance it. so that it will remain suspended in a horizontal position at anj level. The height is so chosen that one of the ball holders is just above the pillar on its side, while the other is just below the lid on the other. The balls are then at the same level, and their upper portions can be seen just above the edge of the casting C. The balls under these conditions hang quite freely, neither touching the instrument nor being deflected by contact between their wires or steel bands with the lid. The steel is necessary to give definiteness to the positions of the lead balls during the cathetometer measures as if they were to hang from cord the twisting and uncertain and variable stretching would make accurate measurement impossible. The central overhead wheel alone is employed in placing the small balls in position. I used at first, after fixing them to their own fibres and hooks, and measuring the distances when hanging from the point of the hooks to the tops and bottoms of the balls, to get them in through the window, supporting the hook by a bent pin held in one hand and passing the fibre over a bent pin held in. tlie other. The process was one of great delicacy and difficulty, but it answered with gold balls '2 inch in diameter. It was, however, next to impossible with balls of double the weight, as the fibre w^ould not, under such a strain, bend round a pin, a polished steel rod, or anything that I could think of. I had therefore to adopt the plan with the overhead wheel, which has never failed. A pin, with the point bent at right angles to form a horizontal hook, is tied to a piece of sewing silk, and allowed to hang from the central pulley. A weight equal to the ball is tied to the other end. The pin-hook is inserted in the eye of one of the hooks and eyes from which the gold ball is suspended, and pulled up till the ball is over the tube. It is then let down until the eye is opposite the window, when its hook is made to rest upon the point of a large pin held in one hand ; by this means it is transferred to the side hook where it is left hanging by its eye, and ready to be placed upon the arm. of the mirror when that is in position.
KEWTONIAt CONSTANT OP GRAVITATION. if
The Steel Tape and its Accessories.
In order to make an accurate determination of the optical distance between the reflecting surface of the mirror and the foot of the perpendicular upon the scale, I have prepared a steel tape to lie upon the beams L^ and L^ already described, and two sliders, one carrying an erecting eyepiece or low power microscope, and the other a sliding brass rod. |
Thomas W. Piper, St. Katherine’s Training College, London. Designed to accomany the ‘ Advanced Arithmetic,’ but may be used with avy other paar as P,
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than the quantity before stated. It will, therefore, sometimes occur in practice (where economy in construction is the primary object), that the quantity of pipe in proportion to a given surface of boiler may be even increased beyond the amount which is given in the preceding Table ; because, in forcing-houses, for instance, the temperature of the air will always be above 60° ; and in the warming of churches, 'warehouses, or other large buildings, the temperature of the water will generally be considerably below 200°-- the pipe not being required to be worked at its greatest intensity, -- and, therefore, in both these instances, a larger proportion of pipe may be applied to a given sized boiler. It therefore follows, that although a smaller boiler surface would really supply a sufficient quantity of heat, under strict management and constant attention, it will generally be better not to reduce the size of the boiler below what has here been stated ; for not only will the apparatus need less attention, but also the required temperature of the building can be thus much sooner attained, as well as more easily continued. A very good proportion, suitable for nearly every purpose, is to allow about one foot of boiler surface (calculated, as already described, Art. 71) to about 40 superficial feet of pipe, or other radiating surface, or about one-fifth more boiler surface than the preceding Table states.
(73.) It may be desirable here to state what are the peculiar characteristics of a good boiler for this purpose, and how the qualifications of each particular shape are to be judged of. A minute detail of the peculiarities of each of the various forms would scarcely be worth the space such a description would require. The principal recommendations of a boiler are, that it shall expose the largest surface to the fire in the smallest space ;
SURFACE OF BOILERS EXPOSED TO FIRE. 83
that it shall effectually absorb the heat given out from the fuel, so that as little heat as possible shall escape up the chimney ; that it shall allow free circulation of the water throughout its entire extent; and that it shall not be liable to get out of order, nor rapidly deteriorate by continued use. The first of these qualifications is of itself a compound question. We have seen (Art. 71) that any surface exposed to the direct action of the fire, or, in other words, to the radiant heat, receives three times as much heat as a similar surface exposed merely to the conducted heat, or that which is afforded by the products of combustion after they are thrown off from the burning fuel. Here, then, is a very important distinction in boilers ; for as radiant heat passes in straight lines in every direction, it follows that the largest possible surface ought to be exposed immediately over the burning fuel, and that, too, at the least possible distance ; because the effect of radiant heat decreases as the square of the distance between the radiating and the recipient bodies (Art. 235). It is no recommendation of a boiler, therefore, to say that it contains a certain number of square feet of heating surface in a given space ; for unless this surface can be acted upon by the radiant heat of the furnace, a boiler of less than one-half the superficial measurement, if judiciously contrived for this object, may greatly exceed it in power.*
* The most remarkable illustration of the effect of exposing a large surface to the direct action of the radiant heat is afforded by the evidence given before the Committee of the House of Commons, in 1798, on the Distillers of Scotland. Owing to the mode of levying the duty at that time, it became an object to work off the liquor from the still as rapidly as possible, irrespective of the cost of the apparatus or the expenditure of fuel. To such an extent was this carried, that the stills were actually charged, the wash distilled, and the refuse discharged about 520 times in 24 hours, or 2| minutes for each charge of
G 2 |
"Whereas the Dodtor mentions a remark¬ able circumftance of thefe waters, viz. that cold Water being fet on the fame fire, at the fame time, with the hot bath water, the cold water boiled a minute before the hot ; it were to be wifhed that this experiment were repeated again, by putting the two veffels of bath and cold wa¬ ter, at the fame time, into a large veflel of boil¬ ing water. It were to be wifhed that Lord Craw¬ ford, or any one that is going to Bareges, would
carry
carry a mercurial thermometer, graduated ac¬ cording to Fahrenheit , that would bear a fcalding heat ; we fhould then know the exa6t de¬ grees of heat of thofe waters, which do not offend in drinking, as equally hot common water will do.
This would alfo be of fervice to regulate thereby the heat of the abovementioned arti¬ ficial baths, if on trial, they fhall be found to be beneficial, which I am perfuaded they will prove, both for bathing and drinking,
I am,
S I R,
„ V . .
Your rnoft humble fervant,
Stepb. Hales .
Monfieur
Lettre de Monf. Hunauld , a Mr. Meighan .
A Paris, cc 3me 1742*
Monsieur*
JE vous fuis bien oblige des marques que vous me donnes de votre fouvenir ; je fais trop de cas de votre amitie, pour n etre pas fort aife den recevoir des preuves. Je vois auffi, avec toute la fatisfa&ion poflible que votre ardeur pour la medecine fe foutiept toujours, & meme qu elle augmente. * * * *
********* pujs qUe vous eftes a portee de continuer l’examen que vous aves deja fait fur Tefficacite des Eaux de Bareges, je vous exhorte, & je vous prie, de le continuer : ces connoiflances font trop intereffantes pour la mede¬ cine pour etre negligees, & vous eftes parfaitement propre a les acquerir. Une obfervation exafte, & fouvent repetee de leurs effets, eft le moyen d’y parvenir.
J’ai receu, avec un tres grand plaifir, le Traite que vous aves compofe, & j y ai trquve aftes de chofes propres a me bien inftruire fur ces Eaux admirables, qui, par le peu qu on en fgait dans ce pais, m’etoient prefque entierement inconfiues.
ponnes
[ 222 j
Donnes moi, je vous prie, de vos nouvelles 3 foies perfuade que je my intereffe, & que je ferois charme de trouver des oceafions de vous donner des preuves de toute Teftinie & de toute Tamitie avec lefquelles j’ai Thonneur d’etre,
Monfieur , f
Votre trh-humhle & tfes bheijjant Serviteur%
Hunauld,
F I N I S.
• V.
''v,:
* i
, V
W-
■X •" B 4
• -A.
i'i ■■■ |
The poeto fMgned the rainbow to be tie *^* ^^' " these manne-bows die conresidence of certain aerial creatures, whose »▼• odes were torned upwards ; the <hx>ps diJigfat ills towantonin the clouds. Milton, ?fZ^ "**« from bokrw, and not fklhnjr in his exquisite pastoral drama, thus alhides "*T ^^VL' •• "* "*^ instances of aenal to *fc^ Platonic idea :-- arehes. They are sometimes formed, abo, I iDok ii ftr ft inrv TMofi ^3^ waves dashing against the rocks : as may
Of «■» nqr uroisiiro m tte iSrifis. frequently be seen on the coast of Carnarvon,
T!?fe*^?5*T!^*l*."*?*^*^ Merioneth, Pembroke, Cardigan, and Car-
Aiidpl«3r>'th*pi%hi«ickmd.. marthen.
The rainbow, which, not improbably, first In some rainbows maybe discovered three
suggested the idea of arches, though beau- arches within the purple of the comtaion
tifitl in all conntries, is mors particularly so bow: 1. yellowiiAi green, daiker green, purin monntainoits ones ; for, iedependent of . pie ; 2 . green, purple ; 9. green, purple.
IS MMLW^fk.
RtmbowBi toOj are somaCimefl seen when the in no shape compete with other mannikctttr*
hoar-firost is desoending ; and Captain Par- ing nations ; so Uiat, on account of the great
ry, in his attempts to reach the north pole importance of the steam engine as a prime
by boats and siedges> saw a fog-bow, and no mover, it will be advisable to devote a com-
less than five arches fi>nned within the main mensurate space to its illustration, one, all beautifully colored. Various are the methods by which mo-
. Aristotle states that he was the first who tion may be communicated from one part of
ever saw a lunar rainbow : he saw only two a machine to another ; and much of the
in fifty years. He assuredly means he was skill of the millwright consists in his adapt-
th^ first who ever described one ; since iu- ing certain methods to his particular pur-
nar rainbows must have been observed in all poses. Sometimes a simple cord, or a cord
ages. That it was unknown to St. Ambrose, with pplleys, may be used. Levers, either
however, is evident, firom his belief that the simple or combined, are employed to com-
bow» which God promised Noah he would municate and also change the direction of
place in the firmament after the deluge, '* as the motion. Rods also are employed, which
a witness that he would never drown the may be earned to a great distance by being
world again,'* was not to be understood of connected together. But of all the modes
the ra^iwow, '' which can sever appear in of communicating motion, that by means of
the night ; but some visible virtue of the wheels is the most frequent. Wheels may
Deity. Notwithstanding this assertion of be made to turn each other even by the sim-
St. Ambrose, I have had Uie good fortune to pie contact of their surfaces when pressed
see several ; two of which were, perhaps, as together ; or their circumferences may be
fine as were ever witnessed in any country, formed into bruriies with short thick hair,
The first formed an arch over the vale of which enable them to ttfrn each other with
Usk. The moon hung over the blorenge ; considerable force ; or they may have cords,
a dark cloud suspended over Myarth ; the or straps of leather, or chains, passing from
river murmured over beds of stones ; and a one to another ; and at other times there are
bow, illumined by the moon, stretched firom points or protuberances on die rims of the
one side of the vale to the oUier. wheels. Tlie most usual method, however.
The second I saw from the castle over- of making wheels drive each other, is by
looking the bay of Carmarthen, forming a means of teeth. These are either cut into
regular semi-circle over the Towy. It was the substance of which the wheel is com-
in a moment of vicissitude ; and fancy wil- posed, when it is of metal ; or formed at the
lingly reverted to that passage of Ecclesias- same time as the rest of the wheel, when it
ticus, where the writer describes Simmi, is cast* |
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102. There are two cases in which we can find the caustic after the rays have been reflected at a circle any number of times ; first, when the incident rays are parallel, and secondly, when they diverge from a point in the circumference.
Let a ray be reflected any number of times at a circle ; and let (?„(?j be the first path of the ray across the circle, making an angle yfr^ with the positive direction of the axis of x, and let the angle GfiA be denoted by 0^. Let 0, i|r be corresponding
angles for the nth reflected ray. Then the equation to this ray will be
y -- csin6 = tan ^^{x -- c cos 6),
or y cos sfr -- x sin i^ + c sin {'<{r -- &) = 0,
where c is the radius of the circle.
But if the angle OGfi^ be denoted by (f>, we have e = 0^ + n (it - 2(j>} = 0, + n7r - 2n<f> and i/r = ilr, + n (27r - 2<^) = V^o + 2»7r - 2n0.
Hence the equation to the nth reflected ray becomes ■X sin {f„ - 2n^) - y cos (f, - 2n^) = (- 1)" c sin (v|r„ - (9„). First, let the rays be incident parallel to the axis of x ; then
118 CAUSTICS BY REFLEXION. [CHAP. VI.
we may write d„ = (/>, •<|^o = tt, and the equation to the reflected
ray is
X sin 2h^ + y cos 2n<j) = (-- 1)" c sin (j).
To find the envelope of this line, we must differentiate the equation with respect to the parameter (/>; we thus get tl^^ equation
iB cos 2n<f) -- y sin 2?i^ = (-- 1)" „- c cos <p.
This equation, combined with the equation to the ray, determines the caustic.
If we solve the equations, we find that any point on the caustic may be represented by the coordinates
y = (- 1)» ^{_ (2n + 1) sin (2?i - 1) ^ + (2re - 1) sin {2n + 1) ^}.
But the equation to an epicycloid in which the radius of the fixed circle is a, and that of the rolling circle h, is
/ 7N /I 7 cs + ft/i x = {a+ 0) cos -- cos -- ^-- 0.
y = {a + h) sin -- 5 sin -- ^-- 6.
The forms of these equations are the same, if instead of 6 we write --(2n--l)<f). Also, comparing the equations in order that they may be identical we must further have
2n+l
a + b = c
b = c
and therefore a = c
4n ' 2n- l
2n'
The caustic is therefore an epicycloid. When n is even, the cusp is on the axis of a; on the positive side of the origin. When n is odd, it is necessary to change the signs of x and y, and therefore the epicycloid points the opposite way, the cusp being on the negative side of the origin.
102 -- 104.] SECONDARY CAUSTICS. 119
103. Next, let the rays diverge from the point A on the circumference. Then ^o = 0, -f „ = tt - ^, and the equation to the reflected ray is
X sin (2n + l)<j> + y cos {2n + 1) ^ = (- 1)» c sin <f>.
t'he envelope of this line may be found as before. Differentiating with respect to the variable parameter, we get the equation
a; cos (2?i + 1) ^ - y sin (2ft + 1) (^ = (- 1)" .^-l-j c cos ^ ;
and these two equations give
( -- VTc y =-^2;^^ { - (^i + 1) sin 20 + »i sin (2ft + 2) </.} ,
which represent the coordinates of any point on the caustic.
This is again an epicycloid, the radii of the fixed and rolling circles being, respectively,
c , n
= ^ zr c.
2ft + 1 ' 2ft + 1
When n is even, the cusp is on the positive side of the origin, and when n is odd, it is on the negative side.
In the case in which n is unity, the values of a and b become equal, and the epicycloid becomes a cardioid.
104. In general, as we have seen, the reflected or refracted rays are the normals to a series of curves, which are sometimes called secondary caustics; any one of these has the reflected or refracted rays for normals and consequently the caustic curve for evolute. It is usually easier to find a secondary caustic than the caustic itself; for instance, for rays refracted at a straight line a secondary caustic is an ellipse, and for rays refracted at a circle, the Cartesian.
There are very convenient constructions for determining secondary caustics for rays issuing from a point and reflected or refracted at a curve.
SECONDARY CAUSTICS.
[chap. VI. |
The mystical or allegorical sense of these fables in a philosophical or historical view, conveyed an obscure explanation of some of the ordinary operations of nature, or the inventions or exploits of some of these pretended gods. In a religious sense, they served as a cloak for vice, and in a political sense, they served to keep a superstitious people in subjection, to those whose interest it was to conceal their mysteries.
• The different parts of nature were portioned out to those whose knowledge was the greatest, or who were most successful in investigating the properties of these parts, and applying that knowledge to the advantage of mankind : and lest these persons, who were afterwards converted into deities, should be thought mortal, their names were changed, and others were given to them expressive of their rank among the gods. Uranus, Auranos, or the Heavens, was considered by them as the oldest of the gods ; and Tithea, Tellus, Terra, or the Earth, his wife, by whom he had the Titans. The chief of these was Saturn or Time, who is said to have disputed superiority with his father ; as these heathens probably thought nothing anterior to time. He married Ops or Terra , also called Ji/iea or Cybele. She was therefore called the mother of the gods, who were nothing else in reality but sons of the earth, or mortals. Saturn, considered then the most remote of the planets, was called after the name of this god ; and hence the planet Herschel has, for the same reason, obtained the name of Uranus, from modem astronomers, being more remote than Saturn. Saturn is represented as a cruel god, who devoured his own children, in allusion to time, which at length destroys every tiling ; and hence human sacrifices were offered to him, by the ignorant and superstitious Pagans. Jupiter, however, -the most illustrious of his offspring, escaped his fury, and afterwards dethroned him for attempting to take away his life, and thus became sole master of the empire of the world, which he divided with his brothers- He reserved the heavens and the earth for himself which, according to the poets, he filled with his natural children, as he became a Proteus to gratify his passions. The empire of the air he gave to Juno, his wife, that of the 6ea to Neptune, and constituted Pluto king of the infernal regions. He was called Jupiter, or Jove, in allusion to the Jehovah of the Jews ; as the Chaldeans, who were so recently descended from Noah’s son, could not be entirely ignorant of the supreme being. The planet Jupiter is so called from this god, being the largest of the planets, and the next in order after Saturn. The three next planets, Mars, Venus and Mercury, the off spring of Jupiter, were emblems of war, pleasure and science, which this god was so famous for. The sun was called the prison of the gods, which shews that they had. some idea of the force of gravity which retains the planets in their orbits it was therefore an emblem of Jupiter, who held all the other deities in subjection. Science, which conveyed the mysteries of these gods and their pretended knowledge, was indicated by Mercury, who, trom his rapid velocity in its orbit, represented their messenger, and hence he was painted with wings, &c. The goddess of love, or rather lust, was represented by Venus, from its beautiful appearance, and its remaining alone with the sun, the emblem of Jupiter, when all die other luminaries disappeared. War was represented by Mars, from his fiery or bloodlike appearance, &c. |
693. Wise physicians should with all diligence inquire what simples nature yieldeth that have extreme subtle parts without any mordication or acrimony, for they undermine that which is hard ; they open that which is stopped and shut; and they expel that which is offensive, gently, without too much perturbation. Of this kind are elder-flowers, which therefore are proper for the stone ; of this kind is the dwarf-pine, which is proper for the jaundice ; of this kind is hartshorn, which is proper for agues and infections; of this kind is piony, which is proper for stoppings in the head ; of this kind is fumitory, which is proper for the spleen; and a number of others. Generally, divers creatures bred of putrefaction, though they be somewhat loathsome to take, are of this kind, as earthworms, timber-sowes, snails, &c. And I conceive that the trochichs of vipers (which are so much magnified) and the flesh of snakes some ways condited and corrected (which of late are grown into some credit), are of the same nature. So the parts of beasts putrified (as castoreum and musk, which have ex* treme subtle parts) are to be placed amongst tbem. We see also that putrefaction of plants (as agarick and iew's-ear) are of greatest virtue; the cause is, for that putrefaction is the subtlest of all motions in the parts of bodies ; and since we cannot take down the lives of living creatures (which some of the Paracelsians say if they could be taken down, would make us immortal ) ; the next is for subtlety of operation, to take bodies putrified, such as may be safely taken.
696. It is affirmed both by the ancient and modern observation, that in furnaces of copper and brass, where chalcites is (which is vitriol) often cast in, to mend the working, there riseth suddenly a fly, which sometimes moveth, as if it took hold on the walls of the furnace ; sometimes is seen moving in the fire below, and dieth presently, as soon as it is out of the furnace, which is a noble instance and worthy to be weighed; for it showeth that as well violent heat of fire as the gentle heat of living creatures, will vivify if it have matter proportionable. Now the great axiom of vilification is, that there must be heat to dilate the spirit of the body, an active spirit to be dilated, matter, vicious or tenacious, to hold in the spirit, and that matter to be put forth and figured. Now a spirit dilated by so ardent a fire as that of the furnacet, as soon at ever it cooleth never so little, congealeth presently. And (no doubt) this action is furthered by the chalcites, which hath a spirit, that will put forth and germinate, as we see in chemical trials.
THIRD PAST OF THE IX8TAUBATIO : -- STLYA. 535
697. It if true that they have (some of them") diaphragm and an intestine; and they have all skins, which in most of the inseeta are oast often. They are not generally of long life ; yet bees have been known to live seven years ; and snakes are thought the rather for the casting of their spoil, to live till they be old; and eels, which many times breed of putrefaction, will live and grow very long; and those that interchange from worms to flies in the summer, and from flies to worms in the winter, have been kept in boxes four years at the least |
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Wisconsin. -- ^Payable at any place without the United States, 5 per cent., with the current rate of exchange at the time of demand ; out of the state, but adjoining the same, 5 per cent ; in either of the states not adjoining this state, 10 per cent.
Iowa. -- Out of the United States and in Oregon, Utah, and New Mexico, 10 per cent; in Iowa, Missouri, Illinois, Wisconsin and Minnesota, 3 per cent ; in Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Pennsylvania, Maryland, District of Columbia, Virginia, Ohio, Indiana, Kentucky, Tennessee, Mississippi, Louisiana, and Arkansas, 5 per cent ; in any other state, 8 per cent.
Texas. -- Payable out of the state, 10 per cent.
California. -- Payabte within the U. S. east of the Rocky mountains, 15 per cent. ; in Europe, or any foreign country, 20 per cent.
Canadas. -- Payable in Europe or the West Indies, 10 per cent damages, with six per cent interest; in North America, except the West Indies, 4 per cent damages, with six per cent interest.
District of Columbia. -- [Rates similar to Maryland.]
USURY. Laws against usury prevail in all the Slates subjecting the offender to different penalties.
USURY. 41
Nothing is legally usurious but what the statutes ptohibit; a usurious contract, therefore, must be so by express words, or merely an evasion to avoid the statutes. Therefore a bargain for an annuity, though under its value, is not usurious ; yet, if the price be manifestly greatly under value, equity would hardly permit the taking of excessive interest.
But, as the statutes of usury are founded upon principles of public policy, it is not consistent with that policy, that those who make profit on money, with comparatively little hazard, should have the same profit as those who employ it in hazardous undertakings ; and a reasonable commission, beyond legal interest, for extra incidental charges, as upon agency for remittance of bills, is not held to be usurious.
But where there is a borrowing and lending of money, and an agreement for interest, any device to have more than legal interest is usurious.
In a question of usury, the intention pf the parties gives character to the transaction, and no matter what the form, when the real truth and substance is a loan of money at usurious interest, no shift or device can take it out of the law against usury.
Every case of usury must depend on its own circumftances ; and the intention of the parties, when it can be come at, and not the words used, must govern.
Though the parties to a usurious transaction may reform it by cancelling the original security, and making a new obligation for the amount due after deducting the usury, they cannot, by any transaction between them, render valid such original security. -- Dec. inN. Y.
Accordingly, where the holder of a usurious mortgage indorsed thereon an amount equal to the sum included in it for usury, it was held that the mortgage was nevertheless void, though the indorsement was made with the assent of the mortgagor. -- ibid.
A bonus of ninety dollars was paid on a loan of three thousand, and a note given for the amount, with interest payable semi-annually. Jury found that the contract was usurious, and that the forfeiture was eight hundred and ten dollars, being three-fold the amount of the bonus and interest for one year. -- Mass. Dec, TG 4*
42 CONTRACTS AND AGREEMENTS.
LAW or CONTRACTS.
I. DEFINITION OP A CONTRACT. |
In 1865, as Chairman of the Committee of Experiments of the U. S. Light-House Board, Henry commenced an extended series of observations on the conduct and intensity of sound at a distance, under varying meteorological conditions. Well aware that for the practical purposes of giving increased security to navigation, the experiments of the laboratory were of little value, he undertook a number of experimental trips on board sailing vessels, and on steamers, in order to make his observations under the actual conditions of the required service. As many of his investigations demanded intelligent co-operation, and sometimes at the distauces of many miles, he associated with him at different times, among members of the Light-House Establishment, Commodore Powell, Commodore Case, Admiral Trenchard, Commander Walker, Captain Upshur, General Poe, General Barnard, General Woodruff, Mr. Lederle, and other engineers of different Light-House Districts, and outside of the establishment, Dr. Welling and others.
At the outset of his experiments, he found that sound reflectors, which play so interesting a part in lecture-room exhibitions, were practically worthless (of whatever available dimensions) for the purpose of directing or concentrating powerful sounds to any con-
* Proceed. Am. Assoc. Albany, Aug. 1856, pp\ 128-131.
MEMORIAL OP JOSEPH HENRY.
siderable distance. At the distance of a mile or two a large steam whistle placed in the focus of a concave reflector 10 feet in diameter could be heard very nearly as well directly behind the reflector, as directly in front of it. In like manner the direction of bellmouths and of trumpet-mouths, was found to be of comparatively little importance at a distance ; showing the remarkable tendency to diifusion, especially with very loud sounds. Most of the observations made on ship-board were afterward repeated on land ; and several weeks were occupied with these important researches.
"During this series of investigations an interesting fact was discovered, namely, a sound moving against the wind, inaudible to the ear on the deck of the schooner, was heard by ascending to the mast-head. This remarkable fact at first suggested the idea that sound was more readily conveyed by the upper current of air than the lower." After citing observations by others apparently confirming the suggestion of some dominant influence in the upper wind, Henry adds : " The full significance however of this idea did not reveal itself to me until in searching the bibliography of sound, I found an account of the hypothesis of Professor Stokes in the Proceedings of the British Association for 1857,* in which the effect of an upper current in deflecting the wave of sound so as to throw it down upon the ear of the auditor, or directing it upward far above his head, is fully explained." t ^ I'ough attempt was made in the course of these observations (which were undertaken at the Light-house near New Haven, Connecticut) to compare the velocity of the wind in the upper regions with that near the surface of the earth. " The only important result however was the fact that the velocity of the shadow of a cloud passing over the ground was much greater than that of the air at the surface, the velocity of the latter being determined approximately by running a given distance with such speed that a small flag was at rest along the side of its pole. While this velocity was not perhaps greater than six miles per hour, that of the shadow of the cloud was apparently equal to that of a horse at full speed." %
* Report Brit. Assoc. Dublin, 1857, vol. xxvii. 2d part, pp. 22, 23. t Report of Light-House Board for 1874, p. 92.
IThis difference has since been established by a number of independent observations Mr. Glaisher from his balloon ascents in 1863-1865, ascertained that
DISCOUESE OF W. B. TAYLOR. |
the fiift plane A a in the diredion of the line G f£* and in its whole paiTage through the intermediar* fpace let it be attraded or impelled towards the me" dium of incidence, and by that adion let it be made to defcribe a curve line HI, and let it emerge in the diredion of the line IK, Let there be e- reded IM perpendicular to Bb the plane of emergence, and meering the line of incidence G H prolonged in M, and the plane of incidence j4m in Jt; and let the line of emergence KI be pioduced and meet HM in L. About the centre L, with the interval LI* let a circle be defenbed cutting both HM in P and Q, and MI produced in N; and firft, if the attraction or impulfe be fuppofed uniform, the curve HI (by what GaUko has demonstrated) be a parabola, whofe property is, that a redingle under its given latus rectum and the line IM is equal to the fquare of HM; and moreover the line HM will be bifeded in L. Whence if to MI there be let fall the perpendicular LO, MO $ OR will be equals and adding the equal lines ON, 01, the wholes MN> IR will be equal alio. Therefore fince IR is given MN is alfo given, and the rectangle NMI is to the rectangle under the latus redum and IM, thar is, to HM\ in a given ratio. But the redangle NMI is e- qual to the re&angle PMQ, that is, to the difference of the fquares ML 1 , and PL 1 or LP; and HAi z hath a given ratio to its fourth fin ML 1 ; therefore the ratio of ML X -- LI X to ML 1 is given, and by converfion the ratio of L/* to ML z y and its fubduplicate, the ratio of LI to ML* But in every triangle as LMI y the fines of the angles are proportional to the oppofite fides. Therefore tie ratio of the fine of the angle of incidence LMR
to
Sect. XIV. of Natural Philofophy. gi}
to the fine of the angle of emergence LIR is given* Q. E. D.
Case 2. Let now the body oafs fucceflively through feveral fpaces terminated with parallel planes* A*bB> BbcC> &c. {PL 15. Fig. x.) and let it be a&ed on by a force which is uniform in each of them feparately, but different in the different fpaces; and by what was juft dcmonftratecL the fine of the angle of incidence on the fir ft plane A a is to the fine of emergence from the fecond plane Bb in a given ratio; and this fine of incidence upon the fecond plane Bb will be to the fine of emergence from the third plane Cc in a given ratio; and this fine to the fine of emergence from the fourth plane Bd in a given ratio; and fo on in infinitum ; and by equality, the fine of incidence on the firft plane to th* fine of emergence from the laft plane in a given ratio* Let now the intervals of the planes be diminifhed, and their number be infinitely increafed, fo that the a&ion of attraction or impulfe, exerted according to any affigned law, may become continual, and the ratio of the fine of incidence on the firft plane to the fine of emergence from the laft plane being all along given, will be given then alfo. Q. E. D.
Proposition XCV. Theorem XLDC The fame things being futoofed, I fay that the velocity of the body before its incidence is to its velocity after emergence as the fine of emergence to the fine of incidence.
Make AH and Id equal (77. 25. Fig. 3,) and ercft the rxipendiculars AG> dK meeting the lines
of
3 14 Mathematical Principles Book I. |
PRESSURE OF FLUIDS.
Experiment 41. -- Object. To test for the pressures in various directions in air.
Use the same pressure gauge as in the preceding experiment. Holding it in the air, there is no indication of pressure. Try it. But remember that the air is on both sides of the rubber, and if there be any pressure on one side it may be balanced by the pressure on the other. To detect pressure we must take air away from one side, so as to leave that on the other side free to push the rubber if it can. Remove the index i ; put the lips to the end of H, and gently suck the air out, watching the rubber for indications of pressure. Test for pressure in various directions by turning the face of g upward, sideways, and slanting.
State the facts revealed by your tests. Can you infer anything in regard to the relative amounts of pressure in various directions ?
Experiment 42. -- Object. To find the relation between the pressure on a given area and the depth of that area below the surface of the fluid.
Apparatus. A tall glass jar or cylinder, A (Fig. 97), 30 to 40 cm. deep, to be filled with water. A bent glass tube, t, with one arm about 8 cm., and the other about 40 cm., long. A meter bar, m. Mercury.
Manipulation and Notes. Fix t against the side of m by rubber bands. Put mercury in t to fill both branches to equal heights about 5 cm. above the bend. Any pressure upon the mercury at a will push the mercury up at 6, and the difference in the levels of a and b will be proportional to that pressure.
Insert this pressure gauge into the water in A with its bend at the bottom of the jar. Note the depth of the mercury surface in the short branch below the surface of the water in A , and also the height of b above a. Read the scale to the nearest . 1 cm.
Raise the pressure gauge, and note again the depth of a, and the distance between the levels of a and 6. Repeat the observations at another still higher level.
Inference. Take two of the depths and their corresponding pressures, and see if you can write the four values so as to form a true proportion. See whether each pair of depths are proportional to the corresponding pressures. Then state the relation thus revealed. (Appendix II.)
~k
Fig. 07.
73. Pressure on the Bottom of a Vessel. -- a. If the base of a vessel is horizontal, and its walls vertical, as shown in sec-
138 FLUIDS AT REST. [§73.
tion by Fig. 98, the weight of the fluid which it contains must be supported by the base. The walls will support the side pressures, but none of the downward pressure, any more than if the fluid were a solid, with perfectly smooth sides, slipped into the vessel. The pressure on the base, ab, is the weight of the fluid, abh.
The pressure on the horizontal base of a vessel with vertical walls is just the weight of the fluid which the vessel contains, b. Suppose the vessel to be a cylinder containing water. Suppose the diameter of the base, aZ), to be 2.5 cm., and the depth of the water, hb, to be 8 cm., and that we desire to know the pressure which the base sustains. We can easily find the volume of the water in abh.
Volume == area of the base x the height;
area of base = \ v x square of the diameter ; .-. volume = \ x 3.1416 x 2.5* x 8 = 39.27 cc.
But the mass of 1 cc. of water, at 4° C, is approximately 1 g. ; so the total mass of water in our vessel is approximately 1 g. X 39.27, or 39.27 g., and the pressure on the bottom is the weight of this mass (§ 52, e).
Notice that the numerical work in this example may be expressed briefly as follows: Mass of 1 cc. of water x area of the base x heigld of the water.
c. The work would be the same for any other fluid, using the mass of 1 cc. of that fluid as we have used the mass of 1 cc. of water. But the mass of 1 cc. is the density of any substance (§ 6, b) ; so that in general :
The pressure on the base = density x area of base x height pf fluid ; or, if we use letters for words :
P=;cl xaxh,
PRESSURE OF FLUIDS. |
electric influence. The torpedo is found in the Mediterranean and North Seas, rarely exceeding eighteen to twenty pounds weight ; and the rapidity with which it communicates the shock is considerable, sometimes amounting to fifty in a minute and a half: it should seem that the shock is dependent on the will of the animal, and each shock accompanied by a depression of the eyes, while the intensity is stated to be four times stronger when the fish is insulated and surrounded by air. We were informed by Signor Mojon, professor of chemistry in the University of Genoa, when there, that it was endeavoured to ascertain by experiment, whether a series of torpedos, arranged in separate tubs, and conjoined with conductors, in the manner of the Couronne des Tasses, would decompose water, as in common electricity : the attempt, however, was unsuccessful ; nor do we think that this might have been expected, because it would have required a series of simultaneous shocks, as well as a continuous succession of them to have produced the effect. * Heat seems to increase the electric property in these animals ; and we were told that the temperature of the water in which one of these fish was placed having been accidentally raised too high, Mr. Walsh, by incautiously handling it at the moment, received so violent a shock as to lay him prostrate. On the authority of Spallanzani, the dying torpedo communicates its shocks more frequently than at other times, but they are then feebler ; and the same naturalist assures us that the youngest torpedo can exercise the property in question. The gymnotus electricus,
* A posthumous paper of that much lamented and distinguished philosopher, in reference to this subject, has been lately read before the Royal Society.
or Surinam eel, abounds in the rivers of Surinam * and Senegal: it is generally about three feet long, but occasionally met with ten to twenty feet long, sufficient even to kill a human being: the nerves immediately connected with these organs are larger than in other parts of the system : these have a reference to temperature, and a comparative relation to the media of air and water, the latter being an inferior conductor, and the former, when quite dry, being an electric of a superior kind, and only changing its character by means of the watery vapour it contains. We are of opinion that the electric organ of the torpedo -- perhaps we may extend it to other electrical animals -- is more subservient to the process of digestion than to that of catching its prey ; and this opinion is also maintained in a late volume of the Transactions of the Linnaean So- ciety. The curious experiments of Dr. Wilson Phillip go to prove that the galvanic influence produces an analogous result to that of the nervous power, and seems, in his researches, to have been successfully substituted for it. From the preceding observations it is evident that the animal machine is intimately connected with electricity, and we may infer this applies not merely to those extraordinary fish now reviewed, but to all animals, though in the torpedo, &c. it be most conspicuous, and the energy more concentrated ; it is sufficiently obvious, therefore, that atmospherical electricity must affect the animal system more or less, and modify its powers of action ; and the same thing applies to the process of vegetation : it is well known that when we rub the back of a cat, electric sparks are
* A physician informed us he has frequently received a shock from the gymnotiis electricus, in the rivers of Surinam, by touching the fish with a dirk : it extends considerably up the arm, inducing a benumbing torpor or paralysis. |
Jlntithenar, Abdutlor Indicis, Extensor Indicis, Hyjiothenar, Extensor Auricularis t Psoa r,
X 443 )
■M-TJ
Psoar, }
Jliacus, V Pedlin&us, )
us, >
Gluteus major, .■Gluteus medius, Gluteus minor, Tricejis, Piriformis, •Gemini, Quadratus, Obturator Internus, 1 Obturator Externus, J Semi
rmis, 1 atus, 3
NT,1
"I
Reclus,
Vastus Externus, Vastus Internus, Crureus, Sartorius, Pojilitaus, JVIembranosus, Tibialis Amicus, 7 . Peronceus Amicus, $ Gastrocnemii, Solaus, Plantari Tibialis Posticus, Peronaus Posticus, Profundus, Si, Li
Longus, } Brevis, j Flexor Pollicis, Extensor Pollicis % Thenar, Antithenar,
Flexor Pollicis Longus \ Flexor Pollicis Brevis.)
ocnemii, ^
s c
arts, ) lis Posticu aus Postit Profundus, ~l ^ublimis, > 'jumbricalis, j
They draw the fingers from the thumb.
It draws the thumb from the fingers, It draws the thumb to the fingers.
It draws the little finger from the rest.
They bend the thigh.
They extend the thigh.
It pulls the thigh inwards.
They move the thigh outwards.
They help to move the thigh obliquely and circularly.
They bend the leg.
They extend the leg.
It makes the legs cross one another. It turns the leg somewhat inwards. It turns it a little outwards.
They bend the foot.
They extend the foot.
It moveth the foot inwards. .It moveth the foot outwards.
They bend the four lesser toes. They extend the four lesser toes.
It draws the great toe from the rest ilt draws it to the rest.
MU
Abdufior minimi Digiti t Jnterossei Interni, Jnterossei Externi, Tran'sversalis,
MV
They draw the toes to the great toe, They draw them from the great toe. It brings all the toes close to one another.
In all, four hundred and forty-six muscles in the body.
Muscovy Glass, a variety of the white species of Mica, consisting of laminje, which frequently are very large, divisible to a great minuteness.
Muscularis Arteria, i.e. Scajiularis Externa Artcria.
Muscularis Vena, the upper branches of the external jugular : it spreads in the muscles which cover the scapula and joint of the humerus.
Muscuh-Cutaneus Nervus. See Cervicales.
Musculorum Communis Membrana, also called Musculosa. Winslow denies its existence. Others describe it as consisting of some small fibres glued together, a proper quantity of which is connected by the cellular membrane, which fills up the interstices of muscles.
Musculus Anterior Mallei, i. e. Musculus Externus Auris.
Musculus Externus Auris du Ver- ■nii. Winslow calls it Musculus An- terior Mallei. It is placed in a fissure on the temporal bone, above the glenoid cavity, where the lower jaw plays, runs inward, and is inserted into the Ravian process of the malleus irregularly forwards from the incus, and by taking off from the vibratory motion of the bones, it is supposed to fit the ear for recovering weaker sounds.
Musculus Externus Mallei, i. e. Tensor Membrana Tymjiani.
Musculus Internus Mallei, i. e. Laxator Membranx Tymjiani.
Musculus Superior Mallei, \. e. Tensor Membrana? Tym/iani.
Musculus Tubus Novus, i. e. Circumftexus Palati.
Muscus, moss. See Musci.
Muscus Pixidatus, cup-moss. It p a species of Lichem.
Muscus Pulmonarius, oaklungs, or lungwort. It grows spontaneously on oak trees.
Mushrooms. See Agaricus. |
port, while M is the bending moment for any section distant x from the left support. Let P, be any concentrated load upon the space jr at a distance kl from the left support, k being a fraction less than unity, and let w be the uniform load per linear unit. Let V be the resultant of all the vertical forces on the left of a section in the given span infinitely near to the 'left support, and let m be the distance of the point of application of that resultant from that support. Then the definition of bending moment gives,
But Vm is the unknown bending moment M' at the left support. Henee
(7) M= M'+ V'x - iwx" --2.P,{x -kl\
from which J/ may be found for any section as soon as Jlf^and
V have been determined.
The vertical shear V at the support may be easily found if the bending moments M^ and M" be known. Thus in equation (7) make ;r = /, then M becomes M\ and hence,
The whole problem of the discussion of restrained and continuous beams hence consists in the determination of the bending moments at the supports. When these are known the values of M and V may be determined for every section, and the general formulas (3), (4), and (5) be applied as in Chapter III, to the investigation of questions of strength and deflection. The formulas (6), (7), and (8) apply to cantilever and simple beams also. For a simple beam M' = M' = o, and
V = R. For a cantilever beam M^ = o for the free end, and Jf is the moment at the wall.
The relation between the bending moment and the vertical
Art. 46. PROPERTIES OF CONTINUOUS BEAMS.
shear at any section is interesting and important. At the section X the moment is M and the shear is V, At the next consecutive section x '\- dx the moment is J/ + dM^ which may also be expressed hy M-\- Vdx. Hence,
dM
V =
dx'
This may be proved otherwise by differentiating (7) and comparing with (6). From this it is seen that the maximum moments occur at the sections where the shear passes through zero.
Prob.* 79. A bar of length 2/ and weighing w per linear unit is supported at the middle. Apply formulas (6) and (7) to the statement of general expressions for the moment and shear at any section on the left of the support, and also at any section on the right of the support.
Art. 46. Properties of Continuous Beams.
The theory of continuous beams presented in the following pages includes only those with constant cross-section having the supports on the same level, as only such are used in engineering constructions. Unless otherwise stated, the ends will be supposed to simply rest upon their supports, so that there can be no moments at those points. Then the end spans are somewhat in the condition ot ^^ a beam with one overhanging end, and the other spans somewhat Fig. 39.
in the condition of a beam with two overhanging ends. At each intermediate support there is a negative moment, and the distribution of moments throughout the beam will be as represented in Fig. 39.
lOO RESTRAINED AND CONTINUOUS BEAMS. CH. IV.
As shown in Art. 45, the investigation of a continuous beam depends upon the determination of the bending moments at the supports. In the case of Fig. 39 these moments being those at the supports 2, 3, and 4, may be designated M^ , M^ ^ and M^ , Let F, , F, , F, , and V^ denote the vertical shear at the right of each support. The first step is to find the moments M^ , -Afg , and M^ . Then from formula (8) the values of F, , F,, F, , and F^ are found, and thus by formula (7) an expression for the bending moment in each span may be written, from which the maximum positive moments may be determined. Lastly,, by formulas (3) and (4) the strength of the beam may be investigated, and by (5) its deflection at any point be deduced.
For example, let the beam in Fig. 39 be regarded as of four equal spans and uniformly loaded with w pounds per linear unit. By a method to be explained in the following articles it may be shown that the bending moments at the supports are, |
There are many inherent difficulties in determining the number of lives lost by lightning in a domain so extensive as that of the United States. In the great majority of States and in all of the Territories systematic mortality returns are not made. In those States where such returns are required by local laws there is unfortunately a lack of uniformity both in the laws themselves and in their enforcement. It has been possible to obtain valuable material from the local au¬ thorities of three States only, viz, Massachusetts, Michigan, and Min¬ nesota.
The statistics upon which this paper is based were obtained chiefly from press dispatches and manuscript reports by reliable persons.
Press dispatches are generally prepared with considerable haste and without, in some instances, sufficient time for independent veri¬ fication ; on the whole, however, they are fairly accurate as to the main facts, but very deficient as to important details. It would seem to be an easy matter to add a simple statement of the circumstances under which casualties by lightning occur; such, for example as would answer the following questions : Was the person struck i’n a house or other building, under a tree or in the open ? If in a build¬ ing, was it provided with lightning rods; and, if so, were they in good condition ? If under a tree, what kind of tree was it and were there other trees near by ? If in an open field or road, were trees or other objects near or was the person near a wire fence ?
An aggregation of facts relating to the above inquiries would en¬ able us to speedily determine the places of danger in thunderstorms and thus minimize, in a measure at least, the loss of life by lightning.
Loss of life by lightning.-- The loss of life by lightning in the United States during each month of the period 1890-1898 is shown in the table below. The number of deaths reported in 1890, the first year of the series, is considerably smaller than for any subsequent year. This fact is probably due to a lack of completeness in the early methods of collecting statistics rather than to natural causes.
The average number of persons killed annually by lightning in the United States, as shown by the figures of Table I, is 312, a number probably under rather than above the true figure. Undoubtedly a greater or less number of persons are killed by lightning each year of which there is no knowledge outside of the immediate communities in which the casualties occur. The uncertainty which attaches to the figures of the table as a result, can not easily be determined. Another cause of uncertainty, which operates, however, in a direction
contrary to the one just mentioned, 4s the tendency to exaggeration sometimes manifest in newspaper reports. An example of gross* exaggeration is afforded in the following item, clipped from the Troy (New York) Budget of September 4, 1898:
During thunderstorms last week in Vermont two men became victims of the lightning’s fury-Samuel Swan, of New Bedford, Mass., a guest at Rutland, and Dr. Royal T. Sawyer, of Worcester. These deaths make a total of twenty-nine from lightning during the past year (1898) in Vermont.
As the figures given in the above article were so much at variance with those derived from other sources, special effort was made to prove their correctness or falsity. The chief local paper of Vermont and all other available sources of information were carefully con¬ sulted, and it was found that but five persons were positively known to have been killed in Vermont during the year. It is but fair to The Budget to say that the item was copied from an exchange. Anyone who has had experience in newspaper work will recognize at once the utter futility of attempting to trace a paragraph of this nature
to a responsible head. |
the otber on the concave or cooipressed aide. Between these two sets of fringes is a black line, indicating the situation where neither compression nor dilatation exists, and where, therefore, double refraction is absent.
Thus, then, the polariscope becomes a valuable means of detecting the existence of unequal tension or strains in transparent bodies, and Sir D. Brewster has suggested its useful application to the determination of the intensity and direction of all the forces which are excited by a superincumbent load in different parts of the aicb, as also the intensity and direction of the compressing and dilating forces which are excited in loaded framings of carpentry. For these purposes, models in glass or copal are to be prepared, and the effects are rendered visible by exposing the models to polarized light. He has likewise constructed a chrotnalic dynamometer for measuring the intensities of forces, founded on the facts already stated. It consists of a bundle of narrow and thick plates of glass, fixed at each end in brass caps. Then when any force is applied to a ring in the middle of the plates, the ends being fixed, the plates of glass will be bent, and the force thus produced is measured by the tints that appear on each side of the black line.
■ the gradual induration, as well as by
DOUBLE REFRACTION.
tlie mechanical compression and dilatation of animal jellies, fringes may be produced, as in glass.
2. Unequal heating causes Double Refraction. -- When heat is applied to bodies it causes them to expand or dilate. If the subst^ce to which the beat is applied be a. bad conductor, the part in contact with the heated body becomes hot, and expands before heat is communicated to the neighbouring parts. Hence the bad conductor endeavours to curve, just as when we heat a compound bar of iron and brass a curvature is induced, owing to the unequal expansive power of these two metals ; and as the brass expands more than the iron, the latter forms the inner or concave side of the cuived bar, while the brass forms the outer or convex side. On this principle is constructed the compensation balance of a watch.
Glass is a had conductor of caloric, and when abeated body is applied to it, the part in contact with this becoming hot, expands, hut owing to the bad conducting quality of the medium, the surrounding parts not being influenced by the heat, do not expand, but resist the dilatation of the heated portion. In this way, therefore, the immediate effect of heat on one part of a piece of glass is to put all the sun-ounding parts into a strained state; one partis expand-
144 OH THE POLARIZATION OF LIGHT.
ing, and other parts are resisting tlie dilatation. When the difference of temperature is extreme, the violence of the strain is such that very thick pieces of glass are sometimes rent asunder. It is very desirable that we should be acquainted with the precise niechanical condition of the glass thus partially subjected to caloric A knowledge of this would greatly assist us in comprehending the optica! phenomena. But the subject is replete with difficulties. Perhaps some assistance may be obtained from the following considerations : --
J7i,.5i. LeUBCJJUis-Sh),
be a rectangular plate of ^ glass, subjected to heat || 9| along its edge J B.
1^ *■ ' ' £i This portion of the glass
being heated, tends to expand : but on account of its connection with other portions of the glass, cannot do so without forcing these to participate in its augmented bulk. These, however, owing to the bad conducting power of the glass, retain their original temperature, and consequently refuse to expand, so that the stratum is subjected to compression ; that is, it is prevented from acquiring that volume which is natural to it in this heated state. The central stratum e/ is in a state of dilatation or
COLOURED POLARIZATION. |
infinitely small sides ; they always stood still before the abyss of the infinite and never ventured to overstep the bounds of clear conceptions. They never spoke of an infinitely close approximation or a limiting value of the sum of a series extending to an infinite number of terms. Yet they must have arrived practically at such a conception, e.g., in the case of the proposition that circles are to one another as the squares on their diameters, they must have been in the first instance led to infer the truth of the proposition by the idea that the circle could be regarded as the limit of an inscribed regular polygon with an indefinitely increased number of correspondingly small sides, They did not, however, rest satisfied with such an inference ; they strove after an irrefragable proof, and this, from the nature of the case, could only be an indirect one. <Ac- cordingly we always find, in proofs by the method of exhaustion, a demonstration that an impossibility is involved by any other assumption than that which the proposition maintains. Moreover this stringent verification, by means of a double reductio ad absurdum, is repeated in every individual instance of the use of the method of exhaustion ; there is no attempt to establish, in lieu of this part of the proof, any general propositions which could be simply quoted in any particular case.
The above general characteristics of the Greek method of exhaustion are equally present in the extensions of the method found in Archimedes. To illustrate this, it will be convenient, before passing to the cases where he performs genuine integrations, to mention his geometrical proof of the property that the area of a parabolic segment is four-thirds of the triangle with the same base and vertex. Here Archimedes exhausts the parabola by continually drawing, in each segment left over, a triangle with the same base and vertex as the segment. If A be the area of the triangle so inscribed in the original segment, the process gives a series of areas
Ag An {ΠΕ eas. and the area of the segment is really the sum of the infinite series A {1444 (D8+ (+. But Archimedes does not express it in this way. He first proves
that, if A,, A,,...4,, be any number of terms of such a series, so that A, =4A,, A,=4A,,..., then
A,+A,+A,+...+4,+44, = $4), or Aa GY oe HG) SSG) 4 - τὶ
exliv INTRODUCTION.
Having obtained this result, we should nowadays suppose n to increase indefinitely and should infer at once that (4)"-? becomes indefinitely small, and that the limit of the sum on the left-hand side is the area of the parabolic segment, which must therefore be equal to 44. Archimedes does not avow that he inferred the result in this way; he merely states that the area of the segment is equal to 4A, and then verifies it in the orthodox manner by proving that it cannot be either greater or less than $A.
I pass now to the extensions by Archimedes of the method of exhaustion which are the immediate subject of this chapter. It will be noticed, as an essential feature of all of them, that Archimedes takes both an inscribed figure and a circumscribed figure in relation to the curve or surface of which he is investigating the area or the solid content, and then, as it were, compresses the two figures into one so that they coincide with one another and with the curvilinear figure to be measured; but again it must be understood that he does not describe his method in this way or say at any time that the given curve or surface is the limiting form of the circumscribed or inscribed figure. I will take the cases in the order in which they come in the text of this book.
1. Surface of a sphere or spherical segment.
The first step is to prove (On the Sphere and Cylinder 1. 21, 22) that, if in a circle or a segment of a circle there be inscribed polygons, whose sides AB, BC, CD, ... are all equal, as shown in the respective figures, then |
Decorate the interior fpace K S B T, with fiich diflFerent paintings as you fliall judge will contribute moft to the pleafuyc of the exhibition. Cover the top of the box, from K to B, with a frame in which is a glafs lined with gauze, that the light may enter the part K S B T. This firft conflrudipn being made in the proportions and with the precautions here laid down, you are next to place the inclined plane, hereafter defcribed, which muft be of a fize to enter this edifice by a back door made at G H.
CoTi/irudtion of the inclined plane. This plane fhould incline to thebafe of the ilrudure in an angle of about thirty
degrees.
io6 RATIONAL
degrees*, that is; it (houldberaifed about one third of the fpace toward the perpendicular, and muft be fupported on its fides by two triangular props, placed at I ML.
On that part of this plane with faces the mirror K F, draw fome pleafing fubjecS, as for example, a garden ornamented with bowers ; or a piece of architecture, &c. in liich manner that it may appear regula,r when feen at E, by refledion from the inclined mirror t.
Jn this plane form a groove made of two thin flips of copper, yexy little elevated above the furfacie ; let this groove be fo difpofed that the ball in going from the
* If the ball that ijs to. run 4own \hh plane make many turnings, the plane ftiould th^ l\ave a grater inclination.
t This drawing need not diffei: much from the common method ; for as the plane IMis but little in^ clined, it will be only necelTary to draw the o^eSt^ a little higher : their width may remain the fame.
top
RECREATIONS. 107
top may make various windihgs, overfuch parts of the drawings as you Ihall thiiik fit, and at lafl defcending near the middle of its inferior fide C D, (Fig. 3.} and running along the channel OP, (Fig. 2,) 'it may fall into a part made to receive it in the wheel hereafter defcribed*
Provide yourfelf with feveral ivory balls of fomething more than half an inch diameter, which are to run freely in the groove above defcribed.
Qn the infide of this box, towards R, place two fijiall tincandlefticks, in which put two wax candles to enlighten the inclined plane* ; there mufl: be a door by which you may take them out at pleafure: fix over them a cover 'of tin, to which there muft be a fujmel to c^rry the fmoke put pf the edificgt
* Tp thefe candlefticks may be joined refleftors, fo difpofed as to thrqw all thp light on the iuclined plane.*
Con-
lod RATIONAL
ConfiruSticn df the wheel for remounting th( balls incejfantly.
In the centre of the toothed wheel A, ^ (PL IX. Fig. 5.) place a barrel with-^a fpring, and let it be alfo in the centre of the brafs rod FG. The pinion of the wheel B is to take the teeth of the firft wheel A ; and its teeth are to turn the fly C, whofe wings muft be moveable, that by being more or lefs inclined, they may accelerate or retard the motion of the machine.
To the wheel A let there be fixed two brafs rods *, and at the extremity of eich there muft be a box D, (fee the profile Fig, 6.) whofe overture M N is clofed by a valve H, that moves freely on the point I : the axis of this valve muft come out beyond the furface of the box, that the check L may be there placed, which
* The axis of this wheel ftiould projeft, thaj it may be wound up by a key, in the fame manner as A clock. ,
fliould
' RECREATIONS. 109
fliould move freely, and at the fame time with the valve. Thefe boxes muft be hrge enough to contain, each of them, one of the balls, that are, as we have faid, to roll on the inclined plane, and that it may enter at the fide M of the valve, which ^mufl then clofe. The fides of thefe boxes muft incline, as in Fig, 5^ |
any desired shape of head being produced, and the whole formed at one blow or squeeze of the machine. As will be seen by reference to the engraving, the machine is driven by two friction-wheels acting alternately on a third frictionwheel covered with leather, the latter wheel being firmly attached to a vertical screw which raises the tup by means of a heavy brass nut into which it works, coupling-rods connecting the nut and tup together. The blow is upward against the end of this screw, and the shock is contained altogether in the machine, requiring no heavy foundations. The weight of the brass nut, coupling-rods and tup is counterbalanced by weights hung at the back of the machine from a swinging lever, so that the whole may move up and down on the guides with the greatest freedom. The top driving-shaft is kept in position longitudinally by balance-weights, and the machine may be made to work in either direction by movement of this shaft, thus bringing over one or the other of the frictionwheels into action. This movement is effected by a long rod connected with a lever and handle below, and having at its lower end a strong coiled spring. The machine reverses itself at the top of its stroke, after making the bolt, by means of a tappet on the large brass nut striking against lock-nuts on a vertical rod which connects with the lever and handle just mentioned, and it returns to the correct position for placing another piece of iron in the die, stopping where required, by striking a lower pair of lock-nuts. In doing this the weight of the tup, etc., is deposited gently on several India-rubber washers lying on the top of a strong adjusting screw, which goes through the bottom cross-piece of the machine, and carries the knocker out for the bolts. The socket into which this screw fits is only held up by two safety-pins, which will shear if the top should descend violently through carelessness. The fall of the tup is then broken by a second lot of washers placed directly on the cross-piece. The amount of metal in the head of the bolt or rivet can be readily fixed by a screw and dividing-plate attached to the under side of the tup, a small catch engaging in notches in the dividing-plate, and serving to hold the screw in position.
A very ready means is provided for changing the tools, only about one turn of the holding-down screws being needed, when the whole can be lifted out. A sheet-iron trough is placed on the top of the tup surrounding the die, for carrying away the water used to keep the dies cool. The speed
MECHANICS AND SCIENCE.
Vincent's Patent Bolt and Rivet Forging Machine ; Greenwood &* Bailey , Leeds, England.
THE INTERNATIONAL EXHIBITION, , 1876.
of the top driving-shaft should be from four to five hundred revolutions per minute.
The manufacturers claim as special advantages in this machine, that the die being made in one piece, all the heads are alike and true with the shanks, the sides being nearly perfectly parallel ; that the top die can be very readily adjusted to form heads of any required thickness ; that the machine possesses great lightness compared with the great power exerted by the screw pulling against itself; and that the speed of production is very great, one man being able to make up to as many as thirty bolts or rivets per minute, according to size. A small furnace of special design is made for use with this machine. The pieces of iron are cut to lengths and placed in holes in the sides, the furnace being square, and all four sides may be used, the body swiveling round as the operator desires. Special retort-furnaces are also used for small bolts and rivets, in which the iron does not come in contact with the flame and does not scale or burn. |
The Count considered it proved by these experiments that heat may be obtaineil, without limitation, by subjecting metal to friction ; and concluded that what can be obtained from insulated bodies without limitation cannot be material, and believed it impossible to account for such phenomena upon any other hypothesis than that of motion among the particles of bodies.
It had been before proved by Boyle that friction in vacuo produces heat, he having obtained this result by making two pieces of brass rub against each other in the exhausted receiver of an air-pump. Tlie same fact was proved by Pictet, who found that the introduction of a soft substance, such as cotton, bebveen the rubbing surfaces, increased the heat. He conjectured that electricity is concerned in the production of heat by friction.
Sir H. Davy made various experiments illustrative of this subject. He insulated an apparatus for occasioning friction, by placing it on ice in vacuo, in which situation heat was produced. Two pieces of ice, similarly circumstanced, being made to rub against each other, neat enough was produced to melt tliem. The heat producetl in this experiment could not arise from any diminution of capacity, as the wafer resulting from the melting of the ice has the greater capacity for heat. It seemed to be satisfactorily shown also, that it could not be derived fr om air, and the same conclusion was drawn from these experiments that (Jount Runiford drew from his, namely, that heat is produced by motion among the particles of bodies.
Having thus detailed the most remarkable experiments favourable to both of the prevailing hypotheses as to the cause of heat, and having stated the conclusions drawn from them, it may be useful to quote the opinions of two philosophers who think differently on the subject, and place them in opposition to each other.
Dr. Murray, (System nf Chemistry, third edition, vol. i. page 468,) after describing the hypothesis upon which heat is supposed to be materiM.proceetls to speak of the other in the following words: -- "The opposite opinion, that caloric is motion, placing it on the same ground, or considering it as an hypo* thesis, docs not afford an explanation of those phenomena equally satisfactory. The most general effect arising from the (meration of caloric, is expansion ; but if caloric is mere motion, or vibration of the particles of the heated body, how is this effect produced ? Vibration is the alternate approximation and retrocession of the particles ; but from this state it is evident that no permanent and uniform increase of volume can fake place. Still less can this cause account for the augmentation of volume which accompanies fluidity and vaporisation. MTien water is converted into vapour, it occupies 1800 times the space w hich it did while in the liquid form. Suppose vibration increased to any intensity, it cannot be shown how it can permanently separate the particles of a body to such distances. The deficiencies of this opinion are likewise evident in its application to other phenomena. The laws of its propagation through bodies arc different from the established laws of motion. Were they the same, the propagation of caloric ought to be momentary through elastic homes, and should be more or less rapid through others, according to their elasticity, which is far from being the case. N either is any cause pointed out why it should be so slowly transmittetl through liquids or airs. We are equally unable to account for its distribution in bodies, and tlie quantities of it required to produce given temperatures in different substances, or the portions of it absorbed when bodies change their forms, on any laws it could observe, supposing it to be any species of motion."
Dr. Young (in his Lectures on Natural Philoso^y, vol. i. page 653,) proceeds thus with the diMussion of the
HEAT. |
Gtanite, fimnation o^ 97, 207. Qrsnville, Dr. A. B. notice of his paper - on Egyptian mummies, 402. Gnqrf X Jk. fBsQ. eadidlaiitte,BOtiaBA»bf»
. of pearls, 27-- on the chemical-enoa-
Green sand, 30. ^^■ . ^
Ornrory, Dr. notice of hii j^apeB;dh,lha loiMRUopnL abiois,. rlii2t«N0M. Mil
Ooodwjn's MSS. 282. ; t , ^ <:. , r^ . J OiiJainHi^ .M.Maartdto.topedtiiig dnNJH
Hannotome, new Twiety i% ^. .... f., .,«« Kept and li^t, 201. ^^ig^^q^M tf ehnel, >f r. on cy^i^ML^Cim^M- dpitate, 151. ' '^' ' :7^^^"^
' vided platinum ph gftsi^cm^i. i_
and its application ift ^j4r>.^ 416. ' ' - • y*«^i
Home, Sir E^^noti^pf bis. lure on naves mAfifl^jw^ of bis paper oa'^e ip^vum 4}!r
!ipi)V.r«4. ;
iiiF^iMiii »aB^^^w^
^Vi^_
HoEsfiOl,. C. Bsq. on i&e .
the cornier ahealhlng in aah^ 301. Hortus Malabaricns, 227* ^ Howard,. Mr. metecMpgleil taUcs, 71,
Hyena cBje^ mJksrv^ui^jn^^
tmum, 313. -.« eaij^
,ih^p^(^np,St
\ of, 284. ^^^g
> >' ., ..- ;*i..r. ,'^o »l»ixo ,lUdo3
/^ .«d
Iamiai)cb»'faiBiwni aO ii|iIi»»loi«iM
by him, 134, 407. ^^^^ rR^^ Lamp, Safety, Si»'ii. IS^o^-tSUBfi^Q ]|iead,oatl^ .1M. . ^^nJ^ io ^b^r fiuoloO subcfaromate of, BtiMli^^aOtqcaod
I^ectures on meteorites, 284e. I O^f J^^t Mr, M. hia deieriptieiir^f ImuirfKI i>W IiigfaMiiid JiiaW20lip8241^394 4|ibaaio:> IdtUi^ipbqiMtiivisjd^ 9<Ii
lioeaUties oif lata numnnb,' 15i« e^^ii
mttl, Ac ft 10-- notice of 1119 Mpor on a
Niagara, Ml ft4lrtt|q|ji mil, »<fc ^^Mfl^ Nitrate of silTet and cymose^ ilfmiiiiiny oompoond of, ISJ; - .- -6«^\
ffe«r At
X^ d«9frr(9» M, })otic9 pf hi9 naM 'ijMllf' ft?»^5^^ fwwatiw* tf )Jctp|
Uathematigal nnniMfi \
tftfeihrj, cyanui^t of. coin^9tkm ^' HeteoiitM^ lactam 00, S34«'
!<• li'm III
atHdston,264.
-- " New Malton, l»4. :^ fitiatftitd, 79; 159,
'f99, S19,999,4T9. Miea, on the presence of titannimpi {n« .999.
BfiU,^N. Em. on chan^g me retddehiDe I, S79.
M;_dM*<
'tis lUies, Mineral, a new, 140. Minerals, doUeetionaelJ 73.
apecifie gravity of, 991.
_ opphcalioii qfJflSf .aioji^ «liecir|r to, 3&Q, ^^^1^ M- ?* fe '^•tWOlPg^
Munmiiefl, Egrptian, Dr. OraiiTille' on,
KurfiUe ortitaninQ], zD*
Ify^us polymcophiu found in the
N,
I^ve kid, ]«4.
M«m in tie jatfMi^tO^ fli^
: j:vi£
Obienrations, astnmomicaI,lS1,'t^l»''
SOa. 358, 480. ' • * v.... •->
Ob«ervaimy«fBoipat,Se9. "£->H
Oo^taiiong, 147, I49i - »t»^^^
Oevflad, Prof, on acgdgrateaaiin<iii|>
Opticd deception, explanation 0^. €7^ M Organic remains in allui^lam, l24Jlb' ' *^d
-«:^-:^ dilMom/^^fil. ^ .>-t«
Oxalate of uranium, S7 1.' ' *>v.«}
Oidtie of eolMdt, iti ieluUBf Jn««MM 69. • • : .?s^'i
■ gas, oonvmon of 1
nlmin by, 890.
P.
Paratonnerres, on, S2» •■'
Patents, new^ 76^^ )59, 9iS,^ tM, fUB
P^ris, )ir. 6mf mi thifar tIriteiaM,- Hi^
Fdpys, lifr. prWftyKfc fna <wjilfayliiiinP
ments \>j cases lined with nnc, 89tL' ^
l^havmaeopetii^ liOi»ion,5iL' " ^-••^•'^
Wilips, Mr.R. reply to liv. Wl^|aatt:
'*iht JLondon Pnarmacopceia, w$i''M^
tartarized antimony^ 878; '- .
Pliotcnneter, ^ new, is. • ^ii
Plao^uta, ftm^ in, 5d, 8tl.' * -^
Planari«j 806. ' ' ' ' * '^^* :
Slatinum, finely divided, ita acMr dTfi*-
seous mixtures, 818, 416, 459. ' ^ Potash, sul])hate of, its jlK^MMlSdQy'ilir '"^ Po^h-rauriate of uranittm, 9^0. ' * '^ -- 7- -- snl^te <)f ditto, *W; ' Bowdl, Rev. B. on eioiar Ikjlit and' Mt^^
!^OI-.o!i &sbtapdiieatm>m'tiiAeirfeilaI ' source^ 859~notioe of his pi^»er Hn'tn-
diant heat from terrestrlid sOuveea, Kl.
r-his additional experimenU tAA"^
livurks on ]gdit and heat, 401. ^ ^ *
PredpftatcSfiit*', 151. * '- ■*' 7-^ Pria^ dis^otatioR of the Me^tU4.CM^i^
-^^^ns of ibk:Aj0i^^i^
9S^ .
Pnunin Uae, iqppUed to dTeing liy Bcrtlionet,89.
^^|iinthf»t Awa tcncttzua loninit 888.
B^ mar], 467.
Refraction, 149.
BoBwick, Prof, on toO^fce, 217.
H/BJiHiUPffltrfli their electxieal oondncting |
linseed cake, and boil the mixture for an hour, then filter it and allow it to cool. I then apply this preparation to the fabrics by a brush or by steeping them therein and when the fabrics are sufficiently coated I put them in a stove to dry. I next take 3 gallons of linseed oil and boil it o?er a strong fire and mix with it \ lb. of tar, | lb. of Prussian blue, } lb. caoutchouc, \ lb. crude litharge, and | lb. of lamp bUck. After the mixture, by continued boiling, is reduced to a proper consistency, I allow it to cool and apply to the aforesaid fabrics one, two, or more layers of it by means of a spreading machine, the fabrics being dried in a stove after each coating of the composition. Lastly, I take 3 gallons of linseed oil, boil it over a strong fire and mix with it 1 lb. of Prussian blue (or such colour as I intend to use), 2 oz. of solution of tin and 2 oz. of white copperas. After the mixture has, by continued boiling, become so thickened that it ignites readily and gets glutinous I allow it to cool and with this composition I coat the aforesaid fabrics and dry them as before, and if necessary I give a thin coating of a solution of copal.** The fabrics should be smoothed with pumice-stone once or twice between the applications of the coatings.
Ward, William, of Sheffield, York, lead chaser. Improvements in stoves. Pa- tent dated December 28, 1854. (^No. 2740.)
These improvements consist in forming radiating bars with two uprights, one at the back end of it, and the other more or less forward, so that when a set of these radi-, ating fire-bars are laid in their places they will, by their several uprights, form a basket or fire-place for the fuel, and the front parts of the radial bars will project beyond this basket or fire-place and cover the hearth as heretofore.
Gray, John, of Strand-street, LiverpooL Improvements in adjustiTig compaues on board ships or vessels. Patent dated December 28, 1854. (No. 2741.)
" Heretofore the compasses in iron ships have been adjusted," says Mr. Gray, ** by permanent magnets fixed in such positions as to cause the compass to give correct indications at the time of adjustment, but should any of the magnetic conditions of the ship afterwards change the indications are no longer correct Now, my invention consists in arranging the correcting magnets so that they may be moved in any direction by screws, or racks and pinions, or otherwise."
Benson, Gerd Jacob, of Christianstreet, St George'B-in-the-East An <m- provement in refining sugar. Patent dated December 28, 1854. (No. 2742,^
Tbii \nveii\\oa tt\iX«% \a ^«X ^^vtN. ^^ *^^
BPECnnOATXONS OF PATENTS BEOENTLT FILED.
refining process which consisU in dissolving sugar in water in order to produce syrups, and the inventor carries on the refining process at a lower temperature than that employed in the present process where free steam is used to " hlow up." The invention mainly consists " in employing numerous streams of air, introduced below the sugar and water when in a suitable open vessel or pan, and heated by pipes having steam or hot fluid within them. For this purpose it is preferred to employ a series of perforated pipes near the bottom of the pan or vessel and above them to have a series of heated pipes capable of being raised out of the fluid."
Nasmyth, James, of Barton-upon-Ir- wfeU, Lancaster, engineer. Certain improved maehinery or apparalut for facilitating the forging of matset rfbron. Patent dated December 29, 1854. (No. 2744.)
These improvements consist of arrangements of hydraulic cylinders and other apparatus, with chains, wheelwork, and pulleys connected therewith and worked by steam or other motive power, by means of which the mass of metal mtended to be manufactured may be removed from the furnace to the anvil, and vice versd, and may be raised, lowered, or turned over in either direction, during the process of manufac- j ture. |
Var'nish-ing. (Photography.) The protection of a finished photographic negative by flooding it with a solution of resin in alcohol or benzole, whereby it receives a hard, glossy surface, and is able to stand the wear and tear of printing.
Var'nish-lens. A small lens made by putting a drop of copal on a flat piece of oiled glars. It congeals into a plano-convex lens.
Vase. A large cup or open-mouthed jar, with handles.
The ample variety of Egyptian forms may be understood whenit is said that the moderu teapot form, the large oil-jar, the China vase, the common pitcher, the water-ewer, theale and wine glasses, the flower-glasses, the drinking-goblet, the beaker, and the bowl areall to be seen iu Egyptian paintings. Analysis and observation prove that the Etruscan and Campanian pottery included most kinds now known, including porcelain, and that they had glazes of glass, lead, and salt. Of the Athenian vases some are fluted, some of a jet black, and others a bright red. The Corinthians had a heavy coarse black ware. That of Athens was the lightest and most elegant, that of Sicyon the brightest and most ancient. The Greeks had also pink vases with black silhouettes.
The Barberini or Portland vase is the largest and best preserved specimeu of ancient paste glass. The figures represent the nuptials of Thetis and Peleus.
For a treatise on vases, sce Fosbroke’s “ Eucyclopeedia of Antiquitics,” IT. 283 - 248.
See also Rawlinson’s ‘‘ Five Great Empires,’’ Vol. I. 389- 3ol.
Vat. A wooden tub; used for many purposes, such as for mash, wash, hop-liguor, in brewing and. distilling. Also known as a back.
As a mere storage vessel, it is a CISTERN or TANK (which see).
Also used in many chemical and manufacturing operations in which the substances nsed are boiled, soaked, steeped, lixiviated, elutriated, etc. See STarcH ; TANNING ; etc.
A vessel used in the wet treatment of ores. See list under
Fig. 6911.
In Fig. 6911, the tailings pass through the perforated bottom of the mixing-hopper, and descend through a pipe of
the mercury in a retort connected with the open yat into which the tailings discharge. Within
ness is removed by means of powdered starch, and the process is finished by rubbing with the hand.
Great care must be takeu that the surface to which varnish is applied be free from grease or smoke, which prevents all oil-varnishes from drying.
Varnish of excellent quality was made in ancient Egypt, and in some cases has retained its brightness during the lapse of thirty centuries. :
They baked their varnish on elay, with a moderate heat, sve may suppose. It does not appear that they had any true glaze. That came from China many a long year after. See GLAzE; POTTERY.
The Chinese are sai gether fresh blood with quicklime, used as a coating for wooden articl to make completely water-tight. Von Scherzer, who first introduced this substance to the uotice of Europeaus, says he has seen in Pekin wooden chests that
had been varnished with it, which, after a journey
a to make varnish by beating towhich is extensively es which they wish
J,
WU?
Amalgamating - Vat.
VAULT.
the vat is a series of horizontal and vertieal concentric perforated copper partitions, which foree the coutents to take a devious course. The vat and retort are snrrounded by steamjackets. The fumes of mercury are injected into the descending body of the tailings within the pipe.
Vault. (Arenitecture.) A passage or room with an arched ceiling. An extended arch covering an apartment.
Vaults are cylindrical, coved, or groined.
1. A cylindrical vault has a semicircular arch (a).
2. A coved vault has an arch which springs from all sides of its plan (6).
= : ae
3. A groined arch is one formed by two intersecting
vault ; d, Gothic groined vault).
The pavement-sidewalks of citics are, to a large extent, used as coal-ellars. Fig. 6913 shows a garbage-box set within
Vaults,
Fig. 6913.
ja?
is
City Vault, with Coal- Chute and Garbage-Boz. |
A. In posting from the cash book to the general ledger of this page on the cash book the amounts on the cash book were properly and correctly carried to the general ledger, but in taking the balances of the accounts on the general ledger, in order to make up his daily balance, be made an error in his addition in the individual depositors’ accounts of the amount he had abstracted that day.
Q. 30. Then I understand there was no error or falsification of the cash book, except that whenever he stole an amount in one day, in adding up his cash book that day he would make an error in addition for the amount he had stolen?
A. Yes, sir.
Q. 31. Then as I understand you, the various items on Exhibit “X” in which you state that the shortage is in adding cash book, do you mean to be understood as saying that on each of those dates, he made an error in addition on this cash book ?
A. Yes, sir. 45 Q. 32. Were there any falsifications of the books to misstate the amounts of discounts and demand loans owned by the bank?
A. No, sir; there were no false entries.
Q. 33. Then if no uotes were abstracted from the bank the amounts of discounts and demand loans would at all times have agreed with the amount shown to be on hand on the books kept by Schardt?
A. It would with the exception of clerical errors, which were liable to occur at any time.
Q. 34. In auswers to questions Nos. 27, 29 and 30 of your crossexamination, do you mean to include all the shortage of Schardt?
A. No, I do not intend to include that part of the shortage occurring by Schardt having collected notes and not accounting for them on the books of the bank,and some few other items as fully appears upon Exhibit “ X.”
Q. 285. Please explain the method pursued by you in order to ascertain that Schardt had collected notes and not accounted for the proceeds.
A. The bank kept a book in which each note owned by the bank was entered and numbered, when the bank received it. And on this book was shown the date of the note, the makers, the collaterals, the date of maturity and the date it was paid. I begun in Septem-
THE MECHANICS’ SAVINGS BANK & TRUST VOMPANY, ETC. 35
ber, 1890, at the time Prof. Jennings’ other examination ended, and I entered upon a new book each note which appeared by the bank’s books to be owned by the bank of that date. I then marked on this book the date of payment, opposite each note owned by the bank, from that time down to the date the bank closed. I then went over the list again and checked off each note owned by the bank, and which was on hand at its failure.
This left certain notes on my book unpaid, and not on hand. I then went to the makers of the notes and found that they had been paid to Schardt and he had not accounted for same.
Q. 36. Could this information have been ascertained at any time after these notes were abstracted or paid, and unaccounted for as well as when you ascertained these facts?
A. Yes, sir; by such an examination as I made.
Q. 37. Then, if I understand you correctly, at any time after Schardt had collected a note and appropriated the money to his own use, if the amount of notes on hand had been counted, would they have agreed with the amount on his books shown to be
on hand, less the amount of the notes he had abstracted ? 46 A. Yes, sir.
Q. 38. Do I understand you to mean that at all times the amount of discounts and demand loans shown on the books kept by Schardt to be due the bank was correct ?
A. Yes, sir; barring clerical errors.
Q. 39. Did you verify the entries on the books kept by Schardt with reference toamount of discount and demand loans to ascertain whether or not that book was correct in this regard ?
A. Yes, sir; the book I made up agreed exactly with the books kept by Schardt. ,
Q. 40. Who collected the discount and demand loans of the bank ?
A. The teller.
Q. 41. Who assisted you in making up this book and arriving at the amount of notes abstracted by Schardt?
A. Professor R. W. Jennings. |
The traiifits of the Moon difcover all things, whether good or evil, which happen to a man daily through the whole courfe of his life ; her application to, or tranfits of, fextiles and trines, (how good ; of quartiles and oppofitions, evil, concerning all thofe things fignified by that houfe in which the tranfit is made ; where if fhe be fignificatrix, the good or evil will alfo fall in part upon the things fignified by her, according to the houfe fhe was lady of, or pofited in the radix; but, if not, the good or evil will fall upon thofe things fignified by the fignificator which is tranfited.
JUDGMENTS to be inferred from REVOLUTIONS.
The judgments of a revolution are ealy to be determined, by confiderinz in what houfe and fign in the revolution the radical fignificators are pofited ; for according to thofe revolutional pofitions and configurations we are to judge. So that, if the lord of the lecond houfe be in the third, it fhovvsgain to come either by travel, or by kindred, or neighbours ; and, if he be alfb in fextile or trine with the lord of the third in the radix, the fame ; if with the lord of the fourth, by a father; if in the medium coeli, or in conjundion, fextile, or trine, with his radical lord, gain by trade, office, preferment, or noblemen. Hence it appears, that the fignificator of fubfiance in a revolution, is not the lord of the fecond in the revolution, but the lord of the fecond in the radix ; the fignificator of lands is not the lord of the fourth in the revolution, but the lord of the fourth in the radix ; the fame is to be understood of the refl ; but, if the fame hgn which afcended radically afcends in the revolution, its efFedls will be the more firm, becaufe the fignificators are the fame ; the like, if the fame planets which were lords of the feveral houfes in the radix be lords of the fame'in the revolution, though they pofTefs not the fame fign.
Whatfoever good or evil is prefaged unto the native, either by direction, tranfit, or revolution, we are to meafure the greatnefs thereof according to the radical flrength or fortitudes of the fignificators, compared with their ftrength or fortitudes at the time of dire6tion ; where, if they are radically ftrong, the good or evil will be great and permanent, the which is confirmed if they be flrong alfo at the time of direction or tranfit; if radically weak, the good or evil will but meanly manifefl itfelf ; and fcarcely at all, if weak at the time of direftion or tranfit ; but, if radically weak, and flrong at the time of the dire6tioa or tranfit, the efFeCfs thereof may appear much beyond the expedation of the native, but will 'lot be very durable.
No. 1 2. 3 L The
43 AN ILLUSTRATION
The SIGNIFICATION of feveral FIXED STARS in
NATIVITIES. |
vel. in hodograph x ang. vel. oc (dist.)'2. 11. LSS' the latus rectum L ; LD, S'D tangents at 7/, S' intersect in directrix at right angles. fi.4:AS = g. (Vel.)* at L = 2ff. DS=p,. (4/1 S)*. conj. diameters equal L and a2 + V* = 2J7, aJ = Z'2 sin ^TT, (a±&)a = 2JZ/2(cos|7r±sini7r)2. 12. CT the change in direc-
tion; h'-h = u.SP, resolve parallel to the axis, \^r, - j- &\iiASP+ £ sinw=M sin ASP, .'. j- e-a = f u + -^ u.SP] si
292 NEWTON.
and -- £p = 1 + e cos A SP. 13. 6 the angle of incidence, v
the vel. of striking ; v sin 6 = vel. parallel plane after every impact, env cos 6 perp. plane after » impact. If first orbit be
a circle, tan 0 = e cot 0, v2 (sin2 0 -f e2 cos2 0) = eva, .-. e. -- = ^ ,
j T. 2/z . /i / r\ r
THE END.
TV. METCALFE, AND SON. PKI.VTBllS, ROSE CRESCEST, CAMBRIDGE.
BY THE SAME AUTHOR.
SOLID GEOMETRY.
PERCIVAL FROST, M.A.,
FORMERLY FELLOW OP ST. JOHN'S COLLEGE, CAMBRIDGE, MATHEMATICAL LBCTUREB OF KING'S COLLEGE.
A NEW EDITION,
REVISED AND ENLARGED, OF THE TREATISE BY FROST AND WOLSTENHOLME.
FOR the convenience of Students who may wish to have in one volume all those portions of Solid Geometry which would be useful to them, in their studies of Physical subjects, I have endeavoured, as far as I could without material departure from the arrangement which I considered best for the proper treatment of the subject, to include in the first volume nearly all that will be required from their point of view.
MACMILLAN AND Co. London and Cambridge.
BY THE SAME AUTHOR.
AN ELEMENTARY TREATISE
CURVE TRACING,
PERCIVAL FROST, M.A.,
FORMERLY FELLOW OP ST. JOHN'S COLLEGE, CAMBRIDGE, MATHEMATICAL LECTURER OF KINO'S COLLEGE.
THE Author has selected the subject of this work with a view of assisting the Student, who is acquainted with the ordinary processes of Algebraical Geometry, in the training which he must undergo in some form, if he wishes to become an accomplished mathematician. It would be difficult to find another subject which requires so limited an extent of reading, and which yet foreshadows so many processes which are employed in all departments of the higher branches of Mathematics, Pure or Applied. Especially the student will acquire in an agreeable manner the power of discriminating the different orders of magnitude of large and small quantities, which will be of avail at the outset of his more advanced studies.
MACMILLAN AND Co. London and Cambridge.
BEDFORD STREET, COVENT GARDEN, LONDON, December, 1879.
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MATHEMATICS.
Airy. -- Works by Sir G. B. AIRY, K.C.B., Astronomer Royal :--
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Ball (R. S., A.M.).-- EXPERIMENTAL MECHANICS. A
Course of Lectures delivered at the Royal College of Science for Ireland. By ROBERT STAWELL BALL, A.M., Professor of Applied Mathematics and Mechanics in the Royal College of Science for Ireland (Science and Art Department). Royal 8vo. l6s. " We have not met with any book of the sort in English. It elucidates instructively the methods of a teacher of the very highest rank. We most cordially recommend it to all our readers" -- Mechanics' Magazine. |
pairs my carriage he has a right to keep the carriage ull [| pay him for hi work, A warehousemat may keep goods until freight, storage and other charges are paid. If he lets the goods go his lien is at an end. He cannot
so and take the articles back, he only holds a personal debt against the owner.
8 Loss of Articles being Built, Repaired, ete. (1) Suppose Brow
hires Smith to build a boat sor him, and he (Brown) furnishes the materials
the work to be paid for whem completed. Ifthe boat were accidentally destroved by fire, Brown would lose his material and Smith his work, because Sinith hac agreed to do a certain job complete: he may have a profit out of it besides
wages, therefore he has the risk. (2) If Brown had engaged Smith to work by the day on the boat then the whole risk would fall upow Brown. If the boat were destroyed Brown
would lose both materials and labor because Smith did not promise any defin
te result or finished work. He could have no profit out of save the pay for his ordinary daw labor.
(3) Suppose Thompson agreed to build a carriage for Henderson and furnish all materials himself tor a specific sum, say, $100, -- If the carriage were destroved anv time before completion and delivery to Henderson, them the
entire loss would happen to the workman, Mr. “ET honypsen
is2 ASTER AND SERVANY
9 Time of Employment. All contracts of hiring where services are not to be rendered within one year, should be in writing, Suppose N agrees on the roth of January, 1891, to work for one year for Y, said year to begin onthe rmstof May i8o2. ‘There should be some memorandum of the same in writing, signed by the parties, beeause it is not to be performed within one year, Which would be roth of January, rSga.
If 1 engage a man for a day, a week or a month, at the termination of this period IT may discharge him or he may leave me without notice, At the end of the time there is no further contract; it is dissolved by lapse of time. If a person is hired for no particular time and is paid so much a day, a week, a month or a year, he is entitled to notice from his employer before being dis charged, and his employer is entitled to notice before the employee leaves him,
If paid by day a day's notice,
If paid by week a week’s notice,
If paid by the month a month's notice, If paid by the year three months’ notice.
If there is good reason for discharge or leaving, such as careless work, etc., notice is not required by either party,
If a person agrees to work say three months, and works only two months,
he is not entitled to anything, because he does not fulfil his part of the contract, If it is the fault of the employer he can collect wages for the full time,
10 Discharge \ servant is expected to serve his master honestly, cheer fully and faithfully, to enter upon his duties at proper time, to obey all lawful commands, to be responsible for loss or damage occurring to his master's pro perty on account of his negligence; therefore, wilful disobedience and habitual neglect, absence without leave, refusal to perform work requested by the employer (unless such work is illegal) are good causes for discharge. If a servant is discharged for good and sufficient cause, he cannot claim wages previously earned and not due at time of discharge,
11 Leaving--TVhe master is expected to give reasonable commands, and commands that are not illegal and that are within the limits of the work the employee agreed to perform, If the master gives commands contrary to the foregoing, and endeavors to enforce such commands, the servant has just cause for leaving. |
Eudo.x muss ein guter Beobacbter gewesen sein, man erzablt von ibm, dass er langere Zeit in Aegypten gelebt, und dort in Heliopolis beobacbtet babe; auf Enidos zeigte man nocb lange nacb seinem Tode den Tburm, welcber ibm als Sternwarte gedient.
Aristoteles wurde zu Staffira, einer Stadt im ndrdlicbea
V. Chr.
AriitoieieB. Griecbenlaud am strymoniscben Meerbusen, geboren. Sein Vater war der Arzt Nikomacbus, der bald mit dem jangen Aristoteles nach Pell a an den Hof des makedoniscben Konigs Amyntas ubersiedelte. Dort lernte Aristoteles den nacbmaligen Eonig Pbilipp kennen and gewann dessen Gunst, was sp&ter fiir ibn von so grosser Bedeutung* wurde. Docb kann er aucb bier nicbt lange geblieben sein, denn als sein Vater starb, und ibm ein bedeutendes Yermogen binterliess, zog* besonders der Ruf des Pbilosopben Plato den eben erst 17jabrigen Jiingling nacb Atben. Dort blieb er bis zu Plato^s Tode , fast 20 Jabre lang, in dessen Umgebung, bielt sicb danacb einige Jabre bei dem Herrscber von Atarneus, Hermeias, auf, der scbon in Atben ^ein Zuborer gewesen, und beiratbete dessen Adoptivtocbter Pytbias, als Atarneus in die Hande der Perser gefallen und Hermeias ermordet worden wai*. Von Mytilene, wobin er sicb gefliicbtet, folgte er dem Ruf des Ednigs Pbilipp zur Erziebung seines damals 14jabrigen Sobnes Alexander. Nacb der Aussage des Alexander „er ebre Aristoteles ebenso sebr wie seinen Vater; denn wenn er dem Einen sein Leben verdanke, so verdanke er dem Anderen, dass er es wertbvoU gemacbt", muss das Verb<niss zwiscben dem beriibmten Lebrer and seinem grossen Scbiiler ein sebr gates gewesen sein. Docb dauerte dasselbe in dieser Weise nur vier Jabre, bis Alexander den Tbron bestieg. Drei Jabre blieb Aristoteles danacb nocb in Makedonien, dann kebrte er, als Alexander nacb Persien gezogen war, wabrscbeinlicb 335, nacb Atben zuriick, und griindete dort im Lykeion (einem Gymnasium) seine berUbmte Pbilosopbenscbule , die nacb den scbattigen Spaziergangen (n£Ql7tatoi\ ia denen Aristoteles gern seine Lebren vortrug, den Namen der peripate-
') Zeitflchrift f. Math. a. Phys. XXII. Jahrgang. Schiaparelli: Ueber die liomocentrischen Bpliareu des Endoxus, Kalippns und Aristoteles.
Naturphilosophie in Aristoteles. 17
tiflchan erhielt. 13 Jabre las er dort yor einer grossen Menge eifriger S84 bia 822 Zuhorer, daim erliapL.die antimakedoniscbe Partei in Athen gegen ihn Aristoteles. die Anklage wegenFreyels gegen die Goiter, und Aristoteles yerliess die Stadt, ,weil er nicbt wollte, dass seine Mitburger sicb znm zweiten ICale^) an der Philosopbie yersundigten^. Er wandte sicb nacb Cbalkis IB £iibda, wo er, kurze Zeit nacb seiner Verbannnng, im Jabre 322 starb.
Aristoteles war klein und scblank yon Gestalt und soil in seinem Benehmen ' ofters geziert gewesen sein. In der Unterhaltung neigte er sum Sarkasmos, ob er aber die Aeusserung des Bacon yon Yerulam, ^dass er wie ein orientaliscber Despot alle seine Nebenbnbler strangubrte", wirklicb Terdient bat, ist mebr als zweifelbafk. Sein eigenes bedeuiendes Yermogen, sowie die Unterstiitzung seines mficbtigen Scbtders, erlaubften ibm, eine bedeutende Bibliotbek zu sammeln; diese fiiblioihek kaufte Ptolem&us Pbiladelpbus spftter fiir das Alezandriniscbe Moseom an. Der eigene bandscbriftlicbe Nacblass des Aristoteles soil jedocb nicht mit abgegeben worden, sondem durcb Sulla sp&ter nacb Rom gekommen sein, wo Andronikus y. Rbodus um 70 y. Chr. wenigstens die rein wissenscbaftlicben Scbriften in der jetzt forhandenen Form yeroffentlicbte. Die bedeutendste Ausgabe derselben wnrde in den 30 er Jabren dieses Jabrbunderts yon der Akademie der Wisaensebaften in Berlin yeranstaltet und yon Imm. Bekker besorgt Wir geben zuerst eine Uebersicbt uber die pbysikaliscben Ansicbten des Aristoteles, um dann eine kurze Inbaltsangabe ^) seiner bierber geborigen Scbriften folgen zu lassen. |
Azote ; ; • . . 40*7
Carbon 24*8
Hydrogen .....•• 34*5
Or of A20te 1 atonis
.Carbon • , 2
Hydrpgen B
Pmssiate of mercury is composed of one iptegrant particle of prussic acid and one integrant particle of red oxide of mfwcury. Sulphureted chyazic acid is a compound of 1 atom sulphur' + 4 integrant particles of chyazic acid* Ferrureted chyazic. acid is a compound of 4 atoms black cnude of iron + 1 atom prussic acid.
UNNAAN SOCIBXy. ■ '
On Tuesday, May 2, a paper^by Geoi^ Mohtagne, Esq. on the ardea nigra^ or black storks was read. This bird wa3 shot in England.
On Wednesday, the 24th of Mav, the anniverlsary of the Society, the folk)wing office-bearers were elected for the ensuing year:-- -
President -- Sit James Edward Smith, M. D. Treasurer -- ^Thomas Marsham, Esq. SECREtARY -- Alex. Maclcay, Esq. UNIIE& SECBKrAAY-r-Mr. Richard Taylor. ..
456 Proceedings of Philosophical Societies » [JuNx>
There were retained of the old Council ;--
The President, The Lord Bishop of Carlisle. Aylmer Bourke Lambert, Esq. William Elford Leach, M. D, Alex. Macleay, Esq. Thomas Marsham, Esq. William George Maton, M. D. Daniel Moore, Esq. F. R. S. Joseph Sabine, Esq. F.R.S. Thomas Smith, Esq.
The five following Fellows were elected into the Councii : --
Thomas Marquis of Bath.
William Kent, Esq.
Rev. Thomas Rackett.
Thomas Thomson* M. D. F. R. S.
John Walker, Esq.
Since last anniversary the Society has lost nine Fellows and five Foreign Members b^ death ; and eleven new Fellows have been elected into the Society.
GEOLOGICAL SOCIETY.
jipril 21. -- A communication from Thomas Hare, Esq. entitled Observations on Basalt, with eight illustrative drawings, was read. In the opinion of the author of this paper, basalt ism crystallised substance, formed by deposition from an aqueous solution ; its reid form is spheroidal, and the columns which it usually presents result from those spheroids being heaped one on another, and from the lateral compression to which each heap is subjected by cohtiguoos and surrounding heaps.
M^y 5. -- ^A paper by the Rev. W. Buckland, M. G. S. etititled a Description of an insulated group of Rocks of Slate- and Greenstone, situated on the east side of Appleby, between M^knerby and Murton, in Cumberland, was read.
The group of rocks here described runs nearly N. and S., and consists principally of slate and gteeu-stone, - the slate lying for the most part on the east of the green-stbhe. 1^ order of the superposition of these two rocks appears to be very indeterminate ; sometimes they abut abruptly against each other ; ^tnetimes tbe'slate b uppermost, but most generally the green-stone. ' A few thin beds of blackish transition lime-stone occur in the slate ; and in some places the slate is intersected by dykes of compact flesh-red felspar with scales of mica. In another place a more perfectly characterized granite makes its ' appearance surrounded -by green^^toney but whether thi^ is a dyke, or a projectihg'mBsa Of tiie subjaccat rock| it is not easy to ascertain.
1815.] ' Royal Institm. 457 |
The galvanometer was one of the earliest results of Oersted's discovery; it was, indeed, in the same year (1820) that the first galvanometer was invented by Prof. Johann S. C. Schweiger, of Halle. He gave it the name of " multiplicator," the olyect of which, as aforesaid, was to multiply the electro-magnetic action of the current. This instrument is actually so sensitive that it serves to detect the weakest electric currents. All parts of the current traversing the elongated parallelogram, p q r o n (Fig. It), in the direction of the arrows, act in a similar manner upon the needle, a b, which rotates in a horizontal plane. If a be the south end and b the north end, the current will show a tendency at- all points to turn the needle in such a manner that b shall project beyond the plan of the figure, while a will retreat behind it. The lower portion of the wire, therefore, supports the action of the upper in the same manner as does the current of the same force, moving in the same direction around the needle in the portions p q and r o. A second current of the same force, moving in the same direction around the needle, will produce as great an effect as the first; so it will be with a third, a fourth, etc. A wire, therefore, wound around a needle in one- hundred convolutions, all of which are traversed by the same current, must produce an action of one hundi'od times greater intensity than one of a single convolution ; the current must not, however, be propagated later-
FlG. 18.-- Schweiger's Multiplier.
A-224
BLEYER.
ally from one winding to the other, but must traverse the wire throughout its whole length, being carried actually around the needle.
The Schweiger multiplier is represented on preceding page. The difference between the rectangular and circular form is merel}^ a matter of detail. Although the ordinary galvanometer, con-
structed as stated, is very well adapted to detect the presence or to indicate the direction of a current for some simple measurements, especially for those in which the deflection is not greater than fifteen or twenty degrees, it is not to be depended upon for any testing in which a greater deflection is produced, for the following reason, that when
Fig. 19. a needle is deflected it is not in the same position
in its coil as when at zero; the greater the deflec-' tion, the farther is the needle removed from the position where its coil most powerfully influences it, and the nearer the needle approaches the right angle, at whicli point the coil has no influence on it at all, the weaker does the action of the current become.
Fig. 20.-- Tangent Gai-vanometer.
In order to overcome this difficulty, and for other mathematical reasons, galvanometers have been invented in which the tangent, or line of the angle of deflection, is proportional to the strength of current measured. These are called tangent, or sine, galvanometers.
The Tangent Galvanometer. -- The tangent galvanometer consists, broadly speaking, of a ring having a groove on its edge filled with in-
GALVANISM.
A-225
sulated wire, and provided with a needle, which must not be longer than one-sixth of the diameter of the ring, hung or pivoted precisely in its centre, as shown in Fig 19.
This instrument, as shown in Fig. 20, is mounted on a hard-rubber base, seven and three-eighths inches in diameter, provided with leveling screws and anchoring points. The galvanometer consists of a magnetized needle seven-eighths of an inch in length, suspended at the centre of a rubber ring, six inches in diameter, containing the coils. The coils are five in number, of the resistances 0, 1, 10, 50, and 150 ohms. The first is a stout copper band of inappreciable resistance ; the others are of different-sized copper wires, carefully insulated. Five terminals are provided, the plug holes of which are marked, respectively, 0, 1, 10,
A 1.73 /O -S ^ ^
Fig. 21. |
8 A oy AS | N * 82 4 5 : TIT! NE. f ; 1 7 . 7 12 8 3 15 . 5 7 72 #23 FRE : 7 „ 5 oe PL £8 Vo; - 4
, TT. is 118 that. egg happens mast; cally in ene hot climates; both with and without storms; even in the most serene weather, if there are any clouds in the atmosphere, sufficient to accumulate the matter of lightning. And that the lightning happens more frequently, and in greater quantity, after the lun has pate 2 meri- N than otherwise. „„
8 f 8 aig : 5 5 u : 5 * ; +, bt 1 7 oh 5 2 2 * e 8 8 £4 4 x F 7 : IF 0 5 - 78 ** . * od : 4 * err 25 5 9 * a 5 * 5 Is * 2. * 4 2
F 95 5 15 5 KH 55 OLE FW",
. . ee lightaing has it
. atmospheric or artificial electricity, dur lente
is precisely the same; in both cases, the fluid is retained, and its effects transmitted by the lame mediums; than which there is not, perhaps, a 5 criterion to determine the Hontity: pag "Ws subtile matter. %% ͤũ 7ù )] Leg ng
wb . F oy
15 85 Lightning. * - -
eee ele - highest degree. I am therefore under klar of ny
1 in a e this _ to deliver my thoughts on this intri-
Oo idea, if not an hypothesis, how, or in what manner, an EY ee.ueent, which indubitably arises from an unequal distribu-
| eleQtrician cannot help forming some
$1 VF the electric fluid, in the earth and atmosphere, is | p e Which spontane ously becomes perhaps the most |
formidable and irresistible agent in the universe. Not- Wijthstanding this; it appears, from various facts and ex-
periments, that the matter of lightning in moderate quan-
tity, is not only perfectly inoffensive, but abfolutely necef- = ary; for the well-being of animals and vegetables, such DE . constantly found connected with moderate hail, show, | rain, fog, and de- Which distribution of che fluid,
ene
may be considered as nature equipt in her best attirez cir-
„ culating this wonderful and extremely subtile and elastic _ + Nuid, to the all wise beneficial purposes, for which it was
originally designed, by the Author of Nature. Bur 15 con- 5
5 dacder uch a. disposition of the elements, as « | Wer ade gt to POS: nature ir in a "AS" of fn arent Git
5 5 + F ; $ I IF 2 J * 7 * N . T 33 „ fy % N IR 22 eh,
The fs: Kind ol diincton | hy 1
-- POO wind, and hurricanes of wind; between mode- ; 1 horns pos inp oregano ee
5 . 5 A Fe 73 oY = Hd Lp el l A; 3 5 Shes > | AE! J ONE Ld I FS Sel ; * % 2 * > 6. 74 : FFP > 54 5
5 X- >
© ns A fort if Vihthing'i 1 Get mes 2 2 ee ee „ fades OS. the ee eg This |
seen in un climate in
: -- „ ewe hand for July 20, and Nov, 12 1% 8 ĩ91⁄81⁄82 1 5 „ Fat + a „% eh: 8 - kind 1 -- CE Ire CHEN Yu : _ $ : 8 4 Ky A \ ö 3 : 8 LES: - 5 525 „
te electricity of the earth. And is probably nothing more than the concourse of two or more oppositely elearified clouds, darting their electrical charges into each other.
86 . beben Objervations kind of glide, generally happens i in warm serene wea⸗
cher, and seems quite harmless; and is never attended with
| thunder? These circumstances. plainly: show, that [some cause or circumstance. is wanting, to produce mischievous.
effects. I conceive that cause to consist, chiefly, i in the -
5 distance of the phenomenon from the earth; which is too
great for the electrical atmospheres of such clouds to disturb
When I have been able to observe the direction of this
: kind of lightning, it was generally observed to be hori-
zZontal, or nearly so; excepting when it was evidently | drawn aside by the adjacent clouds, which seems to indicate that it had but little, if any communication with the earth. Nor have I ever observed my high pointed rod, 9 be more chan Ne ns apts ONES such: and .
; . b 8 . 85 £ oo. 6 HTM % . = a » 4 , 8 7 . 7 j n 8 * 1 2 Ld ”
5 0 1 e 0 5 fort: oY > ge . Show 13 5 5 dreadful effects, L beg leave first, to correct two or three common errors, which seem to have sprung from the prejudice of education in some e and -- . ae en in others. %% | | |
2143, Caslorine is a new animal principle which was discovered by M. Bizio in Castor, and is prepared by boiling castor in 6 times its weight of alcuhol ; the filtered liquor ia Kt aside for two or three days, when castorine is deposited in irregular masses. It is very sparingly soluble in water, mote so in alcohol, and its solution in the latter affords prismatic crj* tals of a white colour. It burns with a brilliant light, ud appears to consist of carbon, hydrogen and oxygen alone.
Skctios VI, Urine, Urinary Calculi, S,-c.
8144, This secretion presents, perhaps, greater diflGcnlties to the analytical chemist, than any other animal product; it is extremely complex, and subject to constant change in the proportions of its components, and in disease several new substances make their appearance.
The chemical history of the urine is of the utmost importance to the medical practitioner ; it teaches the nature of the substances which occasionally predominate, so as to constitute gravel and calculi; and shows the means of influencing and modifying its composition.
The general characters of the urine are too well known to need description. Its specific gravity is of course liable to much variation even in the healthy state, Hucluating between 1005 and 1040. The average is about 1020.
3145. The substances that are always found in urine are, according to Prof. Brande's experiments, the following : ^^
I. Water.
X. Carbonic aciJ,
3. PliDrphoric acidi
4. tjric Dcid.
5. PhoipliBle o( lin S. Phoiphgte ot
10. Sulphite at loda.
3146. The existence of free acid in recently voided urine is easily demonstrated by its property of reddening vegetable
URIC ACID. 557
bhies, and it perforins the important office of retaining some difficultly soluble salts in permanent solution ; so that whenever this natural acidity is diminished, the urine has a tendency to deposit the earthy phosphates.
2147. The presence of carbonic acid may be shown by carbonic placing urine under the receiver of the air-pump ; during ex- *'^**** haustion it escapes, sometimes copiously, but at other times in minute quantities only.
2148. The free Phosphoric acid may be shown by the addi- ^^^SJ/'***"^ tion of carbonate of lime, a portion of which is converted into phosphate of lime.
2149. Uric add is one of the peculiar characteristics of the uriemeia. urine ; its presence may be shown by evaporating urine to half
its bulk, which produces a precipitate consisting of phosphate of lime and uric acid ; the former may be dissolved by dilute muriatic acid, which leaves the latter in the form of a reddish powder. This acid has been very ably examined by Dr Henr}', who made it the subject of a thesis published in 1807 : Dr Prout has also given much valuable information in ^relation to it.
Uric acid, called sometimes lithic acid, as' constituting the How obtain.
1>rincipal ingredient in certain urinary calculi, may be abundant- ***' y obtained by digesting such calculi (2163) in caustic potassa, filtering the solution, and adding excess of muriatic acid, which causes a precipitate of uric acid, which is to be washed with warm water, and dried.
Uric acid, thus obtained, is a grey powder, of scarcely any p^pertw*. taste, and requiring according to Dr Henry 1720 parts of water at 60^, and 1150 parts at 212^ for solution. It reddens infusion of litmus, and readily dissolves iiv.cau8tic potaspa, and soda ; it is sparingly soluble in ammonia, and insoluble in the alkaline carbonates.
According to Dr Prout, uric acid requires at least 10000 parts of water at 60° for its solution, but urate of ammonia requires only about 480 times its weight at the same temperature, and affords a precipitate of uric acid, on the addition of any other acid ; for these, among other reasons, Dr Prout regards urate of ammonia, and not pure uric acid, as existing in urine. |
flecke und Wetter (3 Arb.) $3.1111*, 94. 481. 982. 983; Sonnenfleckperiode und Cirruswolken 28. 803; Sonnenflecke, ihr Flichenraum etc., Beobachtungen zu Greenwich 36(3).58 -- Sonnenfackeln 97(3). 1092, 40(3). 119, 42(3). 122; Litteratur 38(3). 125, zu Palermo 32.1435 -- Corona 28. 1002, 34. 951, 38 (3). 129, 40(3). 277, 42(3). 122; Photometrie der Sonne und des Mondes 40 (3). 118*; Sonnenchemie 37(3). 69; Sonnenphotographie 37(3). 108; Chromosphare $0. 1406.
Einzelne Sonnenfinsternisse. Sonnenfinsternisse 25. 767, 26. 804,
Historisches 96 (3). 87, 37(3). 88, 41(3). 122, 42(3). 120; Sonnenfinsternissexpeditionen 27. 803. 804, 30. 1408, 38(3). 78. 96, 39(3). 90, 42(3). 122, 42(3). 120; Sonnenfinsterniss Okt. 1866: 25.787, Marz 1867: 23. 548, Aug. 1868: 24. 610, 26. 810. 812, 27. 799. 800. 1869: 27.800, Dezember 1870: 26. 810. 812, 27. 789. 800. 802, 238. 801. 1002, 29. 1161, 30. 1407, Dezember 1871: 27. 803, 28. 1004, 1872: 28. 1002, Mai 1873: 29. 1161, 1874: $0. 1408, 31. 1103, April 1875: 932.1423, Marz 1876: 32. 1437, Juli 1878: 35. 938, 9$7(3). 102,
Mai 1882: 98(3). 76. 77. 80. 81. 96.122, 39(3). 11.89, Mai 1883: $8(3). 122,
42 (3). 120, 43(3).127 und Aug. 1887: 48(3). 128; Sonnenfinsterniss, Con- Stitution der Sonne 26. 798.
4le) Kometen.
Kometen = Cometen, Kapitelbezeichnung in allen Banden [An: $98. 1474]. Allgemeines aber Kometen 37(3). 104. 120, 38(3). 151, 39(3). 123, 40(3). 143, 41(3). 129 -- Anonym: (F. A. D., nach ,Mondes*) Ueber Kometen $7(3). 118*. Stichworte und Anonyma: Kometenschweife 38(3). 142; Kometensuchen ib. 38(3). 151; Kometenbeobachtungen 38(3). 149. 162, 39(3). 101. 117. 118; Kometenbahnen 43(3). 49; Kometenlitteratur 32. 1415; Rickkebr von Kometen, Kometen kurzer Periode etc. 30. 1423, 36(3). 98. 99, 40(3). 136, 41(3). 141; Elektricitat der Kometenschweife $7(3). 118"; Spektroskop. Beobachtungen der Kometen $9(3).116; Kometenmaterie 40(3). 144 -- Beobachtung einzelner Kometen: Frthere, altere Kometen 96(3). 101, 37(3). 142. 145, 38 (3). 150, 41(3). 135; Kometen von 1577, 1843, 1879 96(3). 98"; Komet 1644 40(). 134; Komet von 1652 41(3). 136%; Komet 1707 39(3). 121%; Komet von 1717 41(3). 136; Komet 1729 40(3). 145%; Komet 1812 $7(3). 146; Komet 1840 $1 T77*; Kometen 1855 bis 1884 42(3). 185; Kometenverzeichniss von 1861 u. 1882 39 (3). 127; Kometen, Der Schweif des, 1865 I. 43(3). 154; Komet von 1866 und die Novembermeteore 41(3). 157; Komet 1873 VII. 37(3). 146%; Komet von 1874 930. 1359; Spektrum von Komet Winnecke b 1877 33. 492; Kometen
Einzelbeobachtungen von Kometen, den Jahren nach geordnet u. den Benennungen nach bei einigen besonderen Kometen, wo dieselbe Eigenname geworden ist (Brorsens, Enckes Komet u.s.f.). 1880: 36(3). 99. 101, 37(3). 19. 142, 38(3). 150; Komet Gould I (a) 36(3). 101. 102, 37(3). 143; Schaberle ITI (b) 36(3). 102; Faye III (c) 36(3). 103, 37(3). 148; Hartwig, Palisa 1V d. 36(3). 103. 104, 37(3). 143; Swift V (e) 36(3). 105, 37(3). 143; Pechile VI f. 37(3). 142. Verschiedene Beobachtungen uber Elemente der Kometen Hartwig und Swift $6(3). 104" -- 1881 (a) 1 Swift 37(3). 120, $8 (3). 155; (b) 2 Swift $7(3). 123. 132. 137. 138. 146, 38(3). 144 (Spektrum). 145. 146, 40(3). 96. Komet b 1881 und die Elektricitét 37(3). 138"; c¢ (3) Schaberle, Cruls 37(3). 138. 139, 38(). 146; d (Encke) 9$7(3). 120, 38(3). 248; e Barnard 97(3). 121, 38 (3). 149; f Denning $7(8). 121. 122, 38(3). 149; Wendell Swift 3$7(3). 122, 38(3). 149, h (8). Kometenerscheinungen 1880/81 98 (3). 122, die acht Kometen 188! 937(3). 119, 38(38). 142, 41(3). |
2. The loudness of sound is such as is con venient for common purposes. The organs of speech can, in the present constitution of the air, produce, without fatigue, such a tone of voice as can be heard with distinctness and with comfort. That any great alteration in this element might be incommodious, we may judge from the diffi culties to which persons are subject who are dull of hearing, and from the disagreeable effects of a voice much louder than usual, or so low as to be indistinct. Sounds produced by the human organs, with other kinds of air, are very different from those in our common air. If a man inhale
SOUND. 121
a quantity of hydrogen gas, and then speak, his voice is scarcely audible.
The loudness of sounds become smaller in pro portion as they come from a greater distance. This enables us to judge of the distance of objects, in some degree at least, by the sounds which proceed from them. Moreover it is found that we can judge of the position of objects by the ear : and this judgment seems to be formed by comparing the loudness of the impression of the same sound on the two ears and two sides of the head.*
The loudness of sounds appears to depend on the extent of vibration of the particles of air, and this is determined by the vibrations of the sound ing body.
3. The pitch, or the differences of acute and grave, in sounds, form another important pro perty, and one which fits them for a great part of their purposes. By the association of different notes, we have all the results of melody and har mony in musical sound ; and of intonation and modulation of the voice, of accent, cadence, em phasis, expression, passion, in speech. The song of birds, which is one of their principal modes of communication, depends chiefly for its distinc tions and its significance upon the combinations of acute and grave.
* Mr. Gough in Manch. Mem. vol. v.
122 TERRESTRIAL ADAPTATIONS.
These differences are produced by the different rapidity of vibration of the particles of air. The gravest sound has about thirty vibrations in a second, the most acute about one thousand. Between these limits each sound has a musical character, and from the different relations of the number of vibrations in a second arise all the differences of musical intervals, concords and discords.
4. The quality of sounds is another of their differences. This is the name given to the difference of notes of the same pitch, that is the same note as to acute and grave, when produced by different instruments. If a flute and a violin be in unison, the notes are still quite different sounds. It is this kind of difference which dis tinguishes the voice of one man from that of another : and it is manifestly therefore one of great consequence ; since it connects the voice with the particular person, and is almost neces sary in order that language may be a medium of intercourse between men.
5. The articulate character of sounds is for us one of the most important arrangements which exist in the world ; for it is by this that sounds become the interpreters of thought, will and feel ing, the means by which a person can convey his wants, his instructions, his promises, his kindness, to others ; by which one man can regulate the actions and influence the convictions and judg ments of another. It is in virtue of the pos-
SOUND. 123
sibility of shaping air into words, that the imperceptible vibrations which a man produces in the atmosphere, become some of his most important actions, the foundations of the highest moral and social relations, and the condition and instrument of all the advancement and im provement of which he is susceptible. |
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GPT-1900 Physics CLM Data
Physics-domain text for continued pretraining (causal language modeling) of GPT-1900. This dataset contains chunks of text from seminal pre-1905 physics works — Newton's Principia, Maxwell's Treatise on Electricity and Magnetism, Faraday's Experimental Researches, Boltzmann, Gibbs, Hertz, and many others.
Used to specialize the base GPT-1900 model toward physics reasoning before instruction tuning and reinforcement learning.
Stats
| Split | Rows |
|---|---|
| Train | 319,461 |
| Val | 16,814 |
Format
Parquet files with a single text column. Each row is a chunk of physics text.
Source Texts
Includes works by: Newton, Maxwell, Faraday, Boltzmann, Gibbs, Galileo, Hertz, Helmholtz, Kelvin, Lorentz, Rayleigh, Tyndall, Clausius, Carnot, Stokes, Thomson, Young, Huygens, Laplace, Poynting, Larmor, and others. Extended to a 1905 cutoff (includes Planck 1901, Lorentz 1904, Rutherford on radioactivity).
Usage
from datasets import load_dataset
ds = load_dataset("mhla/gpt1900-physics-clm")
Related
- mhla/gpt1900-d34-22btok — GPT-1900 base model
- mhla/gpt1900-d34-v3-sft-physics — Instruct model built on top of this physics data
- mhla/gpt1900-d34-contradiction-rl-v11 — Best RL model (downstream of this data)
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Size of downloaded dataset files:
773 MB
Size of the auto-converted Parquet files:
773 MB
Number of rows:
336,275