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of recovery from a disturbance of the earth’s axis, might equally fit the observations, will be found untenable. For such a suggestion is excluded by the fact that the forces of the sun, moon and planets, acting on the earth |
throughout past ages in the same way as at present, fully account for the whole of the normal cyclical movement of the earth’s axis. These forces, and their effects, are well known, and have been precisely calculated. There is thus |
no room for any other harmonic movement of the earth’s axis. We are, in fact, limited to these forces, because a movement of any appreciable magnitude, due to internal changes within the earth, or to any difference between the centre |
of gravity of the earth and its centre of figure, would at once become apparent as an “Eulerian” oscillation, as already pointed out. It would be observable as a “variation of latitude,” and not as a change in the earth’s |
axial inclination. We have seen that this variation of latitude does, in fact, exist at the present time, but only on an exceedingly minute scale. Therefore, however greatly the recovery curve and its implications may be at variance with present |
beliefs, both in geology and in astronomy, it must necessarily be taken into account, unless, and only unless, the steadily increasing difference between these ancient observations and the normal curve of obliquity, as we trace it backwards into past ages, |
can be rightly ascribed to errors of the ancient observations. We have thus arrived at the crux of the matter. It is the testing ground on which many far-reaching conclusions must stand or fall. For this reason, considerable attention has |
been given in the preceding pages to a description of the chief instrument, i.e. the vertical gnomon used in ancient times. The errors of observation may now be considered first in regard to the nature and amount of the errors |
peculiar to the instrument itself; and secondly, light is thrown on these errors also by internal evidence, in many cases contained in the ancient observations, at different places and times. From an astronomical point of view, there is nothing difficult |
in this; and the general reader will be able easily to form his own opinion on the matter from the data which will now be presented. It is certain, however, that with the possible exception of some of the early |
Arab observations between 800 A.D. and 900 A.D., in all other cases where a gnomon was used, it was either a flat-topped one or a gnomon with a hole at the top, giving a circular image of the sun, the |
centre of which was measured. Further reference to this will be made a little later. Error of measuring scale With regard to the first source of error, connected with the measuring scale, we cannot doubt that finely divided linear scales |
were in use in ancient Egypt. The wonderful Egyptian architecture, in its colossal dimensions, shows that the architectural drawings must have been made with exact drawing instruments, necessitating fine scales for linear measurement. The power of accurately estimating small fractions |
of linear divisions is also indicated by “the perfection of Egyptian drawing and science of form,” referred to by J. Capart, “in the wall drawing on the tombs of the Kings at Thebes.” The artist began by drawing a system |
of very accurate squares. “Horizontal and vertical lines formed a veritable network to guide the hand and eye in the course of the work.”(7) Great artistic accomplishment, both among the ancient Egyptians and their Greek successors, must necessarily have been |
associated with a keen perception of fine linear subdivision. Sir Flinders Petrie says, in reference to the casing stones of the Great Pyramid, that these stones were worked with an accuracy equal to the finest optician’s work, being smooth and |
straight to one hundredth of an inch in a length of 75 inches, and that they were fitted together with plaster of Paris cement at almost imperceptible joints only two hundredths of an inch thick. Such precision implies that the |
Egyptians had attained a high perfection in the art of linear measurement. Antoniadi also expresses the opinion that “the Egyptian cubit was divided into hundredths with very fine subdivisions, comparable to our millimeter.” (8) Evidence of similar accuracy in a |
kindred department of measurement is contained in the statement that “the ancient Egyptians also measured weights to the decimal of a grain.” (9) We may safely conclude that in astronomical measurements, at the time of the Alexandrian astronomers, the error |
introduced by the use of linear scales would be very small. In ancient China the standard gnomon was 8 Chinese feet in height. The Chinese foot (Chih) was slightly longer than the English foot, and was equivalent to 13.32 English |
inches. The gnomon itself was thus 8 feet 9 inches high, expressed in English measure. The Chinese adopted decimal subdivisions. One tenth of a Chinese foot was called a Tsuen (corresponding to our inch). It was thus 1.3 English inches. |
This was subdivided into tenths, or fen, corresponding to 0.13 English inches, or practically 1/8 of our inch. P. Gaubil, who extracted numerous solstitial shadow lengths from the ancient Chinese records, gives these measured shadow lengths in Chinese feet inches |
and fen, i.e., they measured the shadow to the nearest 1/8 of an English inch. Thus the error of measurement of the shadow, so far as it depended on the linear scale, did not exceed half of that amount, viz., |
1/16 of an English inch. In their system of linear measurement the Chinese further subdivided the fen into 10 li, and the li into 10 hao. We see therefore that the ancient Chinese made use of fine scale measurements. In |
their circular measurements, the standard circle was 365 1/4 degrees in circumference, the same as the number of days in the year. Thus, they adopted the standard Year-Day Circle, which was similarly the basis of the ancient Egyptian system of |
measurement; it is also an interesting feature of the famous ancient British circular monument of Stonehenge. In the Chou Pei, instructions are given to level the ground over a diameter of 126 feet, and to “carry out the leveling process |
with the level of water.” On this leveled platform a circle is traced of 365 1/4 feet in circumference. The circle is to be divided carefully into this number of degrees. The instruction is given: “Let there not be the |
very smallest difference between the degrees.” The circle is then divided into 4 quadrants, by stretching a thread exactly north and south, and another transverse to it, east and west. Each of the four parts of the circumference, it is |
stated, will embrace 91 5/16 degrees. In the centre of this standard circle a gnomon is erected, 8 Chinese feet in height, and the Chou Pei then proceeds with instructions for making astronomical observations with it. Besides dividing the standard |
circle into 365 1/4 degrees, it was also divided into 714,000 circular li, each of these small divisions being equivalent to 0.536 linear li. Enough is said to show clearly that the ancient Chinese were extremely careful with fine scale |
linear and circular measurements. The maximum error from this source would be half a “fen,” equivalent to 1/16 inch (English). This would introduce into the measurement of the obliquity, for observations at both solstices, a possibility of a maximum error |
of only 1 1/3 minutes of arc. This would be reduced to a negligible quantity in a result depending on several observations. Error of verticality of the gnomon Since the gnomon was rendered vertical by means of a plumb-bob, any |
error of verticality would arise from lack of parallelism between the plumb-line and the gnomon. An experimental determination shows this would only cause an error in the observed altitude of the sun of approximately a half minute of arc. Error |
of level Experiments with water-level show that it is possible to obtain equality of level of water at two opposite sides of a leveled surface within on twenty-fifth of an inch. With the gnomon, this gives an error of approximately |
one minute of arc n the sun’s alititude. Estimating the edge of the shadow The problem of measuring the edge of the shadow may appear at first sight to introduce considerable uncertainty; and modern writers often ascribe a considerable proportion |
of the supposed errors of the ancient astronomical observations to a difficulty in observing the edge of the solar shadow. This difficulty is not so great as has been suggested. At the edge of the shadow cast by a plain |
gnomon there is a recognizable point where a slight blurring becomes appreciable; from this point onwards the penumbra becomes fainter rapidly till it is lost in full illumination. Experiment shows that the point where the blurring of the shadow commences, |
which is recognized by observers as the “edge of the shadow,” corresponds to a small segment of nearly one-tenth of the solar diameter, just appearing over the top of the gnomon. In order to investigate the errors of such measurements, |
however, the best wa seems to be by actual experimental observation, made under conditions similar to those of the ancient observations; that is to say, with a gnomon whose verticality is tested by means of a plumb-line, and whose horizontal |
surface on which the shadow falls is leveled with a water level. These experiments then throw light not only on the errors of measuring the shadow-edge, but also on the errors due to the plumb-line and the level. This practical |
method of testing the errors of the gnomon was used at Adelaide at the winter solstice in June 1936. A vertical gnomon was constructed at the Adelaide Observatory, using a piece of pine wood 6 feet high, screwed to a |
horizontal measuring board 10 feet 6 inches long. A plumb-bob was used to make the gnomon vertical, and the measuring board was leveled with a water level. Three kinds of measurements were made: This gnomon was set up on June |
12th, 1936, in one of the large window frames of the Physics Department at the Adelaide University, and a lengthy series of observations was made in which 9 observers took part. The edge of the shadow was found to be |
much more clearly defined than had been expected, even when its greatest length was attained, at the winter solstice. With a small 6 foot gnomon, the horizontal measurements were made with a millimeter scale, and the consistency of measuring the |
edge of the shadow was within 1 to 2 millimetres, i.e., 1/25 to 1/12 inch. This is sufficient to indicate that, with a gnomon of 8 feet 9 inches height, corresponding to 8 Chinese feet, the edge of the shadow |
could easily be measured within 2 to 3 millimetres, corresponding to slightly less than 1 Chinese “fen.” Thus the Chinese records of shadow lengths at the solstices, given in Chih (feet) tsuens (inches) and fen (tenths of a Chinese inch) |
may be regarded as reliable measurements of the solstitial shadows according to the linear scales used by the ancient Chinese astronomers. In the Adelaide observations the point marked by the plumb-bob as the zero for the horizontal measurements was easily |
ascertained within 1 millimetre. From these data, the errors in the sun’s observed altitude, due to these three sources – measurement of the edge of the shadow, verticality, and level – can be calculated. On the worst occasions, when the |
errors all accumulate in the same direction, they produce a maximum error of 2’.6 above or below the true mean altitude of the sun. The difference between the highest and the lowest altitude would then be 5’.2. Similar calculation of |
the errors at the summer solstice gives the same result as at the winter solstice. The worst observation may be 2’.6 above or below the true altitude of the sun, and the range from the highest to the lowest observation |
may amount to 5’.2 . At the winter solstice of June 1936, 172 observations of the shadow-edge were made by 9 observers. The mean of the 172 observations shows that the observed altitude of the sun’s upper edge obtained with |
value). The extreme range was thus 4’.9 and the mean of the highest and lowest readings was 12’.85, i.e. only 1/3 minute from the mean of the whole 172 observations. These results show the substantial accuracy attainable with a long |
series of observations with the gnomon. One hundred and seventy-one observations of the circular spot of shadow, cast by the ball, gave the true centre of the sun within 0’.4, the observed altitude being by this amount slightly less than |
the true centre of the sun. The explanation of this is to some extent connected with the fact that the shadow of the ball, as projected on a horizontal surface, is not a true circle, but is slightly elliptical in |
the direction of its length. The estimated centre of this elliptical shadow gives the length [which is] very slightly too great. The sun’s altitude is thus observed to be just a little smaller than the true altitude. The highest reading |
of the circular shadow-spot was 1’.7 above the mean result, and the lowest was 2’.4 below it; so that the range was 4’.1, a little less than in the case of the observations of the shadow-edge. The observations with the |
30 foot gnomon at the top of the University Survey Tower gave the same correction as given by the small gnomon, viz. 13’.2, to reduce the observed altitude of the sun’s upper edge to its centre. The range, from the |
highest to the lowest reading, 4’.1, was slightly smaller for the 30 foot gnomon than for the 6 foot gnomon. This advantage of the higher gnomon is accounted for by the relatively greater accuracy of the vertical and level corrections. |
The results obtained with the 6 foot gnomon, confirming the calculated range with this instrument of about 5’, are of special interest in view of the statement by Ptolemy that the observations of Eratosthenes at Alexandria gave a value for |
says. From this he defined the maximum obliquity of the sun as 23° 51’ 19”.”(10) From the statements of ancient writers it is clear that Eratosthenes used a gnomon for his solstitial observations of the sun, as well as an |
armilla, which was supplementary to the gnomon. It is also clear that the results given by Eratosthenes were obtained from a series of observations at both summer and winter solstices, as Eratosthenes lived for 40 years at Alexandria, during which |
time he carried out his historic astronomical work, including the celebrated measurement of the earth’s circumference. These considerations are a complete and striking verification of the accuracy of the mean value of the obliquity of the ecliptic obtained by Eratosthenes. |
In all cases the gnomon with a triangular top gives a shorter shadow than the plain or straight-topped gnomon. At the winter solstice, a gnomon with an apex angle of 90° requires a correction (to the sun’s observed altitude to |
were obtained with acute-angles gnomons. All, with the exception of a few of the Arab observations, were obtained with the ordinary plain or flat-topped gnomon, or in a few cases, with a gnomon having a central hole at the top. |
An acute-angled gnomon would give too small a value for the obliquity. The striking thing, however, about the ancient observations, (with the exception of a few made by the early Arabs), is that they give a larger value for the |
obliquity than the theoretical one, and the difference increases greatly as we go back to the most ancient observations. The test of their accuracy lies not only in the foregoing practical investigation, but also in the remarkably accurate values of |
latitude which the ancient observations give. Summing up the evidence, therefore, it may be said that when the question of the errors, to which the ancient observations of the obliquity of the ecliptic were liable, is submitted to a practical |
experimental test, by using instruments and methods corresponding to those of ancient times, the results confirm the accuracy of the observations within one or two minutes of arc, and show that, in a long series of such observations by a |
careful observer, no great errors occur. This is of great importance, in view of the far-reaching conclusions derived from the ancient observations, and demonstrates that these conclusions are on a sound basis of observational fact. Chapter 2 Illustrations -- Back |
to beginning of chapter 2 The Gnomon (four illustrations follow) The following two illustrations are of the gnomon called Augustus' Sundial. Augustus had it shipped to Rome from Egypt after conquering Egypt in 31 B.C. The Armilla (two illustrations follow) |
eastern end of the valley of Gedor, in the wilderness south of Palestine. In this passage the Authorized Version has "habitation," erroneously following the translation of Luther. They are mentioned in the list of those from whom the Nethinim were made up Ezra:2:50; Nehemiah:7:52). |
Joystick Engagements and Restrictors A big factor in taking advantage of a joystick comes from how well the directional commands are distributed in the area of joystick movement. If some regions are excessively large (and therefore others too small), your accuracy in quickly hitting the proper region, or in hitting the right series of regions, is going to suffer. Ideally, each of the utilized |
directions should have a significant-sized region, and the regions should be well-proportioned and centered where they are intuitively expected by the player. Obviously, some general precision in the joystick is needed for this to happen to begin with (this is discussed in the joystick attributes section). The neutral needs to be well-centered, the switches well-spaced and proportional and centered, and the opposing restrictor edges |
equally distanced from neutral. Beyond precision, the factors in accomplishing good distribution are the engage distances determined by the joystick actuator and switch structure, and the throw distances determined by a restrictor gate or the structure of the joystick. Neutral is the place where the shaft stands when not touched, ideally midway between each opposing direction. The deadzone is the space between the switches |
where no directions get engaged (including neutral). An engage happens when one or more switches are pressed. Engage distance refers to the distance/angle between neutral and the engagement of a given switch or set of switches. A shorter engage distance means a smaller deadzone and a larger engage distance means a larger deadzone. The engage distances are determined pretty much by how the joystick |
is manufactured with the placement of the switches and sizing of the actuator(s). Engage zones are areas where one or more switches are engaged. These zones are determined by the engage distances, and by the size, shape, and placement of the restrictor. The throw is the place where the joystick gets stopped in a particular direction. Throw distance is the maximum distance/angle the shaft |
can be moved in a particular direction. The edge surrounding the movable area of the joystick (all the throws) is composed by the restrictor. Restrictor gates specifically shorten and redistribute the throw distances. Directional Settings and Restrictors Directional settings can be described from two perspectives: gate or mode. They can be based on the tendencies given by the restrictor (x-way gate), or based on |
the settings of the joystick or game determining what commands or combinations of commands are available (x-way mode). Some examples of gates include octagonal described as 8-way, and plus-shaped described as 4-way. Some examples of modes include Space Invaders only recognizing left or right commands for 2-way, and the Happ/IL Super Joystick being set to the large side of the actuator for 4-way. Settings |
that emphasize a combination of left, up, right, or down to form diagonals are 8-way. 49-way and pretty much any number above 9-way (usually a squared odd number) are used by analog joysticks. In the following images, the shape represents the restrictor gate, the thick lines represent engage boundaries, and the thin lines represent equal division along the edges of the gate (which also |
divide area equally, even on the square). Simple joysticks use four switches arranged in a square, so there are four engage boundaries arranged in a square. The center area is the deadzone, the areas bordering it are single-direction (primary) engage zones, and the remaining are double-direction (diagonal) engage zones. Using a bit of math, percentages are labeled showing what fraction of the total area |
is filled by each engage zone. There are three main choices for restrictor shapes in 8-way play: circular, octagonal, and square. With both circular and octagonal restrictors, the spacing of the engages is usually based toward equal spacing along the restrictor (the throw areas). With square restrictors, the spacing of the engages is usually based toward equal neutral and engage zone sizes (a nine |
square grid of equal sizes). Note, however, that most joysticks are not precise to these goals. It can be difficult to balance the size of each direction's throw edge with the size of each direction's engage zone when eight directions are created using only four switches. With a circular or octagonal gate, you can easily divide the throws equally, but the engage zones for |
diagonals are going to suffer. With a square gate, you can easily divide the engage zones equally, but the throws are going to be twice as long on the diagonals. Even modifying the engage distances to give better throw or engage zone sizes can make problems. If you try to give bigger engage zones to the diagonals, the deadzone will shrink and cause new |
problems. If you try to give more throw size to a certain direction, other engage zones are going to shrink. But the square gate has some advantages. It is not difficult to hit the primary directions (up, down, left, and right) as they compose all the borders around the deadzone, and the diagonal directions are easy to hit because they have large throw sizes. |
While on circle and octagon restrictors, it is a compounding challenge to hit the diagonals when they have no edges on the deadzone, small engage zone sizes, and only an equally-sized region of throw. The square gate assists in finding the diagonals more easily and accurately, while single directions are easy enough because they surround the deadzone. There is a contradiction to having a |
square set of switches with a circular restriction in engaging them. The glory of the square gate is the balance of equally-sized engage zones with the equally-sized combined edges of the deadzone and throws for each direction. The square gate best-accommodates the diagonals. This is why high-quality parts manufacturers generally stock their joysticks with square gates. For circular and octagonal gates, medium to far |
throw distances are necessary so that the diagonals can be located easily. These gates are usually manufactured to have these larger throw distances. The best use of circular and octagonal gates is for play with the stick constantly along the edges or with sparsely needed diagonal movement. If you do not tend to hold your joystick at the edges all the time, the square |
should be better for you. Transitioning to a square gate can take a little time and practice. You should try to understand the structure and goals of the square, and learn to use a gentle touch. The ability to spin the joystick around all directions using a square gate can be just as easily done as on a circle. There are three main choices |
for restrictor shapes in 4-way play as well: circular, rhombus, and plus. Circular restrictors, for the most part, use the same spacing as in 8-way (an exception is the Super with a flipped actuator). Rhombus restrictors use the spacing of the square, the throws are just rotated 45 degrees. The plus restrictor is much like the rhombus, but the diagonals are covered so they |
are physically inaccessible. The two main factors in restrictor choice for 4-way games are the ability to hit accurately the four directions and the potential interference caused by hitting diagonals. The comparison between the ease in hitting the directions is easy enough: the plus shape is best because it is straight-forward, the rhombus is second best because it helps decently, and circle third best |
because the guiding is mild. This is the best order of quality when looking at interferences as well. With interference, a big question is how does the game or joystick interface regard events of two simple directions being engaged at the same time? Some recognize the last-engaged direction, others the first; some remove recognition of previously or newly also-engaged directions, some do not; some |
remove all engagement recognitions when more than one are engaged at once. The best example of a game where diagonals can be a problem is Pac-Man. The game recognizes the last of the four directions newly-engaged in choosing the direction of movement. Say you are turning right, but you accidentally clip the up switch after engaging right. Up will be the saved direction because |
it was last engaged. So you try to fix this by rotating the stick out of the up-right diagonal into only the right engagement. You would intuitively think this would fix the problem and make right the new direction. But right was engaged the entire time and it is not a new command. So up is still the recognized movement even though you are |
specifically holding right and only right. The example shows how many 4-way games can have problems with diagonal commands. The best thing that can be done about diagonals is to avoid them all together. So, again, the plus gate is best because it guides to the four directions well and outright does not allow two directions to be engaged at once. The rhombus is |
second best because it has some guidance for the needed directions, but it still allows diagonals to be engaged (an exception to this is the Sanwa JLW). Do not worry about difficulty in swinging the stick between directions using a plus-shaped gate either; if the gate is contoured (as it should be), changing directions is smooth and easy and not like using a car's |
gear-shift. The main 2-way restrictor is bar-shaped. But restrictors of most shapes work well for 2-way because games using it only recognize the two opposing directions and ignore the other two. You cannot simultaneously engage opposite directions on the joystick, so the interference problems like those in 4-way are not present. The 2-way restrictors enhance feel and make sure you hit the easily engaged |
two directions. As noted in the joystick models section, Happ and many other brand joysticks do not use restrictor gates and are classified as circularly restricted because that is their structure. The square/rhombus restrictor gate comes stocked with Sanwa joysticks with circular or octagonal and bar-shaped gates also available. Seimitsu joysticks (excluding the LS-56) come stocked with square, plus-shaped, and bar-shaped gates. |
Human beings have been burning fossil fuels like they’re going out of style. And they definitely are: We are running out of accessible oil, and we must dramatically cut back on our fossil fuel use to prevent the greenhouse effect |
from wreaking extreme ecological, human, and economic havoc. Biofuels—a better term is agrofuels—are often presented as the silver bullet that will enable us to drive our SUVs merrily into the future. Any burnable plant matter can be an agrofuel, but |
ethanol (fermented from corn, sugar cane, or other food crops) is most common today; biodiesel, derived from soy, palm, or other vegetable oil, is also coming into use. In theory, agrofuels seem like a great idea. Plants are a renewable |
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