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the Pythagorean system was eventually sup- part of the same. We should now express pressed by that now called the Ptolemaic, this by saying that the angle is 87 degrees, which held the field until it was overthrown but Aristarchus knew nothing of trigonomby Copernicus, almost two thousand years etry, and in order to solve his triangle, he later. Pliny tells us that Pythagoras be- had recourse to an ingenious, but long and lieved the distances to the sun and moon to cumbersome geometrical process which has be respectively 252,000 and 12,600 stadia, come down to us, and affords conclusive or taking the stadium at 625 feet, 29,837 proof of the condition of Greek mathematics and 1,492 English miles; but there is no at that time. His conclusion was that the record of the method by which these num- sun is nineteen times further from the earth bers were ascertained.
than the moon, and if we combine that reAfter the relative distances of the various sult with the modern value of the moon's planets are known, it only remains to de- parallax, viz. : 3,422.38 seconds, we obtain termine the scale of the system, for which for the solar parallax 180 seconds, which is purpose the distance between any two more than twenty times too great. planets suffices. We know little about the The only other method of determining early history of the subject, but it is clear the solar parallax known to the ancients that the primitive astronomers must have was that devised by Hipparchus about 150 found the quantities to be measured too B. C. It was based on measuring the rate small for detection with their instruments, of decrease of the diameter of the earth's and even in modern times the problem has shadow cone by noting the duration of lunar proved to be an extremely difficult one. eclipses, and as the result deduced from it Aristarchus of Samos, who flourished about happened to be nearly the same as that 270 B. C., seems to have been the first to at- found by Aristarchus, substantially his valus tack it in a scientific manner. Stated in of the parallax remained in vogue for nearly modern language, his reasoning was that two thousand years, and the discovery of when the moon is exactly half full, the earth the telescope was required to reveal its erand sun as seen from its center must make roneous character. Doubtless this persista right angle with each other, and by meas- ency was due to the extreme minuteness uring the angle between the sun and moon, of the true parallax, which we now know is as seen from the earth at that instant, all far too small to have been visible upon the the angles of the triangle joining the earth, ancient instruments, and thus the supposed sun and moon would become known, and measures of it were really nothing but thus the ratio of the distance of the sun to measures of their inac uracy. the distance of the moon would be deter- The telescope was first pointed to the mined. Although perfectly correct in theory, heavens by Galileo in 1609, but it needed the difficulty of deciding visually upon the à micrometer to convert it into an accurate exact instant when the moon is half full is measuring instrument, and that did not so great that it cannot be accurately done come into being until 1639, when it was ineven with the most powerful telescopes. Of vented by Wm. Gascoigne. After his death course Aristarchus had no telescope, and he in 1644, his original instrument passed to does not explain how he effected the obser- Richard Townley who attached it to a fourvation, but his conclusion was that at the teen foot telescope at his residence in Towninstant in question the distance between the ley, Lancashire, England, where it was used centers of the sun and moon, as seen from by Flamsteed in observing the diurnal paralthe earth, is less than a right angle by 36 lax of Mars during its opposition in 1672.
A description of Gascoigne's micrometer was of Mercury and Venus. In 1677 Halley published in the Philosophical Transactions observed the diurnal parallax of Mercury, in 1667, and a little before that a similar and also a transit of that planet across the instrument had been invented by Auzout in sun's disk, at St. Helena, and in 1681 J. D. France, but observatories were fewer then Cassini and Picard observed Venus when than now, and so far as I know J. D. Cassini she was on the same parallel with the sun, was the only person beside Flamsteed who but although the observations of Venus attempted to determine the solar parallax gave better results than those of Mercury, from that opposition of Mars. Foreseeing neither of them was conclusive, and we now the importance of the opportunity, he had know that such methods are inaccurate Richer dispatched to Cayenne some months even with the powerful instruments of the previously, and when the opposition came present day. Nevertheless, Halley's attempt he effected two determinations of the paral- by means of the transit of Mercury ultilax; one being by the diurnal method, from mately bore fruit in the shape of his celehis own observations in Paris, and the brated paper of 1716, wherein he showed other by the meridian method from ob- the peculiar advantages of transits of Venus servations in France by himself, Römer for determining the solar parallax. The and Picard, combined with those of Richer idea of utilizing such transits for this purat Cayenne. This was the transition from pose seems to have been vaguely conceived the ancient instruments with open sights by James Gregory, or perhaps even by to telescopes armed with micrometers, and Horrocks, but Halley was the first to work the result must have been little short of it out completely, and long after his death stunning to the seventeenth century as- his paper was mainly instrumental in inductronomers, for it caused the hoary and gi- ing the governments of Europe to undertake gantic parallax of about 180 seconds to the observations of the transits of Venus in shrink incontinently to ten seconds, and 1761 and 1769, from which our first accuthus expanded their conception of the solar rate knowledge of the sun's distance was system to something like its true dimen- obtained. sions. More than fifty years previously Those who are not familiar with practical Kepler had argued from his ideas of the astronomy may wonder why the solar parcelestial harmonies that the solar parallax allax can be got from Mars and Venus, but could not exceed 60 seconds, and a little not from Mercury, or the sun itself. The later Horrocks had shown on more scientific explanation depends on two facts. Firstly, grounds that it was probably as small as 14 the nearest approach of these bodies to seconds, but the final death-blow to the the earth is for Mars 33,870,000 miles, ancient values ranging as high as two or for Venus 23,654,000 miles, for Mercury three minutes came from these observa- 47,935,000 miles and for the sun 91,239,000 tions of Mars by Flamsteed, Cassini and miles. Consequently, for us Mars and Richer.
Venus have very much larger parallaxes Of course the results obtained in 1672 than Mercury or the sun, and of course the produced a keen desire on the part of as- larger the parallax the easier it is to meastronomers for further evidence respecting Secondly, even the largest of these the true value of the parallax, and as Mars parallaxes must be determined within far comes into a favorable position for such in- less than one-tenth of a second of the truth, vestigations only at intervals of about six- and while that degree of accuracy is possible teen years, they had recourse to observations in measuring short ares, it is quite unat
tainable in long ones. Hence one of the itational and the photo-tachymetrical. We most essential conditions for the successful have already given a summary sketch of the measurement of parallaxes is that we shall trigonometrical methods, as applied by the be able to compare the place of the near ancient astronomers to the dichotomy and body with that of a more distant one situ- shadow cone of the moon, and by the modated in the same region of the sky. In the erns to Venus, Mars and the asteroids, and case of Mars that can always be done by we shall next glance briefly at the gravitamaking use of a neighboring star, but when tional and photo-tachymetrical methods. Venus is near the earth she is also so close to the sun that stars are not available, and The theory of probability and uniform consequently her parallax can be satisfac- experience alike show that the limit of actorily measured only when her position can curacy attainable with any instrument is be accurately referred to that of the sun, or, soon reached ; and yet we all know the in other words, only during her transits fascination which continually lures us on across the sun's disk. But even when the in our efforts to get better results out of the two bodies to be compared are sufficiently familiar telescopes and circles which have near each other, we are still embarrassed by constituted the standard equipment of obthe fact that it is more difficult to measure servatories for nearly a century. Possibly the distance between the limb of a planet these instruments may be capable of indiand a star or the limb of the sun than it is cating somewhat smaller quantities than to measure the distance between two stars, we have hitherto succeeded in measuring and since the discovery of so many asteroids, with them, but their limit cannot be far off that circumstance has led to their use for because they already show the disturbing determinations of the solar parallax. Some effects of slight inequalities of temperature of these bodies approach within 75,230,000 and other uncontrollable causes. So far as miles of the earth's orbit, and as they look these effects are accidental they eliminate precisely like stars, the increased accuracy themselves from every long series of obserof pointing on them fully makes up for their vations, but there always remains a residuum greater distance, as compared with Mars or of constant error, perhaps quite unsuspected, Venus.
which gives us no end of trouble. Encke's After the Copernican system of the world value of the solar parallax affords a fine and the Newtonian theory of gravitation illustration of this. From the transits of were accepted it soon became evident that Venus in 1761 and 1769 he found 8:58 trigonometrical measurements of the solar seconds in 1824, which he subsequently parallax might be supplemented by deter- corrected to 8:57 seconds, and for thirty minations based on the theory of gravita- years that value was universally accepted. tion, and the first attempts in that direction The first objection to it came from Hansen were made by Machin 1729 and T. Mayer in in 1854, a second followed from Le Verrier 1753. The measurement of the velocity of in 1858, both based upon facts connected light between points on the earth's surface, with the lunar theory, and eventually it first effected by Fizeau in 1849, opened up became evident that Encke's parallax was still other possibilities, and thus for deter- about one-quarter of a second too small. mining the solar parallax we now have at Now please observe that Encke's value our command no less than three entirely was obtained trigonometrically, and its distinct classes of methods which are known inaccuracy was never suspected until it respectively as the trigonometrical, the grav- was revealed by gravitational methods which were themselves in error about one- affected by anything that any of us can do tenth of a second and required subsequent in a lifetime, unless we are fortunate correction in other ways. Here then was a enough to invent methods of measurement lesson to astronomers who are all more or vastly superior to any hitherto imagined ? less specialists, but it merely enforced the Probably the existing observations for the perfectly well known principle that the determination of most of these quantities constant errors of any one method are acci- are as exact as any that can ever be made dental errors with respect to all other with our present instruments, and if they methods, and therefore the readiest way of were freed from constant errors they would eliminating them is by combining the re- certainly give results very near the truth. sults from as many different methods as To that end we have only to form a system possible. However, the abler the specialist of simultaneous equations between all the the more certain he is to be blind to all observed quantities, and then deduce the methods but his own, and astronomers most probable values of these quantities by have profited so little by the Encke-Hansen- the method of least squares. Perhaps some Le Verrier incident of thirty-five years ago of you may think that the value so obtained that to-day they are mostly divided into for the solar parallax would depend largely two great parties, one of whom holds that upon the relative weights assigned to the the parallax can be best determined from a various quantities, but such is not the case. combination of the constant of aberration With almost any possible system of weights with the velocity of light, and the other the solar parallax will come out very nearly believes only in the results of heliometer 8.809" =0.0057"', whence we have for the measurements upon asteroids.
mean distance between the earth and sun means continue the heliometer measure- 92,797,000 miles with a probable error of ments, and do everything possible to clear only 59,700 miles; and for the diameter of up the mystery which now surrounds the the solar system, measured to its outermost constant of aberration, but why ignore the member, the planet Neptune, 5,578,400,000 work of predecessors who were quite as miles.
WILLIAM HARKNESS. able as ourselves? If it were desired to WASHINGTON. determine some one angle of a triangulation net with special exactness, what would be THE BALTIMORE MEETING OF THE AMERIthought of a man who attempted to do so
CAN SOCIETY OF NATURALISTS. by repeated measurements of the angle in The thirteenth annual meeting of The question while he persistently neglected to American Society of Naturalists was held at adjust the net? And yet, until recently Baltimore during the Christmas vacation. astronomers have been doing precisely that considering that Baltimore is the southern kind of thing with the solar parallax. I limit where meetings may be held by the do not think there is any exaggeration in Society, the attendance was large, forty to saying that the trustworthy observations fifty members being present. now on record for the determination of the The first session was called to order by numerous quantities which are functions of the President, Professor Charles S. Minot of the parallax could not be duplicated by the the Harvard Medical School, at 2 P. M. on most industrious astronomer working con- Thursday, December 27th. tinuously for a thousand years. How then A quorum being present, the Society at can we suppose that the result properly once proceeded to the transaction of busideducible from them can be materially
The committee appointed in 1893 to obtain, if possible, the removal of the duty and Hyatt, Dr. Dall, Dr. C. V. Riley and on scientific instruments reported that al- others. though they had succeeded in obtaining the Professor Osborn, of Columbia College, in coöperation of most of the leading scientific opening the discussion, observed that natumen, yet the inception of the movement ralists were reacting from the discussion of had been so delayed that the Gorman Bill theories towards the renewed inductive and was already being considered by the Senate experimental study of the factors of Evolubefore the petitions could be presented to tion. This was due to the feeling that the the House.
prolonged discussion led by Spencer and The following resolution recommended Weismann had assumed a largely deductive by the committee was then adopted: In- character and would not lead to any perasmuch as the repeal of the present iniqui- manent results. The inductive reaction tous duty on scientific instruments is im- had taken two directions : first towards peratively needed by the interests of the the exact study of Variation, and second country, we recommend that a committee towards experimental Evolution. As rebe appointed to present our just demands gards Variation we should not expect to to the President, to the Chairman of the form any laws so long as variations were Committee on Finance of the Senate and considered en masse without regard to the the Chairman of the Committee of Ways past and present history of the organisms and Means of the House of Representatives, studied. That organisms vary with their enand to take such other steps as may be vironment is a truism. What we need is a practicable to secure the immediate repeal clearer conception and interpretation of this of the duty."
relation as a basis for experimental study The report of the committee on the revi- in the laboratory and in the field. The first sion of the Constitution and By-Laws was misconception to be removed is that which unanimously adopted. By the new consti- has sprung up from the misuse of the terms tution The American Society of Naturalists en- Heredity and Variability. Nägeli pointed courages the formation of other societies out many years ago as Weismann and of similar name and object in other parts Hurst have insisted more recently that of the country and invites other societies Heredity includes one phenomenon seen whose chief object is the encouragement from two sides which may conveniently be of the study of Natural History to become termed Repetition and Variation. A large affiliated with it. The affiliated societies number of the variations recorded by Bateshall have a common place and time of son, for example, are simple repetitions of meeting with the American Society of Nat- ancestral structure, and every new variation uralists, the expenses of which are to be is to be regarded as the expression of herepaid from a common treasury supplied from ditary forces working under new conditions. a common fee. The records of the secre- The first object of investigation is to decide taries of the different societies are also to the time of origin of a variation, first in race be published at common expense.
history, second in individual history. VariThe discussion upon Environment in its ations which arise as practical repetitions Influence upon the Successive Stages of Develop- of past experience may conveniently be ment and as a Cause of Variation, took place termed 'palingenic,' while those which are in the Physical Lecture Room, Thursday new to the organism may be termed 'cenoafternoon. It was opened by four papers genic. As regards individual history the and followed by remarks by Professors Cope most important question is to determine