ASTRONOMY precise knowledge of the moon’s mass. The uncertainty of this mass impairs the accuracy of the method. I. To begin with the results of the first method. The transits of Venus observed in 1874 and 1882 might be expected to hold a leading place in the discussion. 'o^Vemis ■^° Purcly astronomical enterprise was ever carried out on so large a scale or at so great an expenditure of money and labour as was devoted to the observations of these transits, and for several years before their occurrence the astronomers of every leading nation were busy in discussing methods of observation and working out the multifarious details necessary to their successful application. In the preceding century reliance was placed entirely on the observed moments at which Venus entered upon or left the limb of the sun, but in 1874 it was possible to determine the relative positions of Venus and the sun during the whole course of the transit. Two methods were devised. One was to use a heliometer to measure the distance between the limbs of Venus and the sun during the whole time that the planet was seen projected on the solar disc, and the other was to take photographs of the sun during the period of the transit and subsequently measure the negatives. The Germans laid the greatest stress on measures with the heliometer; the Americans, English, and French on the photographic method. These four nations sent out well-equipped expeditions to various quarters of the globe, both in 1874 and 1882, to make the required observations; but when the results were discussed they were found to be extremely unsatisfactory. It had been supposed that, with the greatly improved telescopes of modern times, contact observations could be made with much greater precision than in 1761 and 1769, yet, for some reason which it is not easy to explain completely, the modern observations were but little better than the older ones. Discrepancies difficult to account for were found among the estimates of even the best observers. The photographs led to no more definite result than the observations of contacts, except perhaps those taken by the Americans, who had adopted a more complete system than the Europeans ; but even these were by no means satisfactory. Nor did the measures made by the Germans with heliometers come out any better. By the American photographs the distances between the centres of Venus and the sun, and the angles between the line adjoining the centres and the meridian, could be separately measured and a separate result for the parallax derived from each. The results were :— Distances ; par. = 8 ‘SSS". Transit q/-1874 : Pos. angles ; ,, =8-873". Distances ; ,, =8 •873". Transit q/11882 : Pos. angles; ,, =8'772". The German measures with the heliometer gave apparently concordant results, as follows :— Transit q/-1874 : par. = 8 ‘876". Transit of 1^2 : ,, =8'879". The combined result from both these methods is 8-857", while the combination of all the contact observations made by all the parties gave the much smaller result, 8-794". Had the internal contacts alone been used, which many astronomers would have considered the proper course, the result would have been 8-776". In 1877 Gill organized an expedition to the Island of Ascension to observe the parallax of Mars, with the Planetary heliometer. By measurements giving the paralposition of Mars among the neighbouring stars taxes. in the morning and evening, the effect of parallax could be obtained as well as by observing from two different stations; in fact the rotation of the earth carried the observer himself round a parallel of latitude,
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so that the comparison of his own observations at different times would give the same result as if they had been made at different stations. The result was 8-78 . The failure of the method based on transits of Venus led to an international effort carried out on the initiative of Sir David Gill to measure the parallax by observations on those minor planets which approach nearest the earth. The scheme of observations was organized on an extended scale. The three bodies chosen for observation were: Victoria, 10th June to 26 th August 1889; Iris, 12th October to 10th December 1888; and Sappho, 18th September to 25th October 1888. The distances of these bodies at the times of opposition were somewhat less than unity, though more than twice as great as that of Mars in 1877. The drawback of greater distance was, however, in Gill’s opinion, more than compensated by the accuracy with which the observations could be made. The instruments used were heliometers, the construction and use of which had been greatly improved, largely through the efforts of Gill himself. The planets in question appeared in the telescope as starlike objects which could be compared with the stars with much greater accuracy than a planetary disc like that of Mars, the apparent form of which was changed by its varying phase, due to the different directions of the sun’s illumination. These observations were worked up and discussed by Gill with great elaboration in the Annals of the Cape Observatory, vols. vi. and vii. The results were for the solar parallax nr; From Victoria, 7r=:8-801,,+ 0"006". ,, Sappho, 7r = 8 "798"+ 0-011". ,, Iris, 7r = 8-812"±0-009". The general mean result was 8-802". From the meridian observations of the same planets made for the purpose of controlling the elements of motion of the planets Auwers found tt = 8-806". All other methods of directly measuring the parallax fall so far behind this in certainty that we may regard Gill’s result as the best yet derived from measurement. But the difficulties of the measures are such that other methods may be yet better and in any case are not to be neglected. II. The velocity of light has been measured with all the precision necessary for the purpose. The latest result is 299860 kilometres per second, with, a probable error of perhaps 30 kilometres; that is, about the ten-thousandth part of the quantity itself. This degree of precision is far beyond any we can hope to reach in the solar parallax. The other element which enters into consideration is the time required for light to pass from the sun to the earth. Here no such precision can be attained. Both direct and indirect methods are available. The direct method consists in observing the times of some momentary or rapidly varying celestial phenomenon, as it appears when seen from opposite points of the earth’s orbit, the only phenomena of the sort available being eclipses of Jupiter’s satellites, especially the first. Unfortunately these eclipses are not sudden but slowly changing phenomena, so that they cannot be observed without an error of at least several seconds, and not infrequently important fractions of a minute. As the entire time required for light to pass over the radius of the earth’s orbit is only about 500 seconds, this error is fatal to the method. The indirect method is derived from the observed constant of aberration or the displacement of the stars due to the earth’s motion. The minuteness of this displacement, about 20"50", makes its precise determination an extremely difficult matter. The most careful determinations are affected by systematic errors arising from those diurnal and annual changes of temperature, the effect of which cannot be wholly eliminated in
