556 



NATURE 



[Septemuhr 27, 1S94 



that of Jupiter, and both having the sun for their centre, it is 

 evident that the distance between the two planets must vary 

 from the sun to the difference of the radii of their respective 

 orbits, and the lime required by light to travel from one plane; 

 to the other must vary proportionately. Consequently, if the 

 observed times of the eclipses of Jupiter's satellites are com- 

 pared with the times computed upon the assumption that the 

 two planets arc always separated by their mean distance, it will 

 be found that the eclipses occur too early when the earth is at 

 less than its mean distance from Jupiter, and too late when it 

 is further off, and from large numbers of such observations the 

 value of the light equation has been deduced. 



The combination of the motion of light through our 

 atmosphere with the orbital motion of the earth gives rise to the 

 annual aberration, all the phases of which are computed from 

 its maximum value, commonly called the constant of aberration. 

 There is also a diurnal aberration due to the rotation of the 

 ear'h on its axis, but that is quite small, and does not concern 

 us this evening. When aberration was discovered the corpus- 

 cular theory uf light was in vogue, and it ofi'ered a charmingly 

 simple explanation of the whole phenomenon. The hypothetical 

 light corpuscles impinging upon the earth were thought to behave ' 

 precisely like thedrops inashowerof rain, and you all know that 

 their apparent direction is oflTected by any motion on the part of i 

 the observer. In a calm day, when the drops are falling per- 

 pendicularly, a man standing still holds his umbre'la direcly 

 over his head, but as soon as he begins to move forward he in- 

 clines his umbrella in the same direction, and the more rapidly 

 he moves the greater must be its inclination in order to meet 

 the descending shower. Similarly the apparent direction of on- 

 coming light corpuscles would be affected by the orbital motion ' 

 of the earth, so that in effect it would always be the result.int ; 

 arising from combining the motion of the light with a motion ' 

 equal and opposite to that of the earth. But since the falsity I 

 of the corpuscular theory has been proved that explanation is ! 

 no longer lenaWe, and as yet we have not been able to replace 

 it with anything equally satisfactory based on (he now univers- 

 ally accepted undulatory theory. In accordance with ihe latter 

 theory we must conceive the earth as ploughing its way through 

 the ether, and the point which has hitherto balllsd us is whether 

 or not in so doing it produces any disturbance of the ether 

 which affects the aberration. In our present ignorance on that 

 point we can only say that the aberration constant is certainly 

 very nearly equal to the ratio of the earth's orbital velocity to 

 the velocity of light, but we cannot aflirm that it is rigorously so. 



The luminifeious ether was invented to account for the 

 phenomena of light, and for two hundred years it was not sus- 

 pected to have any other function. The emission theory postu- 

 lated only Ihe corpuscles which constitute light itself, but the 

 undulatory theory tills all space with an imponderable substance 

 possessing properties even more remarkable than those of 

 ordinary matter, and to some of the acutest intellects the m-ig- 

 niludeofthis idea has proved an almost insuperable objection 

 against the whole theory. So late as 1862 Sir David Brewster, 

 who had gained a woild-wide reputation by his optical re- 

 searche", expressed himself as staggered by the notion of filling 

 all space wiih some substance merely to enable a little twinkling 

 star to send its light to us ; but not long after Clerk Maxwell 

 removed that difficulty by a discovery coextensive with the un- 

 dulatory theory itself. Since 1845, when Karaday first per- 

 formed his celebrated experiment ol magnetising a ray of light, 

 the idea that electricity is a phenomenon of the ether had been 

 ileadily growing, until at last .Maxwell perceived that if such 

 were ihe fact the rate of propag.ation of an electromagnetic wave 

 must be the same as the vclocilyof light. At that lime no one 

 knew how 10 generate such waves, but Maxwell's theory showed 

 him that their velocity must be equal to the number of electric 

 unit! of quantity in the electromagnetic unit, and careful experi- 

 ments soon proved that that is the velocity of light. Thus it 

 was put almost beyond Ihe possibility of doubt that the ether 

 gives rise to the phenomena of electricity and magnetism, as 

 well as to those of light, and perhaps it may even be concerned 

 in the pro<luclion of gravitation itself. What could be apparently 

 more remote than these electric quantities and the solar paral- 

 lax 1 And yet we have here a relation between them, but we 

 make no use of it, because as yet the same relation can be far 

 more accurately determined from experiments upon the velocity 

 of light. 



Now let U5 recall the quantities and methods of observation 

 which we have found to be involved either directly or indirectly 



with the soKir parallax. They are the solar parallax, obtained 

 from transits of Venus, oppositions of -Mars, and oppositions of 

 certain asteroids ; the lunar parallax, found both directly, and 

 from measurements of the force of gravity at Ihe earth's surface ; 

 the constants of precision, nutation, and aberration, obtained 

 from observations of the stars ; the parallactic inequality of the 

 moon ; the lunar inequality of the earth, usually obtained from 

 observations of the sun, but recently found from heliometer 

 observations of certain asteroids ; the mass of the earth, found 

 from the solar parallax, and also from the periodic and secular 

 perturbations of Venus and Mars ; Ihe mass of the moon, found 

 Irom Ihe lunar inequality of the earth, and also from the ratio 

 ollhe solar and lunar components of the ocean tides ; the m.isses 

 of all the planets, obtained from observations of their satellites 

 whenever possible, and when no satellites exist, then from 

 observ.ations of their mutual perturbations both periodic and 

 secular ; the velocity of light, obtained from experiments with 

 revolving mirrors and toothed wheels, together with laboratory 

 determinations of the index of refraction of atmospheric air : the 

 light equation, obtained from observations of the ellipses of 

 Jupiter's satellites; Ihe figure of the earth, oblainedfrom geodetic 

 triangulations, measurements of the length of Ihe seconds pendu- 

 lum in various Latitudes, and observations of certain per- 

 turbations of the moon ; the mean density of the earth, obtained 

 from measurements of the attractions of mountains, from 

 pendulum experiments in mines, and from experiments on the 

 attraction of known m.isses of matter made either with torsion 

 balances or with the most delicate chemical balances ; the 

 surface density of the earth, obtained from geological examin- 

 ations of the surface strata ; and Lastly, the law of distribulion 

 of density in the interior of the earth, which in the present sl.ate 

 of geological knowledge we can do little more than guess at. 



Here then we have a large group of astronomical, geodetic, 

 geological and physical quantities which must all be considered 

 in finding the solar parallax, and which are all so entangled with 

 each other that no one of them can be varied without affecting 

 all the rest. It is therefore impossible to make an accurate 

 determination of any one of them apart from the remainder of 

 the group, and thus we are driven to the conclusion that they 

 must all be determined simultaneously. Such has not been the 

 practice of astronomers in the past, but it is the method to 

 which they must inevitably resort in the future. .V cursory 

 glance at an analogous problem occurring in geodesy may be 

 instructive. When a country is covered with a net of triangles 

 it is always found that the observed angles are subject to a 

 certain amount of error, and a century ago it was the habit to 

 correct the angles in each triangle without much regard to the 

 elTect upon adjacent triangles. Consequently the adjustment 

 of the errors was imperfect, and in computing the interval 

 between any two distant points the result would vary somewhat 

 with the triangles used in the computation— that is, if one 

 computation was made through a chain of triangles running 

 around on the right-hand side, another through a chain of 

 triangles running straight between Ihe two points, and a third 

 through a chain of triangles running around on the left-hand 

 side, the results would usually all diiVer. At that time things 

 were less highly specialised than now, and all geodetic opera- 

 tions were yei in the hands of first-rate astronomers who soon 

 devised processes for overcoming ihe difficulty. They im.agined 

 eveiy observed angle to be subject to a small correction, and as 

 these corrections were all entangled with each other through 

 the geometrical conditions of the net, by a most ingenious 

 application of the method of least squires they determined then 

 all simultaneously in such a way as to satisfy the whule of the 

 geometrical conditions. Thus the best possible adjustment was 

 obtained, and no matter what triangles were used in passing 

 from one point to another, the result w.as always the same. 

 That method is now applied to every important triangulation, 

 and its omission would be regarded as proof of incompetency 

 on Ihe patl of those in charge of the work. 



Now let us compare ih; conditions existing respectively in n 

 triangulation net and in Ihe group of quantities for the 

 determination of Ihe solar parallax. In llie net every angle is 

 subject to a small correction, and the whole system of 

 corrections must be so determined as to make the sum of their 

 weighted squares a minimum, and at Ihe same time satisfy all 

 ihe geometrical conditions of Ihe net. Like the triangles, the 

 quantities composing the group from which Ihe solar parallax 

 must be determined are all subject to error, and therefore we 

 must regard each of them as requiring a small correction, and 



NO. 1 30c, VOL. 50] 



