488 



NATURE 



{April 23, 1874 



hence we cannot find the sun's distance with any exact- 

 ness by this method. 



But if any one of the planets ever came so close to the 

 earth as to make its parallax tolerably large, then we 

 could determine the scale upon which the solar system is 

 built up. Now Venus and Mars are two planets which at 

 certain times come closer to the earth than any other 

 planet. But, unfortunately, when Venus is most near to 

 the earth she is generally invisible, because the whole of 

 her illuminated side is turned away from us. Mars, how- 

 ever, is a planet that gives us a very favourable oppor- 

 tunity for determining its distance. The advantage is 

 increased by this peculiarity, that every fifteen years Mars 

 is at its shortest distance from the sun, at the same time 

 that the earth is at its greatest distance, the two planets 

 being also in the same line with the sun, so that they are 

 closer than we might have thought possible. In fact, on 

 these occasions Mars is nearer to the earth by -nVth part 

 than she is if the conjunction take place when both the 

 earth and Mars are at about their mean distances from 

 the sun. Suppose then that under such circumstances 

 two observers, one at Greenwich and the other at the 

 Cape of Good Hope (where there is a fine observatory), 

 observe the position of Mars as compared with that of a 

 star at the same time. The position of Mars will be 

 displaced by parallax ; and by comparing the apparent 

 distance of the planet from the fixed star at these two 

 places we can find the sum of the parallaxes in these 

 cases. Hence we can find the distance of Mars, as al- 

 ready explained. 



This was the first method to give a value of the solar 

 parallax with anything like accuracy. At the suggestion 

 of Cassini, the French sent out an expedition to 

 the Cape, under the astronomer Picard. The value ob- 

 tained for the sun's parallax was 9"'5. Prof. Henderson 

 in 1836, and Mr. Stone, in 1S62, utilised this method. 

 Another opportunity will occur in 1878. 



Before proceeding to the method of the Transits of 

 Venus, it will be well briefly to allude to some other 

 methods by means of which the solar parallax, or the 

 sun's distance, has been estimated. 



It has been found that light takes a sensible time to 

 propagate itself through space. Hence, when one of 

 Jupiter's satellites passes into the shadow of the planet, 

 this fact is not communicated to our vision for something 

 like 38 minutes, the time taken by light to pass from 

 Jupiter to the earth. Now, when we are on the same 

 side of the sun as Jupiter, this distance is shorter by the 

 whole diameter of the earth's orbit than when we are at 

 the opposite side of the sun. Hence, in the former case, 

 the eclipses will seem to take place sooner than the pre- 

 dicted time, and in the latter case later. The difference 

 in either case is about 8 minutes, and as we know that 

 light travels over 298,500 kilometres per second,* this 

 tells us that our distance from the sun is about 91,000,000 

 miles. 



But our knowledge of the velocity of light has been 

 utilised in another manner to solve the same problem. 

 You see that if we know the earth's velocity in miles, we 

 can find its distance from the sun. For if it goes li mil- 

 lion miles in one day, it must go over 365 times that in a 

 year, and tliat measures in miles llie ciieiimfercnee of our 

 earth's orbit, and hence we can get our distance from the 

 sun. How then are we to find the velocity of the earth 

 in miles. This depends on a curious property of light. 

 In a steady down-pour of rain you hold your umbrella 

 upright if you are standing still, but incline it forward if 

 you are walking fast. This is to make the umbrella catch 

 the rain-drops. The amount of inclination you give it 

 depends upon the rate at which you arc walking compared 

 with the velocity with which the drops fall. The same 

 thing happens with light. We have to incline our tele- 



* As determined by FoucauU. Compies Rendus lie I' Acad, ties St-if/ues, 

 vol. Iv. p. 502 ; also by Cornu, i^omptes Jieutius, Feb, 10, 1873. 



scopes forward a little in the direction in which the earth 

 is moving to catch the rays of light ; and at opposite 

 seasons of the year the earth is moving in contrary direc- 

 tions, and the telescope has to be pointed in sensibly differ- 

 ent directions. The inclination that a telescope receives 

 is known, and the velocity of light being known, we can 

 find the velocity of the earth, and hence, as I have shown, 

 the distance of the earth from the sun. 



There is another method of peculiar interest depending 

 upon the motions of the moon. The law of gravitation 

 says that the attraction of each body for each other one 

 depends upon the distance between them. The moon is 

 attracted to the earth by a force, depending upon the 

 distance of the moon, which is known in miles. But the 

 moon is caused to deviate from its natural course on ac- 

 count of the sun's attraction. This depends upon the 

 distance of the sun from the earth, and if this be not 

 known exactly in miles we shall see that it is impossible 

 to apply calculation to foretell the motions of the moon ; 

 for, if upon any scale we attempt to lay down upon paper 

 the relative positions of the sun, earth, and moon, we 

 shall place the moon at its proper distance, and the sun, 

 though in its proper direction, will not be placed at the 

 proper distance, and we shall not know the direction in 

 which it attracts the moon, nor the magnitude of this 

 attraction, and we shall make our calonlation wrongly, 

 and the moon's observed place will differ considerably 

 from its calculated place. 



Such a difference was actually detected by the illustrious 

 Hansen, whose tables of the moon are the best we pos- 

 sess. Hansen saw that this must be due to a wrong 

 assumption as to the distance of the sun, and communi- 

 cated his doubts to the Astronomer Royal * in the year 

 1S54, This led to a re-discussion of our knowledge of the 

 subject which has confirmed Hansen's views, and which 

 leads us to see the importance of knowing accurately the 

 sun's distance, if we wish ever to have our tables of the 

 moon so accurate that we may determine the longitude by 

 their aid. This method for investigating the solar parallax 

 was first used by Laplace.f 



More recently, M. le Verrier has suggested a new 

 method that promises in time to be the best.| In the 

 lunar theory, an equation appears connecting the relative 

 masses of the earth and sun with the solar parallax, so 

 that if we know the one we can find the other ; and from 

 a peculiarity in the equations, a small error in determining 

 the relative masses will affect only very slightly the de- 

 duced parallax. Le Verrier finds the ratio of the masses 

 of the earth and sun by determining the effect of the 

 earth's attraction upon Venus and Mars. This being 

 applied to the lunar theory, a value of the solar parallax 

 is obtained. 



The method, however, which has found most favour up 

 to the present time, is the employing of transits of Venus 

 to measure the sun's distance. When a transit of Venus 

 occurs, the first evidence of the phenomenon is given by 

 a slight notch being made in the contour of the sun's 

 edge at a certain spot. This notch increases until the 

 full form of the planet is seen. The first appearance of 

 a notch is called the time of first external contact. But 

 when the planet appears to be wholly on the sun, her 

 black figure is still connected with the sun's limb by a sort of 

 black ligament, of which we shall say more hereafter. 

 When the whole of the planet is just inside the sun's 

 edge, the time of first internal contact has arrived. The 

 breaking of the ligament is a very definite occurrence, 

 and was, until lately, taken to indicate the true moment 

 of internal contact. The second internal and external 

 contacts take place as the planet leaves the sun. 



In 1663, the celebrated James Gregory, in his famous 

 work the " Optica Promota," proji. 87, Scholium, alludes 



• Monthly Notices, R.A.S., vol. 

 t Systcme ciii Monde, t. ii. p. 91. 

 i Comptcs Rendus, July 22, 1872. 



r., Nov, 1854. 



