April 23, 1874] 



NATURE 



487 



THE COMING TRANSIT OF VENUS * 

 II. 

 'T*HERE is perhaps no problem which has been so 

 -'• constant a source of interest to the learned in all 

 a^es as the soU'ing of the mystery of the solar system. 

 The labours of Copernicus, Tycho Braht?, Kepler, and 

 Newton have given us a general knowledge of the nature 

 of the planetary motions ; and the investigations of later 

 mathematicians have enabled us to predict, with wonder- 

 ful accuracy, the future positions of the planets. But the 

 dimensions of the solar system are not known with the 

 same precision. 



It is true that we know the relative distances of all the 

 planets from the sun with tolerable exactness. This pro- 

 blem has been attacked in two totally different methods. 

 The first is by measuring directly the changes that are 



produced in the motions of the planets when the earth 

 has moved through a certain portion of its orbit. In the 

 case of the plaaets Mercury and Venus, which move in 

 smaller orbits than that of the earth, the direct observa- 

 tion can easily be made. For let us suppose VV and 

 EE' (Fig. 8) to be the orbits of Venus and the earth, and 

 S to be the sun. Let us watch the position of Venus 

 night after night until she is as far away from the sun as 

 possible. If we measure her apparent distance from the 

 sun by astronomical means, we shall know that the sun, 

 Venus, and the earth occupy positions such as S, V, ani 

 E ; the directions ES and EV being known from our ob- 

 servations. By measuring off the distances SV and SE 

 on the diagram, we actually find the relation between the 

 earth's distance from the sun and that of Venus. The 

 same can be done with Mercury ; but for the superior 

 planets the direct mode of observation is more difficult. 



But there is an indirect niclhod which is much more 

 easy to apply. Kepler's three laws have been shown to be 

 necessary consequences of Newton's theory of gravitation. 

 Now Kepler's third law tells us how to find the relative 

 distances of two planets from the sun wlien we know 

 the relation between their periods of revolution. The 

 exact law is this : — Multiply the number of years taken 

 by a planet to go round the sun, by the same number. 

 This gives us a first number. Then find a second num- 

 ber which, multiplied by itself twice, gives us the first 

 number ; this second number is the distance of the planet 

 from the sun (the earth's distance being called i). To 

 take an example: Jupiter takes about 11 years to go 

 round the sun ; 1 1 multiplied by 1 1 gives us a first num- 

 ber, 121. Now if 5 be mukiplied by S we get 25, and if 



* Conlir.jcJ from p. 419. 



this be again multiplied by 5 we get 125, which is almost 

 the same as the first number, 121. Hence we are right in 

 saying that Jupiter is about five times as far from the sun 

 as the earth. If we had used the exact number of years 

 we should have got the exact distance. Now it is ven' 

 easy to find the period of revolution of a planet. For we 

 can easily measure the interval between two dates when 

 Jupiter and the earth, for example, are in the same line 

 with the sun ; in other words, we can measure the " syno- 

 dical revolution" of Jupiter ; and from this it is easy to 

 calculate the time of Jupiter's revolution round the sun. 



By applying these methods to all the planets 

 we can lay down their orbits upon a plan ; all we 

 liiisli now is to find tlie scale upon wliieh our plan is 

 drawn. If we knew the distance of the earth from the 

 sun, or if we knew the distance between any two of the 

 planetary orbits, we should know the scale upon which 

 our plan is laid down. Various methods have been 

 adopted for this, but the one which makes use of a transit 

 of Venus has generally been considered to be the most 

 accurate. 



One method which has successfully been applied to 

 measuring the moon's distance is that used by surveyors. 

 The surveyor chooses two spots, B, C, whose distance he 

 measures. Suppose it to be one mile. He draws this 

 distance, say, to one inch on a sheet of paper. He then 



takes a telescope, mounted so as to enable him to mea- 

 sure any angle through which it is turned. He places the 

 telescope at B, pointing towards C. He then turns it till 

 it points at the distant object, and finds what the an:;le of 

 B is. He then draws the line BA upon the paper, and he 

 knows that the distant object lies somewhere on the line 

 IjA. He then dojs the same with C, and thus he knows 

 that the remote object lies on CA. But A is the only 

 point lying both on BA and CA ; hence A corresponds to 

 the distant object. If on measuring CA he finds it to be 

 30 inches, then since CB, which is I inch, means one 

 mile ; CA, which is 30 inches, means 30 miles, and this is 

 what he wanted to find out. 



If, instead of taking a base-line (as it is called) of one 

 mile, the diameter of the earth, or 8,000 miles, be taken ; 

 then, if the moon be the distant object, we can determine 

 its distance in almost the same way. It is in this 

 manner that the moon's distance has been measured. 

 It is easy to see that if the angle at A (Fig. 9) 

 were very small, a slight error in measuring either ol tha 

 angles B or C would make a great difference in the dis- 

 tance deduced for the remote object. Hence, if the moon's 

 parallax were very small, this method would be unsuit- 

 able. But the parallax of the sun is very small, and 



