68 PLEASANT WAYS IN SCIENCE. 



The first of the methods which I here describe as 

 new methods must next be considered. It is one which 

 Leverrier regards as the method of the future. In fact, so 

 highly does he esteem it, that, on its account, he may almost 

 be said to have refused to sanction in any way the French 

 expeditions for observing the transit of Venus in 1874. 



The members of the sun's family perturb each other's 

 motions in a degree corresponding with their relative mass, 

 compared with each other and with the sun. Now, it can be 

 shown (the proof would be unsuitable to these pages,* but 

 I have given it in my treatise on "The Sun") that no change 

 in our estimate of the sun's distance affects our estimate of 

 his mean density as compared with the earth's. His substance 

 has a mean density equal to one-fourth of the earth's, whether 

 he be 90 millions or 95 millions of miles from us, or indeed 

 whether he were ten millions or a million million miles from 

 us (supposing for a moment OUT measures did not indicate 

 his real distance more closely). We should still deduce from 



* It may be briefly sketched, perhaps, in a note. The force neces- 

 sary to draw the earth inwards in such sort as to make her follow her 

 actual course is proportional to (i) the square of her velocity directly, 

 and (ii) her distance from the sun inversely. If we increase our esti- 

 mate of the earth's distance from the sun, we, in the same degree, 

 increase our estimate of her orbital velocity. The square of this velocity 

 then increases as the square of the estimated distance ; and therefore, 

 the estimated force sunwards is increased as the square of the distance 

 on account of (i), and diminished as the distance on account of (ii), and 

 is, therefore, on the whole, increased as the distance. That is, we now 

 regard the sun's action as greater at this greater distance, and in the 

 same degree that the distance is greater ; whereas, if it had been what 

 we before supposed it, it would be less at the greater distance as the 

 square of the distance (attraction varying inversely as the square of the 

 distance). Being greater as the distance, instead of less as the square 

 of the distance, it follows that our estimate of the sun's absolute force is 

 now greater as the cube of the distance. Similarly, if we had diminished 

 our estimate of the sun's distance, we should have diminished our esti- 

 mate of his absolute power (or mass) as the cube of the distance. But 

 our estimate of the sun's volume is also proportional to the cube of his 

 estimated distance. Hence our estimate of his mass varies as our 

 estimate of his volume ; or, our estimate of his mean density is constant 



