156 NEWTON S TRINCIPIA. 



that of the Sun weighs 10,000, at that of Jupiter 943, 

 and at that of Saturn 549, 



2. So too the masses of matter in each planet and in 

 the satellites may be ascertained. The motions of the 

 satellites of Jupiter and Saturn afford the easiest means 

 of determining the masses of those planets ; and the 

 motions of the other planets round the Sun enable us to 

 solve the problem, though not so accurately, as to them. 

 The mass of Jupiter compared with that of the Earth 

 may be easily supposed to be prodigious, when we find all 

 his satellites revolve round him so much more rapidly than 

 the Moon does round the Earth, although all of them but 

 one have much larger orbits. Thus the second satellite 

 revolves in a seventh of our lunar month, though its path 

 is half as long again : and hence, its velocity is between 

 10 and 11 times as great. Sir Isaac Newton ascertained 

 the masses of Jupiter, Saturn, and the Earth to be to 

 that of the Sun as TTT ^ 7 , ^T* T^gV 02* to 1 respectively. 

 In like manner the densities are found, being as the 

 weights (first found) divided by the axes. Thus he 

 determined the relative densities of Jupiter, Saturn, and 

 the Earth to be as 94 J, 67, and 400, to 100, the density 

 of the Sun. Laplace has ascertained the masses of the 

 heavenly bodies by an entirely different calculus, founded 

 upon the comparison of numerous observations with 

 the formula? for determining the disturbances. The result 

 is extremely remarkable in one particular. It agrees to 

 a fraction, as regards Jupiter, with the calculation of 

 Newton, making the mass of the planet y^Vy -^ u ^ the 

 observations of Pound respecting Saturn s axis, on which 

 Newton had estimated Saturn s mass, were subject to 

 considerable uncertainty ; so at least Laplace explains 

 the difference of his own results; but he admits* that 



* Mec. Cel. liv. vii. eh. 16, s. 44. 



