SECT, i.] UNIVERSAL GRAVITATION. 7 



of their mean distances from its centre (N. 26). Hence the 

 intensity of gravitation of all the bodies towards the sun is 

 the same at equal distances. Consequently, gravitation is 

 proportional to the masses (N. 27) ; for, if the planets and 

 comets were at equal distances from the sun, and left to the 

 effects of gravity, they would arrive at his surface at the 

 same time (N. 28). The satellites also gravitate to their 

 primaries (N. 29) according to the same law that their pri- 

 maries do to the sun. Thus, by the law of action and reac- 

 tion, each body is itself the centre of an attractive force 

 extending indefinitely in space, causing all the mutual dis- 

 turbances which render the celestial motions so complicated, 

 and their investigation so difficult. 



The gravitation of matter directed to a centre, and attract- 

 ing directly as the mass, and inversely as the square of the 

 distance, does not belong to it when considered in mass only ; 

 particle acts on particle according to the same law when at 

 sensible distances from each other. If the sun acted on the 

 centre of the earth, without attracting each of its particles, 

 the tides would be very much greater than they now are, 

 and would also, in other respects, be very different. The 

 gravitation of the earth to the sun results from the gravita- 

 tion of all its particles, which, in their turn, attract the sun 

 in the ratio of their respective masses. There is a reciprocal 

 action, likewise, between the earth and every particle at its 

 surface. "The earth and a feather mutually attract each other 

 in the proportion of the mass of the earth to the mass of the 

 feather. Were this not the case, and were any portion of 

 the earth, however small, to attract another portion, and not 

 be itself attracted, the centre of gravity of the earth would 

 be moved in space by this action, which is impossible. 



The forms of the planets result from the reciprocal attrac- 

 tion of their component particles. A detached fluid mass, 

 if at rest, would assume the form of a sphere, from the reci- 

 procal attraction of its particles. But if the mass revolve 



