228 A Short History of Astronomy [Cn. IX. 



which the comparison is possible, the force is proportional 

 not only to the mass of the attracted body, but also to 

 that of the attracting body, as well as being inversely pro- 

 portional to the square of the distance. Gravitation thus 

 appears no longer as a property peculiar to the central 

 body of a revolving system, but as belonging to a planet 

 in just the same way as to the sun, and to the moon or 

 to a stone in just the same way as to the earth. 



Moreover, the fact that separate bodies on the surface 

 of the earth are attracted by the earth, and therefore in 

 turn attract it, suggests that this power of attracting other 

 bodies which the celestial bodies are shewn to possess 

 does not belong to each celestial body as a whole, but to 

 the separate particles making it up, so that, for example, 

 the force with which Jupiter and the sun mutually attract 

 one another is the result of compounding the forces with 

 which the separate particles making up Jupiter attract 

 the separate particles making up the sun. Thus is 

 suggested finally the law of gravitation in its most general 

 form : every particle of matter attracts every other particle 

 with a force proportional to the mass of each, and inversely 

 proportional to the square of the distance between them* 



182. In all the astronomical cases already referred to 

 the attractions between the various celestial bodies have 

 been treated as if they were accurately directed towards 

 their centres, and the distance between the bodies has 

 been taken to be the distance between their centres. 

 Newton's doubts on this point, in the case of the earth's 

 attraction of bodies, have been already referred to ( 173) ; 

 but early in 1685 he succeeded in justifying this assumption. 

 By a singularly beautiful and simple course of reasoning 

 he shewed (Principia, Book I., propositions 70, 71) that, if 

 a body is spherical in form and equally dense throughout, 

 it attracts any particle external to it exactly as if its whole 

 mass were concentrated at its centre. He shewed, further, 

 that the same is true for a sphere of variable density, 

 provided it can be regarded as made up of a series of 

 spherical shells, having a common centre, each of uniform 



* As far as I know Newton gives no short statement of the law 

 in a perfectly complete and general form ; separate parts of it arc 

 given in different passages of the Principia. 



