140 NEWTON S PBINCIPIA. 



surface in which the particle is situated were collected 

 in the centre. 



From these theorems it follows, that where bodies move 

 round a sphere and on the outside of its surface, what was 

 formerly demonstrated of eccentric motion in conic sections, 

 the focus being the centre of forces, applies to this case of 

 the attraction being in the whole particles of the sphere; 

 and where the bodies move within the spherical surface, 

 what was demonstrated of concentric motion in those 

 curves, or where the centre of the curve is that of the at 

 tracting forces, applies to the case of the sphere s centre 

 being that of attraction. For in the former case the cen 

 tripetal force decreases as the square of the distance in 

 creases; and in the latter case that force increases as the 

 distance increases. Thus it is to be observed, that in the 

 two cases of attraction decreasing inversely as the squares 

 of the central distance (the case of gravitation beyond the 

 surface of bodies), and of attraction increasing directly with 

 the central distance (the case of gravitation within the sur 

 face), the same law of attraction prevails with respect to 

 the corpuscular action of the spheres as regulates the 

 mutual action of those spheres and their motions in re 

 volution. But this identity of the law of attraction is con 

 fined to these two cases. 



Having thus laid down the law of attraction for these 

 more remarkable cases, instead of going through others 

 where the operation of attraction is far more complicated, Sir 

 Isaac Newton gives a general method for determining the 

 attraction whatever be the proportions between the force 

 and the distance. This method is marked by all the geo 

 metrical elegance of the author s other solutions ; and 

 though it depends upon quadratures, it is not liable to the 

 objections in practice which we before found to lie against 

 a similar method applied to the finding of orbits and forces ; 



