360 PHILOSOPHICAL TRANSACTIONS. [aNNO I687. 



SO near ; to which, the demonstration of Mr. Huygens de Cycloide is but a 

 corollary. And in another proposition is shown the velocity in each point, and 

 the time spent in each part of the arch described by the vibrating body. After 

 this, the effects of two or more bodies, towards each of which there is a tend- 

 ency, is considered ; and it is made out that two bodies, so drawing or attract- 

 ing each other, describe about the common centre of gravity, curve lines, like 

 to those they seem to describe about each other. And of three bodies, at- 

 tracting each other, reciprocally as the square of the distance between their 

 centres, the various consequences are considered and laid down, in several 

 corollaries of great use in explaining the pheenomena of the moon's motions, the 

 flux and reflux of the sea, the precession of the equinoctial points, and the 

 like. 



This done, our author, with his usual acuteness, proceeds to examine into 

 the causes of this tendency or centripetal force, which from undoubted argu- 

 ments is shown to be in all the great bodies of the universe. Here he finds 

 that if a sphere be composed of an infinity of atoms, each of which have a 

 conatus accedendi ad invicem, which decreases in duplicate proportion of the 

 distance between them ; then the whole congeries shall have the like tendency 

 towards its centre, decreasing, in spaces without it, in duplicate proportion of 

 the distances from the centre ; and decreasing within its surface, as the dis- 

 tance from the centre directly ; so as to be greatest on the surface, and nothing 

 at the centre : and though this might suffice, yet to complete the argument, 

 there is laid down a method to determine the forces of globes composed of parti- 

 cles whose tendencies to each other decrease in any other ratio of the distances ; 

 which speculation is carried on likewise to other bodies not spherical, whether 

 finite or indeterminate. Lastly, is proposed a method of explaining the refrac- 

 tions and reflections of transparent bodies, from the same principles ; and several 

 problems solved of the greatest concern in the art of dioptrics. 



Hitherto our author has considered the effects of compound motions in mediis 

 non resistentibus, or wherein a body once in motion would move equally in a 

 direct line, if not diverted by a supervening attraction or tendency towards 

 some other body. Here is demonstrated what would be the consequence of a 

 resistance from a medium, either in the simple or duplicate ratio of the velocity, 

 or else between both : and to complete this argument, is laid down a general 

 method of determining the density of the medium in all places, which, with a 

 uniform gravity tending perpendicularly to the plane of the horizon, shall make 

 a project move in any curve line assigned ; which is the 10th prop. lib. 2. Then 

 the circular motion of bodies in resisting media is determined, and it is shown 



