ON THE MOTIONS OF SIMPLE MASSES. 57 



remains the same, the attraction will be simply as the bulk of the other. 

 Hence the quantity of matter, in every body surrounding us, is considered as 

 proportional to its weight; for it is inferred from experiment, that all material 

 bodies are equally subject to the power of gravitation towards the earth, and 

 are, in respect to this force, of the same kind. For the apparent difference 

 in the velocity, Avith which different substances fall through the atmosphere, 

 is only owing to the resistance of the air, as is sometimes shown by an ex- 

 periment on a feather and a piece of gold, falling in the vacuum of an air 

 pump; but the true cause was known long before the invention of this ma- 

 chine, and it is distinctly explained in the second book of Lucretius: 



" In water or in air when weights descend. 

 The heavier weights more swiftly downwards tend. 

 The limpid waves, the gales that gently play, 

 Yield to the weightier mass a readier way, 

 But if the weights in empty space sliould fall. 

 One common swiftness we should find in all." 



We are therefore to suppose, that the different weights of equal bulks of 

 different substances, depend merely on the greater or less number of particles 

 contained in a given space, independently of any other characters that may 

 constitute the specific diff^erences of those substances. 



In some cases it is necessary to consider the sum of the masses of two bo- 

 dies, in order to estimate their mutual action, that is, when we wish to know 

 the whole relative motion of two bodies with respect to each other; for here 

 we must add together their single motions with respect to the ceutre of iner- 

 tia, which are inversely in the same ratio. This consideration is sometimes 

 of use in determining the action of the sun on the seveial planets. 



If two bodies act on each other with forces proportional to any power of 

 their distance, for instance to the square or the cube of the distance, the forces 

 will also be proportional to the same power of either of their distances from 

 their common centre of inertia. Thus, in the planetarj' motions, when one 

 body performs a revolution by means of the attractive force of another, this 

 other cannot remain absolutely at rest; but because it is more convenient to 



VOL. I. I 



