44 LECTURE VI. 



the same kind. For the apparent difference in the velocity with which 

 different substances fall through the atmosphere, is only owing to the 

 resistance of the air, as is sometimes shown by an experiment 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 machine, and it is dis- 

 tinctly 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 should 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 parti- 

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

 may constitute the specific differences of those substances. 



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

 bodies, 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 

 centre of inertia [gravity], which are inversely in the same ratio. This 

 consideration is sometimes of use in determining the action of the sun on 

 the several 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 dis- 

 tances from their common centre of inertia [gravity]. Thus, in the 

 planetary 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 determine the effect of the attraction as 

 directed to a fixed point, we consider the force as residing in the common 

 centre of inertia [gravity] of the two bodies, which remains at rest, as far as 

 the mutual actions of those bodies only are concerned, and it may be shown, 

 that the force diminishes as the square of the distance of the bodies, either 

 from this point or from each other, increases. The reciprocal forces of two 

 bodies may therefore be considered as tending to or from their common 

 centre of inertia [gravity] as a fixed point ; but it often happens that the 

 difference of magnitude being very great, the motion of one of the bodies 

 may be disregarded. Thus we usually neglect the motion of- the sun, in 

 treating of the planetary motions produced by his attraction, although, by 

 means of very nice observations, this motion becomes sensible. But it is 

 utterly beyond the power of our senses to discover the reciprocal motion of 

 the earth produced by any terrestrial cause, even by the most copious erup- 

 tion of a volcano, although, speaking mathematically, we cannot deny that 

 whenever a cannon ball is fired upwards, the whole globe must suffer a 

 minute depression in its course. The boast of Archimedes was therefore 

 accompanied by an unnecessary condition : " give me," said he, " but a 

 firm support, and I will move the earth ;" but, granting him his support, 



