58 LECTURE VI. 



detenuine the effect of the attraction as directed to a fixed point, \vc consider 

 the force as residing in the common centre of inertia of the two bodies, whicli 

 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 reci- 

 procal forces of two bodies may therefore be considered as tending to or from 

 their common centre of inertia, as a fixed point; but it often happens that, the 

 dift'erence 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 bis 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 eruption 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 unneces- 

 sary condition: " give me," said he, " but a firm support, and I will move the 

 earth;" but granting him his support, he could only have displaced the earth 

 insensibly by the properties of his machines; and without any such sup- 

 port, when he threw rocks upon the ships of Marcellus, he actually caused 

 the walls of Syracuse and theisland of Sicily to move northwards, with as much 

 momentum, as carried his projectiles southwards against the Roman arma- 

 ments. 



