Mechanical Illustrations of the Planetary Motions. 321 



'yet only approximately true. Such a thing as a fixed centre 

 of gravity exists not in nature, or at least but one, — the 

 centre of the whole material universe. The idea of a con- 

 stant centre of gravity in any particular body depends upon 

 the supposition that the force of attraction is equal at 

 all distances from the attracting centre. Let us con- 

 ceive a straight uniform rod to be placed in a ver- 

 tical position, and divided into two equal parts : the 

 lower half will be the heavier, because nearer to the 

 earth's centre ; the centre of gravity will therefore be 

 below the middle of the rod. Let us now conceive the 

 position of the rod to be reversed, the upper end ex- 

 changing places with the lower : the centre of gravity 

 ■will then be on the other side of the middle — in that 

 half which was formerly the higher — it will have changed 

 its position in the rod. It follows, then, that in any mass of 

 matter the centre of gravity will not be a fixed point, but 

 will depend upon the position of the mass, and that it will 

 always be in that side of the mass which is nearest to the 

 attracting body. 



The centre of momentum, however, though commonly con- 

 founded with the centre of gravity, is not the same ; but as 

 this is a rather nice point, and not usually taken notice of, 

 I hope to be excused in saying a few words in explana- 

 tion . 



If two solids, of the same size, differ in weight from a dif- 

 ference in their specific gravity, the heavier has the greater 

 momentum ; but if they are alike both in size and in specific 

 gravity, and their difference in weight is caused by a differ- 

 ence in their height above the surface of the earth, then 

 their momenta are equal notwithstanding their difference 

 in weight. Thus, if a cannon-ball were fired from the sum- 

 mit of a mountain, it would strike an object with as much 

 force as it would do if fired, with the same velocity, at the 

 level of the sea, although the weight would be much less. 



Apply this now to the case of the straight rod. The lower 

 end is the heavier, but it has not the greater momentum. 

 The centre of momentum is therefore in the middle of the 

 rod, while the proper centre of gravity is not so. In fact, 



