ON THE MOTIONS OP SIMPLE MASSES. 51 



matter ; but in the mean time we must have, for our experimental illustrations, 

 some measure of the mass or bulk as here defined. We might employ spheri- 

 cal bodies, composed only of homogeneous substances, that is, of substances of 

 the same kind, and we might estimate the mass by the comparative magnitude, 

 imagining all the particles of each sphere to be united in its centre. But it is 

 more convenient to anticipate, from the gravitation of matter, a measure of 

 the mass derived from the weight : since it can be proved that the weight of 

 a body is proportional to its absolute quantity of matter, supposing all matter 

 to be alike in its affections relative to motion. So that instead of numberino- 

 the particles of each body, the same purpose is answered by determining their 

 comparative weight. 



?•• 

 Inertia, -or a tendency to persevere in a state of rest, or of uniform rectilinear 

 motion, is a property attached to all matter, and may be considered as propor- 

 tional to the mass or weight of a body. When the motions of a system of bo- 

 dies are considered, their inertia may in some respects be referred to a single 

 point, which is called the centre of inertia. The centre of inertia of two bo- 

 dies is that point, in the right line joining them, M'hich divides it into two such 

 portions, that the one is to the other, as the mass of the remoter body to that 

 of the adjacent body. For instance, if one body weighs a pound, and another 

 two pounds, and their distance is a yard, then the centre of inertia is at the 

 distance of two feet from the smaller body, and one foot ftom the larger : and 

 the distance of each is to the whole distance, as the weight of the other to the 

 whole weight. Also the products obtained by multiplying each weight by its 

 distance are equal : thus two multiplied by one, is equal to one multiplied by 

 two. (Plate II. Fig. 39.) 



This point is most commonly called the centre of gravity ; it has also some- 

 times been denominated the centre of position. Since it has many properties 

 independent of the consideration of gravity, it ought not to derive its nam<5 

 from gravitation, and the term centre of inertia begins now, with great propri- 

 ety, to be generally adopted. 



The centre of inertia of any two bodies initially at rest, remain's at rest, not- 

 withstanding any reciprocal action of the bodies ; that is, notwithstanding any 

 action which aftccts the single particles of both equally, in increasing or diniif- 



