ON THE MOTIONS OF SIMPLE MASSES. 39 



of bodies in motion. This may however be done, without considering the 

 actual magnitude or extent of the body. We may easily conceive different 

 masses or bulks to be concentrated in a mathematical point ; and it is most 

 convenient to define a moveable body, as a moveable point or particle com- 

 posed of other elementary particles, differing only in number, and thus 

 constituting the proportionally different mass or bulk of the body. 



Although in our experiments on motion we are obliged to have recourse 

 to material bodies, and although such bodies differ considerably from this 

 definition of a single moveable body, yet they serve sufficiently well to 

 represent such bodies, especially when they are small and regularly formed ; 

 and we are here considering the doctrine of motion rather in a mathe- 

 matical than in a physical sense ; so that we are able to neglect all such 

 properties of matter as are not immediately necessary to our purpose. In- 

 deed though the general properties of matter are usually placed at the 

 entrance of elementary works on mechanics, it has yet been found 

 necessary to omit the consideration of their effects, in examining the laws 

 and affections of motion. The forces of cohesion and repulsion, for exam- 

 ple, act, in general, in a very complicated manner, in almost all cases of 

 the communication of motion ; but to consider these operations minutely 

 in treating of collision, would be to involve the subject in very great 

 and very unnecessary difficulties ; and the complete investigation of these 

 properties of matter would require the employment of various branches of 

 mechanical and hydrodynamical science. We may therefore take a much 

 simpler course, by deferring entirely all theoretical consideration of actual 

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

 tions, some measure of the mass or bulk as here defined. We might employ 

 spherical bodies, composed only of homogeneous substances, that is, of sub- 

 stances of the same kind, and we might estimate the mass by the compara- 

 tive 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 numbering 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 recti- 

 linear motion, is a property attached to all matter, and may be considered 

 as proportional to the mass or weight of a body. When the motions of a 

 system of bodies are considered, their inertia may in some respects be 

 referred to a single point, which is called the centre of inertia. [See the 

 next paragraph.] The centre of inertia of two bodies is that point, in the 

 right line joining them, which divides it into two such portions, that the 

 one is to the other as the mass of the remoter body tp 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 from the larger : and the dis- 

 tance 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 



