TflOMMM AXP TATrt NATURAL PHILOSOPHY. 



fr- tan* anfeM that tone actually spends itself upon it, what sort of 



laft to be the subject-matter of abstract dynamics ? 

 W aw MppOMd to have mastered so much of kinematics as to be able 

 > describe all poMble motions of points, lines, and figures. In so far as real 

 to|Bt< 1^ figare. and motions, we may apply kinematics to them. 



*t^ new y m appropriate to dynamics is that the motions of bodies are 

 not independent of each other, but that, under certain conditions, dynamical 

 UmiMBctioM take place between two bodies, whereby the motions of both bodies 



mn aftoted. 



Brery body and every portion of a body in dynamics is credited with a 

 attain quantitative value, called its mass. The first part of our study must 

 ikmforo be the distribution of mass in bodies. In every dynamical system 

 there M a certain point, the position of which is determined by the distribution 

 of nan. This point was called by Boscovich the centre of mass a better 

 HfH^ we think, than centre of inertia, though either of these is free from 

 the enor involved in the term centre of gravity. 



In every dynamical transaction between two bodies there must be some- 

 thing which determines the relation between the alteration of the motions of 

 the two bodies. In other words, there must be some function of the motions 

 of the two bodies which remains constant during the transaction. According 

 to the doctrine of abstract dynamics it is the motion of the centre of mass 

 of the two bodies which is not altered on account of any dynamical trans- 

 action between the bodies. This doctrine, if true of real bodies, gives us the 

 means of ascertaining the ratio of the mass of any body to that of the body 

 adopted as the standard of mass, provided we can observe the changes in the 

 motions of the two bodies arising from an encounter between them. 



We then confine our attention to one of the bodies, and estimate the 

 magnitude of the transaction between the bodies by its effect in changing the 

 momentum of that body, momentum being merely a term for a quantity mathe- 

 matically defined in terms of mass and motion. The rate at which this change 

 of momentum takes place is the numerical measure of the force acting on the 

 body, and, for all the purposes of abstract dynamics, it is the force acting on 

 the body. 



We have thus vindicated for figures with mass, and, therefore, for force 

 and stress, impulse and momentum, work and energy, their places in abstract 

 science beside form and motion. 



