OF NATURAL PHILOSOPHY. 



caloulu*. for example, is at once recognised ad the method of reasoning applicable 

 to quantities in a state of continuous change. This is Newton's conception of 

 Fluxions, and all attempts to banish the ideas of time and motion from the 

 mind must fail, since continuity cannot be conceived by us except by following 

 in imagination the course of a point which continues to exist while it m 



in 



"The arrangement of the book differs from that which has hitherto been 

 adopted in text-books. It has been usual to begin with those parts of the 

 subject in which the idea of change, though implicitly involved in the very 

 conception of force, is not explicitly developed so as to bring into view the 

 different configurations successively assumed by the system. For this reason, 

 the first place has generally been assigned to the doctrine of the equilibrium 

 of forces and the equivalence of systems of forces. The science of pure statics, 

 as thus set forth, is conversant with the relations of forces and of systems of 

 forces to each other, and takes no account of the nature of the material systems 

 to which they may be applied, or whether these systems are at rest or in 

 motion. The concrete illustrations usually given relate to systems of forces in 

 equilibrium, acting on bodies at rest, but the equilibrium of the forces is 

 established by reasoning which has nothing to do with the nature of the body, 

 or with its being at rest. 



The practical reason for beginning with statics seems to be that the student 

 is not supposed capable of following the changes of configuration which take 

 place in moving systems. He is expected, however, to be able to follow trains 

 of reasoning about forces, the idea of which can never be acquired apart from 

 that of motion, and which can only be thought of apart from motion by a 

 process of abstraction. 



Professors Thomson and Tait, on the contrary, begin with kinematics, the 

 science of mere motion considered apart from the nature of the moving body 

 and the causes which produce its motion. This science differs from geometry 

 only by the explicit introduction of the idea of time as a measurable quantity. 

 (The idea of time as a mere sequence of ideas is as necessary in geometry as 

 in every other department of thought.) Hence kinematics, as involving the 

 smallest number of fundamental ideas, has a metaphysical precedence over statics, 

 which involves the idea of force, which in its turn implies the idea of m: 

 as well as that of motion. 



In kinematics, the conception of displacement comes before that of velocity, 





