116 Definition of the Terms ^^ Energy'''' and ''Work." 



The lack of explicitness in the current statements of this 

 law is noteworthy. The first clause in Newton^s statement of 

 the law, " Actioni contrariam semper et eequalem esse reac- 

 tionem," does indeed imply^ but does not explicitly state, that 

 the reaction is exerted upon a body from which the action 

 must emanate. In all the authorities which I have noticed 

 even the implication is wanting, the law being stated in the 

 hypothetical form — when one body acts upon another, the 

 other acts upon it, &c. This statement can scarcely be said 

 even to imply that there is never any action upon one body 

 except such as emanates from another body. 



We may now give precision to the definition of work by 

 putting it in this form : — 



The tvork done hy a force is the product of the intensity of 

 the force into the amount by lohich the tivo material points 

 between which it acts approach to or recede from each other ; the 

 work being positive when the approach or recession is in the 

 direction of the force, negative in the opposite case. 



The quantity of work thus defined is independent of the 

 point to which we refer the motion of the two bodies, since 

 only the relative motion is involved, and since two bodies 

 must, and two only can, come into play in the case of any one 

 force. 



The case is different with energy. It cannot be defined in 

 terms of the relative motion even of two bodies ; because, in 

 this simplest case, if the masses are different the energy will 

 be greater when we refer the motion to the body of smaller 

 mass. Hence, in defining the quantity of energy, we must 

 always implicitly assume some point of reference ; and this 

 point being arbitrary, the total energy either of a body or of 

 a system is necessarily an arbitrary quantity. 



Moreover, whether the work is done upon a body or by a 

 body in changing its motion from one state to another, depends 

 altogether upon the mass and motion of the foreign body from 

 which the action emanates. The law of the conservation of 

 energy assumes that we refer the motions of all the bodies 

 whose energy is considered, to some foreign body of infinite 

 mass, from which emanate the forces which give motion to 

 the system. The energy of the system is then equal to the 

 work it would do by being brought to a state of rest by forces 

 acting between its own parts and the body of reference. In 

 the familiar problems of kinetic energy we take as our body 

 of reference a point on the surface of the moving earth, and 

 then regard the energy of the moving body as the work done 

 or to be done upon it by reaction against the earth, or some 

 body fixed with reference to the earth. 



