978 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



being made in physical science, appear to have an important 

 bearing. 



Without expecting to add any essentially new ideas to those 

 heretofore expressed, on a subject which has been so thoroughly 

 discussed bv the most profound thinkers, an attempt is made in 

 this paper to simplify the presentation, if possible, of principles 

 so important in .every branch of mechanical and physical science, 

 in order that the nature of the diiference between the two measures 

 may be clearly seen. At the same time a definition of the word 

 force is proposed, which appears to involve the recognition of the 

 Newtonian measure as the true one. 



Let us, then, define force, in the most direct and obvious manner, 

 as that iddch causes matter to move, and see to what conclusions we 

 are thereby led. According to this definition we do not admit 

 that force ever produces mere tendency to motion. On the con- 

 trary, motion always takes place when force acts upon matter. 



Nor does the production by force, of " change of motion," 

 whether by accelerating, retarding, or altering its direction, require 

 a change in our definition, if we admit the principle, fully con- 

 firmed by experience, that all motions are relative, i. e., only to 

 be known by referring them to the motions of other bodies, which 

 motions must, in turn, be again referred to others since there is 

 no known absolute point of rest. Any change of motion, there- 

 fore, is virtually a new motion in another direction. It obviously 

 follows, from these premises, that equal increments or decrements 

 of velocity, added to or taken from a moving body, are accom- 

 panied by equal increments or decrements to or from its force. 



Suppose, for example, that two equal bodies move side by side, 

 and that their velocities are equal, when referred to some object 

 which we will suppose is a third body of equal weight assumed 

 to be at rest. Relatively to each other the two bodies are at rest, 

 and if we suppose the velocity of one of them to be doubled and 

 then refer it to the other which is thus assumed to be at rest, we 

 find that it sustains precisely the same relations to the other in 

 regard to quantity of associated force that each of the two bodies 

 did to the first object of reference. Its associated force must, 

 therefore, be just doubled in quantity if we again assume that the 

 first object of reference is at rest. In the same manner it may be 

 shown that an increase or diminution in the velocity of a moving 

 body in any proportion whatever, is accompanied by an increase 



