On the Definition of Force as the Cause of Motion. 337 



Let lis observe also that we have no concern now with the 

 question whether mechanical or molar force or pressure does or 

 does not rest upon molecular kinetics as its ground. That is aD 

 exceedingly interesting and important physical question, but one 

 with which, we submit, pure dynamics has nothing to do. 



Before proceeding further we must ask what is the definite 

 scientific meaning of " force ?" Of course we do not presume to 

 answer this question from ourselves. Force is simple pressure or 

 tension which can be measured in pounds weight. It is generally 

 agreed that we get our notion of it from the muscular sense of 

 resistance. It is just what we have said, whether existing under 

 statical or kinetical circumstances. When existing under kine- 

 tical circumstances it is proportional to the rate of change of the 

 momentum of the free body concerned. 



We must now define " impulse," as we shall have to use the word 

 frequently. " Impulse " means, in this paper, the correlate and 

 numerical equivalent of momentum. It is the quantity signified 



by ft in the equation /^ = momentum, or by f fdt in ffdt = 



momentum. This name is thus applied by Clerk Maxwell and 

 others. Intrinsically it is an excellent name for the thing 

 intended ; but it has this objection, that it is generally used, as 

 by Newton, with reference to a sudden, intense, and short-lasting 

 action ;* whereas no such meaning is now intended. The force 

 concerned may be as smaU and the time concerned as prolonged 

 as we please. 



The following are either instances of the inconvenience arising 

 from defining force as the cause of motion, or else illustrations of 

 the form of conception which has given rise to that definition. 



(1.) This definition is inconsistent with the fundamental equa- 

 tion of motion, viz, : momentum = jfdt, from which we have 



/ = -^-77 — . Force then is, or is proportional to, the time-rate of 



increase of momentum, and therefore cannot be called the cause 

 of the momentum. To call it so is analogous to saying that the 

 death-rate was the cause of the aggregate of deaths in a given 

 city in a given year, or that density is the cause of mass. 



* We use "action " here and elsewhere in a free non-technical sense, as is often done by 

 dynamicists. 



