Kev. M. H. Close on the Meaning of "Force." 249 



if applied to force proper, but are quite appropriate to impul- 

 sion. And, agreeably to this, " mutatio motus" means amount, 

 not rate, of change of momentum ; for in the exposition it 

 appears as " motus" which may be added to (&c.) that which 

 may have been originally possessed by the body. It is im- 

 plied by some writers and expressly stated by others, who 

 have not considered the exposition, that the change of mo- 

 mentum of Law II. is rate of change ; they have been led to 

 say this through the still existing ambiguity of " force." It 

 is actually the case that, in consequence of this ambiguity, 

 competent dynamicists unconsciously differ as to what is the 

 subject matter of one of the fundamental Laws of Motion ! 



(6) When force is defined as that which produces momen- 

 tum, or change of momentum, either " force " means impulsion, 

 or else a very incongruous statement is made respecting force 

 proper. Force proper, being the rate of change of momentum, 

 cannot be the cause of momentum — -just as the death-rate in 

 some city for a certain week was not the cause of the aggre- 

 gate of deaths in that week, and as velocity, the rate of dis- 

 placement, is not that which produces the displacement, and 

 as density, the volume-rate of mass, is not the cause of mass. 

 Some other considerations show that force proper must not be 

 called the cause of momentum: e. g. if we call it so we must, for 

 a similar reason, also say that it is the cause of kinetic energy; 

 so that the same cause may have two totally disparate effects, 

 which is absurd. In accordance with Newton's language in 

 the exposition of Law II., we may style impulsion the gene- 

 rator or cause of momentum ; though it might be perhaps 

 more correct to say that it is the power of producing momen- 

 tum, just as energy is the power of performing work. 



(c) W hen, as frequently occurs, force is said to be expended, 

 either " force " means impulsion, or else a very incongruous 

 statement is made respecting force proper. Under statical 

 circumstances there is clearly no expenditure of force ; and 

 this is equally so in a kinetical operation. A force of one 

 pound is applied to an immovable obstacle ; an equal force is 

 simultaneously applied to a free mass; at the end of some 

 period of time both forces are all there, as at the beginning ; 

 there has been no expenditure of either in any ordinary non- 

 transcendental sense of the word. That the point of appli- 

 cation of the latter is not where it was at first is quite irrele- 

 vant to the present question. Force proper, or the rate of 

 production of momentum, is not expended in producing the 

 momentum, any more than the death-rate in some city is 

 expended in producing the mortality therein. It is the im- 

 pulsion, or Ft, which is expended pari passu with the produc- 



