160 Mr WHEWELL, ON THE NATURE OF THE TRUTH 



must consider what circumstances make it requisite that the force 

 should be greater or less. If we have to lift a stone, the force which 

 we exert must be greater when the stone is greater : again, we must 

 exert a greater force to lift it quickly than slowly. It is clear, there- 

 fore, that that property of a force with which we are here concerned, 

 and which we may call the motive quantity of the force,* increases both 

 when the velocity communicated, and when the mass moved, increase, and 

 depends upon both these quantities, though we have not yet shewn 

 what is the law of this dependence. 



The condition that a quantity P shall increase when each of two 

 others V and M does so, may be satisfied in many ways : for instance, 

 by supposing P proportional to the sum M+ V (all the quantities being 

 expressed in numbers), or to the product, MV, or to MF'-, or in many 

 other ways. 



When, however, the quantities ^ and M are altogether hetero- 

 geneous, as when one is velocity, and the other weight, the first 

 of the above suppositions, that P varies as M + V, is inadmissible. 

 For the law of variation of the formula M+ V depends upon the 

 relation of the units by which M and V respectively are measured; 

 and as these units are arbitrary in each case, the result is, in like 

 manner, arbitrary, and therefore cannot express a law of nature. 



« 



12. The supposition that the motive quantity of a force varies as 

 M^-V, where M is the mass moved and V the velocity, being thus 

 inadmissible, we have to select upon due grounds, among the other 

 formulae MV, MV\ M'V, &c. 



And in the first place I observe that the formula must be propor- 

 tional to M simply (excluding M.^ &;c.) for both the forces which 



* The motive quantity of a force {vis cujusvis quantitas matrix of Newton) is sometimes 

 called moving force; we are thus led to speak of the moving force of a force, as we 

 have already observed concerning accelerating force. Hence, as in that case, we might 

 employ a single term, as motivity, to denote this property of force; and might thus speak 

 of it and of its measures without the awkwardness which arises from the usual phrase. 



