332 THE MECHANICAL EQUIVALENT OF HEAT. 



difficulty. For instance, just as we speak of absolute weight, 

 specific weight, and combining weight, without its ever enter 

 ing any one s head to want to construct a generic idea out of 

 these distinct notions, so two or more meanings may be at 

 tached to the word force. This is what is actually done in 

 the higher mechanics, and hence in this branch of science we 

 meet with no mention of a generic conception of &quot; force.&quot; 



There has been no lack of recommendations to carry, in 

 like manner, the notions of &quot; dead&quot; and &quot; living force&quot; as 

 distinct and separate through the other departments of sci 

 ence ; it has, however, been found impossible to put in prac 

 tice such recommendations ; for the use of ambiguous ex 

 pressions, which can in no case contribute any thing to clear 

 ness, is altogether inadmissible if confusion can possibly arise. 

 It is true that the mathematician is in no danger of confound 

 ing in his calculations a product with one of its factors ; but 

 in other departments of knowledge a systematic confusion of 

 ideas exists on this point ; and if any thing is to be done 

 toward clearing it up, the source of the error must be stopped ; 

 for if we once recognize two meanings of the word &quot; force,&quot; 

 it would be the labour of Sisyphus to try to distinguish be 

 tween them in each separate case. In order, then, to arrive 

 at any result, we must make up our minds to do without any 

 common denomination of the magnitudes mentioned above, 

 as I. and II., and either to give up the use of the word 

 &quot; force &quot; altogether, or to employ it for one only of these two 

 categories. 



The notion of force was consistently employed in the lat 

 ter sense by Newton. In solving his problems, he decom 

 poses the product of the attraction into the effective space 

 into its two factors, and calls the former by the name &quot; force.&quot; 



As an objection to this mode of proceeding, it must, how 

 ever, be remarked that in many cases it is not possible thus 

 to decompose the product in question. Let us take, for in 

 stance, the following very simple case : a mass M, originally 



