Dr. J. R. Mayer on the Mechanical Equivalent of Heat. 505 



however, been found impossible to put in practice such recom- 

 mendations; for the use of ambiguous expressions, which can 

 in no case contribute anything to clearness, is altogether inad- 

 missible if confusion can possibly arise. It is true that the 

 mathematician is in no danger of confounding in his calcula- 

 tions a product with one of its factors ; but in other departments 

 of knowledge a systematic confusion of ideas exists on this point ; 

 and if anything is to be done towards clearing it up, the source 

 of the error must be stopped ; for if we once recognize two mean- 

 ings of the word " force," it would be the labour of Sisyphus to 

 try to distinguish between 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 

 " force " altogether, or to employ it for one only of these two 

 categories. 



The notion of force was consistently employed in the latter 

 sense by Newton. In solving his problems, he decomposes the 

 product of the attraction into the effective space into its two 

 factors, and calls the former by the name " force." 



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

 be remarked that in many cases it is not possible thus to decom- 

 pose the product in question. Let us take, for instance, the 

 following very simple case : a mass M, originally at rest, is 

 caused to move with the (uniform final) velocity c; from the 

 knowledge of the magnitudes M and c it is certainly possible to 

 deduce thevalueof the product of the force(in Newton's sense)into 

 its effective space, but we are not thereby enabled to conclude 

 as to the magnitude of this force itself. 



As a matter of fact, the necessity soon made itself felt of treat- 

 ing and naming this product as a whole. It also has been called 

 "force," and the expressions "vis viva of motion," "moving 

 force," " working force," " horse-power " (or force), " muscular 

 force," &c. have been long naturalized in science. 



However happy we may, in many respects, think the choice of 

 this word, there is still the objection that a new meaning has been 

 fixed upon an already existing technical expression, without the old 

 one having been called in from circulation at the same time. This 

 formal error has become a Pandora's box, whence has sprung a 

 Babylonian confusion of tongues. 



Under existing circumstances no choice is left us but to with- 

 draw the term "force" either from Newton's dead force or from 

 Leibnitz's living force; but in either case we come into conflict 

 with prevailing usage. But if once we have made up our minds 

 to introduce into our science a logically accurate use of terms, 

 even at the cost of existing expressions which have become easy 



