Br, J. R. Mayer on the Mechanical Equivalent of Heat. 503 



ing of a given weight of water from 0° to 1° C. corresponds 

 to the fall of an equal weight from the height of about 365 

 metres." 



It is plaiD that the expression " equivalent '* is here used in 

 quite a different sense from what it bears in chemistry. The 

 difference will be shown most distinctly by an example. When 

 the same weight of potash is neutralized, first, with sulphuric 

 acid, then with nitric acid, the numbers which express the ratio 

 which the absolute weights of these three substances bear to one 

 another are called their equivalents ; but there is no thought here 

 either of the quantitative equality or of the transformation of 

 the bodies in question. 



This peculiar signification which the word " equivalent " has 

 acquired in chemistry, is doubtless connected with the fact 

 that the chemist has been able to determine the object of his 

 investigation by a common quantitative standard, their abso- 

 lute weights. Let us suppose, however, that we could determine 

 one body, for instance water, only by weight, and another, water- 

 forming or explosive gas, only by volume, and that we had 

 agreed to choose 1 lb. as the unit of weight, and 1 cubic foot as 

 the unit of volume ; we should then have to ascertain how many 

 cubic feet of explosive gas could be obtained from one pound of 

 water, and conversely. This number, without which neither the 

 formation nor the decomposition of water could be made the 

 subject of calculation, might then be suitably called "the explo- 

 sive-gas equivalent of water." 



In this latter sense a raised weight might, in accordance with 

 the known laws of mechanics, be called the "equivalent" of the 

 motion resulting from its fall. Now, in order to compare these 

 two objects, the raised and the moving weight, which admit of 

 no common measure, we require that constant number which is 

 generally denoted by g. This number, however, and the mecha- 

 nical equivalent of heat, whereby the relation subsisting between 

 heat and motion is defined, belong both of them to one and the 

 same category of ideas. 



In the paper that I have mentioned it is further shown how we 

 may arrive at such a conception of force as admits of being con- 

 sistently followed to its consequences and is scientifically tenable ; 

 and the importance of this subject induces me to return to it 

 again here. 



The word "force" {Kraft) is used in the higher or scientific 

 mechanics in two distinct senses. 



I. On the one hand, it denotes every push or pull, every effort 

 of an inert body to change its state of rest or of motion ; and 

 this effort, when it is considered alone and apart from the result 

 produced, is called " pushing force," " pulling force," or shortly 



