CONNECTION OF HEAT AND MOVING FOKCE. 329 



weight] and motion requires that the space fallen through in 

 a given time, e. g. the first second, should be experimentally 

 determined; in like manner, the solution of the equations 

 subsisting between falling-force and motion on the one hand 

 and heat on the other, requires an answer to the question, How 

 great is the quantity of heat which corresponds to a given 

 quantity of motion or falling-force ? For instance, we must 

 ascertain how high a given weight requires to be raised above 

 the ground in order that its falling-force may be equivalent to 

 the raising of the temperature of an equal weight of water 

 from to 1 C. The attempt to show that such an equation 

 is the expression of a physical truth may be regarded as the 

 substance of the foregoing remarks. 



" By applying the principles that have been set forth to 

 the relations subsisting between the temperature and the vol- 

 ume of gases, we find that the sinking of a mercury column 

 by which a gas is compressed is equivalent to the quantity of 

 heat set fire by the compression ; and hence it follows, the 

 ratio between the capacity for heat of air under constant press- 

 ure and its capacity under constant volume being taken as 

 = 1*421, that the warming of a given weight of water from 

 to 1 C. corresponds to the fall of an equal weight from 

 the height of about 365 metres." 



It is plain 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 ex- 

 press the ratio which the absolute weights of these three sub- 

 stances 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 



