210 TRANSFORMATION AND EQUIVALENCE OF FORCES. 



further becoming manifest that the physical forces stand 

 not simply in qualitative correlations with each other, but 

 also in quantitative correlations. Besides proving that one 

 mode of force may be transformed into another mode, ex- 

 periments illustrate the truth that from a definite amount of 

 one, definite amounts of others always arise. Ordinarily it 

 is indeed difficult to show this; since it mostly happens that 

 the transformation of any force is not into some one of the 

 rest but into several of them: the proportions being deter- 

 mined by the ever-varying conditions. But in certain cases, 

 positive results have been reached. Mr. Joule has ascer- 

 tained that the fall of 772 lbs. through one foot, will raise 

 the temperature of a pound of water one degree of Fahren- 

 heit. The investigations of Dulong, Petit and Neumann, 

 have proved a relation in amount between the affinities of 

 combining bodies and the heat evolved during their combi- 

 nation. Between chemical action and voltaic electricity, a 

 quantitative connexion has also been established : Faraday's 

 experiments implying that a specific measure of electricity 

 is disengaged by a given measure of chemical action. The 

 well-determined relations between the quantities of heat 

 generated and water turned into steam, or still better the 

 known expansion produced in steam by each additional de- 

 gree of heat, may be cited in further evidence. Whence it 

 is no longer doubted that among the several forms which 

 force assumes, the quantitative relations are fixed. The con- 

 clusion tacitly agreed on by physicists, is, not only that the 

 physical forces undergo metamorphoses, but that a certain 

 amount of each is the constant equivalent of certain amounts 

 of the others. 



§ 67. Everywhere throughout the Cosmos this truth 

 must invariably hold. Every successive change, or group of 

 changes, going on in it, must be due to forces affiliable on 

 the like or unlike forces previously existing ; while from the 

 forces exhibited in such change or changes must be derived 



