430 Prof. Tait on the Conservation of Energy. 



occurs, completely proved for a single moving particle, in Sect. 

 VIII. Prop. XL. of the Principia. 



So that when Davy experimentally showed that " the imme- 

 diate cause of the phenomenon of heat is motion, and the laws 

 of its communication are precisely the same as the laws of the 

 communication of motion," the dynamical theory of heat was so 

 far completed that it required only a quantitative determination 

 of the mechanical equivalent. The immense additions it received 

 from Carnot, and subsequently from Clausius,Rankine, Thomson, 

 &c, are really only the development of the theory ; and much of 

 them must rest on hypotheses until we know the intimate struc- 

 ture of matter, and the kind of motion to which heat belongs. 



But the general principle of conservation of energy is founded 

 on the experimental determination of relations of equivalence 

 between the various forms of energy, and especially between heat 

 on the one hand, and each of the others in succession. This was 

 begun by Joule in 1840, and had already produced a vast amount 

 of important results, before the appearance of Mayer's first paper. 



That paper, about which so much has lately been written, con- 

 tains in its fundamental statements an essentially false analogy 

 between the falling together of material masses by gravitation 

 and the condensation of a gas by the external application of me- 

 chanical force. The idea that heat developed by compression is 

 an equivalent for the work spent (radically fallacious as it is) is 

 so important a part of Mayer's theoretical speculations, that he 

 has repeated it in his ' Celestial Dynamics' (1848), and his 

 'Remarks on the Mechanical Equivalent of Heat' (1851). 



So far from being a step in advance, the method suggested by 

 Mayer for the deduction of the mechanical equivalent of heat was 

 a retrograde step, and tended only to introduce confusion. 



Joule saw that experiment, not hypothesis, was required to 

 arrive at knowledge regarding the heat evolved by compression. 

 He thus arrived experimentally in 1844 or 1845 at the know- 

 ledge that when air is compressed the heat evolved is very nearly 

 the true equivalent of the work spent. In later investigations he 

 verified Thomson's deductions from Carnot's theory as to the 

 heat evolved by the compression of liquids (mercury and water), 

 and application of pressure or tension to solids. Thus while, as 

 a general principle, Mayer's hypothesis is essentially false and 

 misleading, and is signally at variance with the truth when ap- 

 plied to liquids, it is, as Joule's experiments have shown, approxi- 

 mately verified in air and gases. Having obtained this result, 

 Joule, finding no such agreement between Mayer's equivalent 

 and his own as might have been expected, was led to investigate 

 the specific heat of air ; and this important datum, without which 

 Mayer's method (even supposing it had been founded on correct 



