Quantities occurring in the Mechanical Theory of Heat. 255 



yet duly elucidated second proposition of the mechanical theory 

 of heat. Accordingly a rigorous, indisputable proof, a purely 

 dynamical demonstration of the Second Proposition is of pre- 

 eminent interest, not merely for the theory of heat, but also 

 for every department of physics. 



Of late years it has already been repeatedly attempted to 

 deduce the Second Proposition without the aid of thermic 

 axioms or hypotheses, merely resting it upon mechanical prin- 

 ciples or at least purely mechanical assumptions. In the year 

 1866, Boltzmann showed that, for a system of material points, 

 one can, on certain special hypotheses, construct a dynamic 

 proposition which in form and meaning appears to be identical 

 with the second proposition of the mechanical theory of heat. 

 In 1871, Clausius somewhat extended and generalized the pro- 

 position. In the same year the author of this submitted to 

 the Hungarian Academy a memoir in which he called atten- 

 tion to the fact that the dynamic proposition of Boltzmann 

 and Clausius, at least in form, agrees with Hamilton's prin- 

 ciple, whence he inferred that the Second Proposition plays 

 the same part in thermodynamics that Hamilton's principle 

 does in dynamics. 



All these dynamic deductions, however, although free from 

 thermic hypotheses, were not free from mechanical assump- 

 tions ; and on this account they were inadequate to excite 

 absolute confidence in the universal validity of the proposition 

 in question. This circumstance determined me to investigate 

 the question afresh (in a memoir submitted to the Hungarian 

 Academy of Sciences, May 10, 1875*), and, resting on an 

 almost prophetic utterance of Eankine's, endeavour to deduce 

 the Second Proposition directly from the principle of the 

 conservation of energy without making any further mechanical 

 assumption. 



I must confess that in this attempt I at that time encoun- 

 tered very great difficulties : the thoughts move rather heavily ; 

 and the deduction rests on perhaps a not quite indisputable 

 basis f. Since then I have been continually pursued by the 

 thought whether the deduction could not be effected more 

 naturally, simply, and secure against every objection. I 

 finally came to the conviction that the chief difficulty consists 

 in this — that the mechanical conceptions which have been formed 



* Phil. Mag. [V.] vol. i. p. 22 ; Pogg. Ann. Ergaimmgsband vii. p. 154. 



t Thus, for example, in the May Number of the Philosophical 

 Magazine the remark of Mr. Nichols, that in the memoir in question no 

 solid reason was given why the differential of the quantity of heat com- 

 municated is to be regarded as a mean value of energy-differentials, is 

 perfectly just. 



