4 ' Prof. Clausius on the Determination of the 



But before I proceed to do this, I wish to make a few remarks 

 on a passage in Bauschinger's paper. 



At page 114 of the paper, the following equation, likewise 

 relating to the second fundamental theorem of the mechanical 

 theory of heat, is discussed : 



dQ A / . .s dp 



Here -j- is the differential coefficient which has already been 



once mentioned above, p denotes the pressure to which the body 

 is exposed, t the temperature of the body reckoned from the 

 freezing-point, and a the reciprocal of the coefficient of expan- 

 sion of gases (that is, approximately the number 273), so that 

 a-\-t is the same quantity that has been previously denoted by T y 

 lastly, A denotes the thermal equivalent of the unit of work. 

 This equation is referred to by Bauschinger as " the equation 

 already established in another form by Carnot." 



These words might easily lead to a misconception. The equa- 

 tion which occurs in the older expositions of Carnot's theory, 

 but which, strictly speaking, is not due to Carnot, having been 

 first deduced by Clapeyron from Carnot's theorem, when put 

 into a form the most closely resembling the above that it is ca- 

 pable of assuming, runs thus, 



dQ,_„dp 

 dv dt 



where C denotes an undefined function of the temperature, which 

 has often been called Carnot's function. If now this function, 

 previously left undefined, is replaced in this equation by the de- 

 finite function A(a + t), there is certainly something more than 

 what we are accustomed to understand by a mere change of form. 

 I now pass on to the developments above announced. 



§i. 



We will in this development again take as our starting-point 

 the two fundamental equations already mentioned, by means of 

 which I have expressed the two fundamental theorems in my 

 paper " On a Modified Form of the Second Fundamental Theo- 

 rem of the Mechanical Theory of Heat." 



The first fundamental equation, when taken as relating to an 

 infinitely small change of condition in any body chosen for con- 

 sideration, is 



dQ = dV + AdW (I) 



Here, as before, A denotes the thermal equivalent of work (that 

 s to say, the heat-equivalent of the unit of work), and dQ, the 



