THE ENTROPY INTEGRAL 223 



was found bearing on this controversy. It is valuable as showing that 

 Tait's views were fully endorsed by his friend. The letter begins abruptly 

 with a quotation from Thomson's 1852 paper "On a Universal Tendency 

 in Nature to the Dissipation of Mechanical Energy " (Proc. R. S. E. in ; 

 also Phil. Mag. iv, Oct. 1852 ; Math, and Phys. Papers, Vol. i, No. LIX). 

 To make the quotation quite intelligible, a preliminary sentence seems to 

 be necessary (see Math, and Phys. Papers, Vol. I, p. 512). 



"'Let S denote the temperature of the steam...; T the temperature of the 

 condenser; /* the value of Carnot's function, for any temperature t; and R the value of 



The letter begins with the integral, and then continues the quotation : 



" ' Then ( I R)w expresses the greatest amount of mechanical effect that can be 

 economised in the circumstances from a quantity wjj of heat produced by the expendi- 

 ture of a quantity w of work in friction, whether of the steam in the pipes and entrance 

 ports, or of any solids or fluids in motion in any part of the engine ; and the remainder, 

 Rw, is absolutely and irrecoverably wasted, unless some use is made of the heat dis- 

 charged from the condenser." The whole thing is included in this illustration and the 

 preceding ' universal ' generalisation of it, of which this is a particular illustration. 

 I don't believe Clausius yet to this day understands as much of the fact of dissipation 

 of energy as is stated in that first paper in which the theory is propounded and the 

 name given, and it does not appear that he has ever made any acknowledgment what- 

 ever of T in the matter. This must be because he does not understand it ; not because 

 he would consciously appropriate what is not his own. 



" As for the very letters of the formula, T in the same article says, ' If the system of 

 thermometry adopted be such that 



M= t+a' 



Accepting Clausius' statement that 'neither the expression (4>/-rJ nor anything of 



like meaning can be found in the article referred to by T',' the only conclusion is 

 that he is ignorant of the fact that 



' dt T+ a 



and so had his eyes closed to the fact that RwjJ means the same as 



or t,-j according to the notation of T'. 



