141 



without any cuiiJucliuii ot lieiil, is iuvestigalcd. If ( be the initial 

 teniperatuiu (estiniateii accortling to any arbitrary system) at any 

 point xy z of the soHd, T the final uniform temperature, and c the 

 thermal capacity of unity of volume of the solid, the required mecha- 

 nical effect is of course equal to 



'Iff' "-^' 



dx dy dz. 



being simply the mechanical equivalent of the amount of heat put 

 out of existence. Hence the problem becomes reduced to that of 

 the determination of T. The following solution is obtained, — 



,^ JJj^ ^4' '^^''^tdxdydz 

 JJJ € .r/'*'*' cdxdydz. 



- If the system of thermometry adopted* be such that /<* = » 



that is, if we agree to call - — a the temperature of a body, for which 

 /* 



//, is the value of Carnot's function, (a and J being constants.) the 

 preceding expression becomes 



JJjTVi 



c dx dy dz 



dx dy dz 



t + a ^ 



The following general conclusions are drawn from the propositions 

 stated above, and known facts with reference to the mechanics of 

 animal and vegetable bodies : — 



1. There is at present in the material world a universal tendency 

 to the dissipation of mechanical energy. 



2. Any restoration of mechanical energy, without more than an 

 equivalent of dissipation, is impossible in inanimate material pro- 

 cesses, and is probably never effected by means of organised matter, 



* According to " Mayer's hypothesis,'' this system coincides with that in 

 which equal differences of temperature are defined as those with which the same 

 mass of air under constant pressure has equal differences of volume, provided 

 .1 be the mechanical equivalent of the thermal unit and - the coefficient of 

 expansion of air.— See the author's previous paper " On the Heat produced by 

 the Compression of a tias," &c., ^ 5. 



