and Pyroelectric Properties of Matter. 7 



6. We conclude that the quantity of heat absorbed by the 

 body in being strained from one state to another at the same 

 temperature is quite independent of the particular succession of 

 states through which it is made to pass, provided it has through- 

 out the same temperature. Hence we must have 



H = >/r {x, y, z, f, v, £ — f Oo> yo,*oj So, Vo, &, 0> • ( 2 ) 



where yjr denotes a function of the variables. Now the me- 

 chanical value of the heat taken in by the body while it passes 

 from one condition to the other, together with the work spent 

 in compelling it to do so, constitutes the whole augmentation 

 of mechanical energy which it experiences ; so that if e denote 

 this augmentation — that is, if 



e = (f>(x, y, z, f, V , f, t)-(f>(x , Vo, ZQ, So) V , &, *), . (3) 



and if w denote the work done by the applied forces and J the 

 mechanical equivalent of the thermal unit, we have 



e=w> + JH (4) 



From this we conclude that the work required to strain the 

 body from one to another of two given mechanical states, 

 keeping it always at the same temperature, is independent of 

 the particular succession of mechanical states through which 

 it is made to pass, and is always the same when the initial and 

 final states are the same. This theorem was, I believe, first 

 given by Green (as a consequence of the most general con- 

 ceivable hypothesis that could be framed to explain the mutual 

 actions of the different parts of a body on which its elasticity 

 depends), who inferred from it that there cannot be 36, but only 

 21, independent coefficients [or "moduluses "] of elasticity, with 

 reference to axes chosen arbitrarily in any solid whatever. It 

 is now demonstrated as a particular consequence of the Second 

 General Thermodynamic Law. It might at first sight be re- 

 garded as simply a consequence of the general principle of 

 mechanical effect ; but this would be a mistake, fallen into 

 from forgetting that heat is in general evolved or absorbed 

 when a solid is strained in any way ; and the only absurdity 

 to which a denial of the proposition could lead would be the 

 possibility of a self-acting machine going on continually draw- 

 ing heat from a body surrounded by others at a higher tem- 

 perature, without the assistance of any at a lower temperature, 

 and performing an equivalent of mechanical work. 



7. The full expression of the Second Thermodynamic Law for 

 the circumstances of elastic force is, as is shown in the pas- 

 sage referred to above (Trans. Roy. Soc. Edinb. May 1, 1854, 

 p. 126), that if H t , W t , &c. denote the quantities of heat emitted 



