10 Sir W. Thomson on the Thermoelastic, Thermomagnetic, 



an expression which shows how the " intrinsic energy " of the 

 body may be determined from observations giving w as a 

 function of the seven independent variables, and N as a func- 

 tion of the temperature, for a particular set of values of the 

 geometrical elements. Conversely, by (5) we have 



H =jjl-*; < 10 ) 



and by (6) and (7), or simply by (4), 



w = 6 -JHf (11) 



which show how H and w may be determined for all tempera- 

 tures from a knowledge of the intrinsic energy of the body, 

 and of [one of] those functions themselves for a particular tem- 

 perature. 



8. Let K denote the specific heat of the body at any tempe- 

 rature t, when it is allowed or compelled to vary in form and 

 dimensions with the temperature, according to any fixed law — 

 that is, when each of the variables x, y, z, f , rj, f is a given 

 function of t ; and let N denote what this becomes in the par- 

 ticular case of each of these elements being maintained at a 

 constant value ; or, which is the same, let N" be the specific 

 heat of the body at any temperature when maintained at con- 

 stant dimensions (x, y, z, % , ?;, £). We have 



JN =S> ( i2 > 



_ de cZ(JH ) dx rf(JH) dy rf(JH) dz 

 ~ dt dx dt dy dt dz dt 



d(JH)rfg d(m)dy d(JR)dZ 

 + d% dt* di) dt* d£ dt' ' ^ 6) 



Since JH is equal to e—w, this expression may be modified 

 as follows : — If D denote the total differential of e, 

 „ _ De /div dx dw dy div dz 

 dt \dx dt dy dt dz dt 



dw d% dw dt) dw d£\ /1 „ . . 



+ df di + dv di + d? It)' ■ • ( 1Shs > 



9. These equations may be applied to any kind of matter ; and 

 they express all the information that can be derived, from the 

 general thermodynamic principles, regarding the relations be- 

 tween thermal and mechanical effects produced by condensa- 

 tions, rarefactions, or distortions of any kind. For the case of 

 a fluid they become reduced at once to the forms investigated 

 specially for fluids in my previous communications. Thus, if 

 the mass considered be one pound of any kind of fluid, we may 



