6 SirW. Thomson on the Thermoelastic, Thermomagneticj 



in any way, is shown to lead to the most general possible 

 theory of elasticity, whether of solids or fluids, and to point 

 out various thermodynamic properties of solids and various 

 thermal effects of magnetism [and of electricity] not hitherto 

 discovered. 



Section I. — Elasticity of Solids or Fluids not subjected to 

 Magnetic Force. 



4. Let x, y, z, f , r], £ be six independent variables expressing 

 the mechanical condition of a homogeneous solid mass, ho- 

 mogeneously strained in any way *, and let t be its tempe- 

 rature ; and (in accordance with the preceding explanations) 

 let e denote its intrinsic energy, reckoned from a certain 

 " standard state " defined by particular values, x , y , z , 

 f , 770, J , t 0y on which its physical condition depends. Thus, if 

 (f> denotes a certain function depending on the nature of the 

 substance, and vanishing for the values x , yo,... t of the inde- 

 pendent variables, we have 



e = cj>(x,y,z, %,r),£,t); . . . . (1) 

 and a knowledge of the function (p [with besides a knowledge 

 of w for one particular temperature f] comprehends all the 

 thermoelastic qualities of the solid. 



5. Now let us suppose the body to be strained so as to pass 

 from the mechanical state (x , y , z 0y % 0j rj 0j J ) to (x, y~ z, £, rj, J) 

 while it is constantly kept at the temperature t ; and let H de- 

 note the quantity of heat that must be supplied to it during 

 this process to prevent its temperature from being lowered (a 

 quantity which of course is zero;' or negative, for such strains 

 as cause no thermal effects, or which cause positive evolutions 

 of heat). Let the body be brought back to its mechanical con- 

 dition (x , y , z , f j Voj Jo) through the same or any other of 

 all the infinitely varied successions of states by which it may 

 be made to pass from one to the other of the two which have 

 been named, its temperature being kept always at t. Then, 

 by the second Fundamental Law of the Dynamical Theory of 

 Heat (see Trans. Eoy. Soc. Edinb. May 1, 1854, p. 126), we 

 must have tt tt/ 



+ — =0, 



and therefore H / = — H . 



* The terms a strain, or to strain, are used simply with reference to 

 alterations of dimensions or form in a solid — the forces by which " a 

 strain" is produced being called the straining tensions or pressures, or 

 sometimes merely the tensions or pressures, to which the solid is subjected. 

 This distinction of terms is adopted in accordance with the expressions 

 used by Mr. Rankine in his paper on the Elasticity of Solids (Cambridge 

 and Dublin Mathematical Journal, February 1851). 



t [See equations (10), (11) of § 7 below.] 



