THERMODYNAMIC THEORY. 225 



properties of matter here in question. Their indication seems to point dis- 

 tinctly to the possibility of accumulation of truly elastic strains over periods 

 of time much greater than those involved in the oscillatory movements 

 commonly pointed to as witness to the existence of true elasticity. A 

 reasonably complete theory would doubtless have to include the simul- 

 taneous contemplation of both elasticity and viscous plasticity, of volume 

 and of shape, so as to complicate the theoretical deductions enormously. 



To allow comparison it may, then, be of use for the present purpose to 

 inquire what modifications are needed to give the previous theory the 

 added definiteness which may come from a complete definition of the ther- 

 modynamic substance, but on the supposition that this possesses the oppo- 

 site extreme property, of perfect elasticity of volume under all conditions. 

 There remains, of course, the same possibility as before of variety in the 

 secondary features; the following developments give in some detail a 

 single form as illustration, one which has the advantage of relative sim- 

 plicity in the analysis. 



Let e now represent the total intrinsic energy per unit-mass; then a per- 

 fect fluid in the thermodynamic sense, or a substance which can do work 

 only through hydrostatic pressure, and has perfect volume-elasticity in the 

 sense described, finds its complete description conveniently in the analytic 



form of p and e as functions of 6 and v = —. The condition of conservation 

 of energy as embodied in the first law 



iQj^de + {j> + f^4v (134) 



gives the following determinations of auxiliary quantities 



dp 



a=-yr o' =a—[p + -z—)-z: — «=— (135) 



dd V dvj dp a ^ ^ 



dv 

 where o, a' are the specific heats, at constant volume and at constant pres- 

 sure; also 3p 



K = -v^ H=kK a=-^ (136) 



dv K 



where K, H, are the isothermal and isentropic bulk-moduli and a the co- 

 efficient of volume-expansion. The existence of a definite entropy-function 

 £ imposes the condition of integrability 



1 ae d 



in which case 



= A/'P^ (137) 



e^dv dd\d ) 



%-j 1-%-^^ (i^«> 



so that the condition of integrability is equivalent to 



1 da ^ d(Ka) (139) 



e dv dd 



