﻿756 Deduction of Ihermodynamical Relations. 



In illustration o£ the method Dr. Houstoun's problems 

 may here be solved. In the first we have : 



dU=Tds + Fdx + Ijd0, 



which may be written as follows : 



</(U-Ts— F#-L0) = -sdT-xdF-OdL; 



and therefore at once 



da _ d<9 

 BLtf BFtl* 



In the problem on magnetostriction the equation * is : 

 dJJ=Tds + Fdx + ^-dB, 



_7T 



which we write in the form 



dh -Ts-Fx- ^KB\ = -sdT- j>dF-~dR, 



which yields the " clastic " relation 



S.v . v -dB 



and two Maxwell relations 



and 



^Thf BFht 4tt ^Tfh BHft' 



The same problem was discussed by Heydweiller |, who 

 takes into account the change of volume, and uses the 

 equation 



dU = Tds + Fdx+ l ^dB+^-dv, 

 or as before, 



d (u_T._F.r- *-?-) = - _T-_fl!- f ffl ; 



\ _7T / 4?T 



so that 



Sx _ v 3B _B 3u 



^Htf _7tBFth -7t BFth' 



* I follow Dr. Houstoun's equation -without taking into account 

 Dr. K. Gans's criticism of the equation itself (Bebilatter, xxxv. p. 717, 

 1911). 



t Heydweiller, Ann. d. Phys. [4] xii. p. 602 (1903) : again I leave out 

 of account the criticism by Dr. Gans, /. c. xiii. p. 634, xiv. p. 638 (1904). 



