STRAINED ELASTIC SOLIDS 503 



we regard €r' as a function of riv, an, an, . . . ass, Va, Tb , . . . 

 and the result just written embodies the equations 



dev' dev' dtv' 



^y. = ^' a"^ = ^^'' "^"•' ^ = ^^ '*'• 



leading to [471] and other similar results. Also regarding 

 \j/v'( = ev' — t-qv') as a function of t, an, a^, . . . flss, T/, Tb, etc., 

 we can write 



d\pv' = d{ev' — triv) 



= -riY'dt + S2Zx'£/aii + 2/iaC?r„', 



and this is equivalent to the equations 



dypv' dypv' d\pv' 



~^ = - ^'"' a"^ = ^^'' '^'•' ^ = ^- '^'•' 



which yield 



dr]v' dXx' 



dan dt 



and similar results. 



Also from either of these we obtain by repeated differentiation 



dXx' d^ey djXq 



dVa' ~ dVj dan ~ dan 



and so on, where Xx', etc. and Ha, etc. are regarded as func- 

 tions of r]v' (or 0, an, an, . . . ass, Ta, Tb, etc. 



We can also introduce a function 0r' of t, an, an, . . . ass, 

 Mo, fib, etc. defined by 



<j>V' = €v' — trjv — HaTa' — jJ^bTb — etC, 



whose differential satisfies the equation 



d<f)v' = —rjv'dt + ZiXXx'dan — ^Tadna. 

 This will lead to the second group of [472]. 



