500 RICE 



ART. K 



if this is done and we write ro(ei2 + 621) for/e we obtain Gibbs' 

 result. But this amounts to putting en or 622 equal to unity in 

 one part of the complete formula for /e and equal to r^ in 

 another. We should obviously approximate from 66/(6162)* 

 and not from ea. 



If the writer is correct, then we should write equation [449] as 



R = To - — [449a] 



with of course an = 022 = 033 = ro and the remaining apg 

 coefficients put equal to zero; for we are considering the value of 

 R for the state of vanishing stress. This will change equa- 

 tions [455] and [457]. Thus 



and we have to differentiate this partially twice with respect to 

 an. The term multiplied by e will yield 2e. In the term which 

 is multiplied by /, four of the Ap^ minors involve an, viz., 

 ^33^ Azi"^, Ais^, ^2^^ so that this term yields 



aAsa . , 3^31 . , 9^23 . dA 



2/i^33 z~ + As, -^' + A,3 z-^ + A 



21 



5ai2 aai2 aai2 da 



12 



On passing to the limit when 023, 032, 031, ais, ai2, 021 are zero and 

 On = ^22 = 033 = To it will be easily seen that the only surviving 

 part of the derivations from this term is 2/A21 (9^21/9^12) which 

 becomes 2/a332 or 2/rol Hence [449a] becomes 



R = 2ero + 2/ro^ [455a] 



which replaces [455]. It will then appear that in place of [457] 

 we shall find 



J 6 -I ~ 2 > 



ro^ ro 



h = - i- - V. 



[457a] 



