2 

 The necessary value of S may be found most easily by rearranging 



Equation [T5a] , giving the value of the determinant as follows: 



- 0.^ (m + m^) I k(l^ + h^m^ - U:^m^) - l[co^ (l^ + h^m^ ) - k] | 



+ w^h m \- i/lh m + BS^ [l + h^m - Lh m ] [ 

 oo' oo o oo oo' 



+ [h^m^ - L(m + m^)] \/k h^m^ - BS^ ["^(Iq + h^m^) - k]} = 



(Here the leading factors are the coefficients of v in the v, 6, 9 

 equations, the coefficients of v having been chosen because they contain 



the only imaginary term when c = 0.) 



2 

 Now the value of w given by Equation [l6] causes the first brace 



(i.e., the coefficient of -u (m + m )) to vanish. The second brace can 



o 



2 

 be made to vanish by assigning the proper value to BS . Then it is easily 



seen that the third brace also vanishes. For, the ratio of the first 



term in the third brace to the first term in the second brace, and the 



similar ratio of the second terms, are, respectively; 



2(1 + h2m ) - k 

 k '^ o o o 

 J and - 2 



I + h m - Lh m 



o o o o o 



But the vanishing of the first brace makes these fractions equal. Hence, 

 the third brace is proportional to the second, so that if the second is 

 made zero, the third brace also vanishes, and, consequently, the whole 



determinant is zero. 



2 

 The value of BS obtained in this way, when c = but c^^ + BS > 0, is: 



86 



