290 Proceedings of the Royal Irish Academy. 



with the understood condition (c) 



w'^r' > 1. 

 If »ii = - 7, we find 



r' = 1-4183, o>'2 - 0-65623, w'V = 0-93078. 



This solution must be rejected, for w'-r' is less than unity. 

 If mi = - 8, we find 



r' = 1-1768, 0)'- = 0-88959, wV = 1-04690. 

 This solution satisfies the conditions of the problem. 



Hydrochloric Acid. — Here we have ^ = 35-5, and eq[uations {a) 

 and (5) become 



„ _ 35-5 (»ii+ 35-5)2 

 *" ' ~ 36^ ^ ~rn^T^b^ ' 



?»i-+35-5 



»?i (???!+ 35-5) 

 If jWi = - 16, we find 



/ = 1-1263, w'2 = 0-87290, ia'-r' = 0-98322. 



This solution must be rejected, for ao'-r' is less than unity. 

 If nil - - 17, we find 



r' = 1-0128, w'2 = 1-0646, w'^/ = 1-0782. 



This solution satisfies the conditions of the problem. 



Hydrolromic Acid. — Here we have /3 = 80, and equations {a) and 



(h) become 



80 (wi + 80)2 



r'- ^ -— X 



1 m^^ + 80 ' 



»h- +80 

 ?»i('Wi + 80) 

 If OTi = - 38, we find 



r' = 1-06920, (o'- = 0-91180, w'-r' = 0-97490. 



This solution must be rejected, for w'-r' is less than unity 



