SIE B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 849 



These equations in all cases admit of the minimum solution, 



m =2a:+l, n =1, 



wii=2ar+l, «i=0, 



and the above equation becomes 



the symbols being thus expressed : 



Prime factor. Weight in giro. Belative weight. 



§1. 4-783 53-5 



Symbol. 



Silver ug] 9-654 108 



Chloride of silver . (axfi)"*' (2ar+l)6-423 (2x + l)71-75 



(2) If X=2a;i, an even number, ^i=l, y2=^v ^3=^1' ^'^^ 



m =Xi(l+«), 

 mi=a^i(24-«i), 



which admit of the minimum solution, 



m =iri, n =0, 



7»2=^l? ^2 = 1. 



This hypothesis is, however, untenable for the following reason. 



According to the definition given of the weight A (Sec. VII. Group 2 (1)), the weight 

 A is the smallest weight of silver formed by the decomposition of the unit of any che- 

 mical substance. Hence, if y be the number of units of the substance decomposed, 

 and X the number of imits of silver in that equation in which the weight A appears, 



And putting gj as the symbol of sUver, 



and 



ty=:^x: 



but since W=2A,y=2ar, whence 2^=1, to which equation there is no integral solution. 

 This hypothesis is therefore to be rejected. 



If, however, in the above equation we select 2 as the value of »2» 



mj=2a:i, 

 W2=2a:i, 

 in which case 



(«x'f?)"=^.(«;tHe?); 



and we have 



and ty=.1x and f=l. 



