Functions given by Groups. 325 



taining both 0i and 0^, so that 0iG/= QJ^f-, is under S, the 

 ;Same column of L products. 

 If 



were two values of G/, obtained from two different derivates 

 of G/, the function G/ having two values alike would have 

 fewer than Q values, which is contrary to our hypothesis in 

 article 8. 



We deposit a second d in the line G/, and are prepared 

 for the necessity of writing a third d if it arises. 



After hearing the /— m charges of G^, we find the number 

 t' of different groups, marked out by them, to be less than 

 t—7n. We then release G^^ with thanks from the post of 

 standard. 



What the exact number t' is, it would be a question no 

 less absurd to reply to in general symbols than to ask. We 

 are handling perfectly general terms, where n and 2 are 

 anything you please, so that their meaning remains the 

 same during our discussion of table (AJ of definite equiva- 

 lents. The author of the two pages proved himself to be 

 Something of a dunce, in forsaking the path of symmetric 

 analysis, in order to turn his clear t—ni into something 

 clearer. The talkee about t' and tx does neither good nor 

 harm, and the 'we conclude' (article 59) is nothing more 

 than the wise decision, that, p and t' being neither of them 

 either given or found, 



P _ P 



We can predict, with assurance, that when our work is 

 done on our table (AJ, every /' for every standard under 

 every S will be exactly recorded in it, and numerically 

 given when Gi, G2, &c., are actual groups, and not mere 

 symbols. 



12. Our next step is to select from the unmarked 

 equivalents in (A„) any group Gaa that has, in common with 



