852 SIE B. C. BRODIE ON THE CALCULUS OF CHEMICAL OPEEATIONS. 



of hydrogen, 1 volume of chlorine, and 1 volume of nitrogen. Whence, putting u^'x"'*'* 

 as the symbol of the unit of sal ammoniac, 



and 



2m =3, 



2mi=l, 



2m2=l, 

 and the symbol of sal-ammoniac is (u^xi/f, and cannot be expreseed by an integral number 

 of the prime factors «, x> "• 



We may now inquire whether, seeing this expression of the symbol of chloride of 

 ammonium to be impossible on the assumption that the symbols of the elements hydrogen, 

 chlorine, and nitrogen are of the forms a, «%'', uv^, it be possible on any other hypothesis 

 as to these symbols, consistent with knovra facts. Now every possible hypothesis as 

 to these symbols consistent with their expression by an integral number of prime 

 factors in the equations from which the symbols have been derived, and with the expres- 

 sion of the symbol of hydrogen by one prime factor, a, is, as has been shown (Sec. VII. 

 (5) and (8)), implicitly contained in the general forms of the symbols of chlorine and 

 nitrogen, which are respectively u^-^^p-^^^+p^^ and a'+'^i'*^'*'''; whence, putting 



2m=3+p+q, 

 2mi=l+^i, 



2»l2 = l+?i, 



and 



m =2, J) +q=:l, 



mi = l, jpi =1, 



m2=l, ji =1, 



a minimum. 



On the hypothesis, ^ = 0, j^l, we have 



Symbol of chlorine «%*, 

 Symbol of nitrogen aV. 



On the hypothesis, j)=l, g'=0, we have 



Symbol of chlorine a'x*> 

 Symbol of nitrogen uv*. 



Neither hypothesis is absolutely inconsistent with any known fact, for it is possible 

 thus to express the symbols of chlorine and nitrogen in every equation into which those 

 symbols enter ; and if it were placed beyond doubt that the true density of chloride of 

 ammonium in the gaseous condition were 12*88, we might thus accept the fact and 

 assert that the factors x 8Jid v were composite, so that either x^')C*i ^^^ y=a^ii'„ or 

 Xi^^^^Xa ^^d v=vl, and our view of the possible system of chemical substances, and of 

 tne laws of combination to which they were subject, would be profoimdly modified. I 



