430 Sir B. C. Brodie on the Calculus 



Effecting this substitution not in one but in two combined 

 units of hydrogen, we have :— 



Symbol of two combined units of hydrogen a 2 (1, 1, 1, 1), 



Symbol of the unit of ammonia , a 2 (v, 1, 1, 1). 



It hence appears that we can effect in the unit of ammonia 

 three substitutions of % (or of any value of %) for 1, but no 

 more. Now uk is the symbol of such a value of %, a fact as- 

 certained by repeated experiments ; and the symbols of these 

 three derivatives are : — 



u 2 v(uk, 1,1), 

 u 2 v(uk, uk, 1 ), 

 u 2 v{uk, uk, ate) ; 

 hence the equation 



3u 2 K(D + 0?V = 3«G) + ol 5 k 3 v 



expresses not only a result, but the final result of the action 

 of iodide of methyl on ammonia. 



In the case of the chloride of ammonium, « 3 %v, putting 



• a? (1,1, 1,1, 1,1) 



as the symbol of three combined units of hydrogen, we have, 

 effecting the substitution of % for 1 and of v for 1, 



aV=a 3 (%, v, 1, 1,1,1), 



in which four substitutions, and no more, of uk for 1 may be 

 effected; whence we have 



a 3 (%, v, arc, uk, arc, uk) 



as the symbol of the unit of the chloride of tetra-methyl-am- 

 monium. 



From the point of view of general algebra, «1 2 = «, aVl 3 = «V, 

 u 2 k1* = u 2 k, a 3/ xyl i = u 3 'xy; we are therefore at liberty either 

 to suppress the symbol 1 or to exhibit it according to our 

 convenience. We may compare the symbol u 2 v (1, 1, 1) to 

 an open fan, u 2 v to the same fan folded up. I have said 

 enough to clear up the difficulty of M. Naquet; and this is 

 not the place to further pursue the subject. 



With reference to the problem of the expression of u Iso- 

 mers " on the principles of the Calculus, I will venture to ask 

 M. Naquet and others to suspend their judgment for a time*. 



It is a significant fact that a very large proportion of" the 

 class of elements which I have termed composite elements have 

 not been found in the sun. In reply to inquiries on my part, 

 Mr. W. Huggins writes to me thus : — 



* The following passage and also the footnotes have "been added since 

 the publication in the Moniteur Scientifique. 



