52 Sir B. Brodie on the relative [Jan. 24, 



elusion that chemical events occnr by the transference to and fro 

 among the nnits of matter and space of certain portions of matter 

 w (a) . iv (x) , w (£) . . . , there termed simple weights, which are 

 the results of the performance of the operations a,x,f • . . ; the 

 same unit therefore may be constructed in varions ways corresponding 

 to the differences in order in which these simple weights are trans- 

 ferred so as to build up the same unit of matter. Some explanation 

 is necessary on this point. 



There is nothing in the laws of combination (and these alone we 

 are now considering) from which we can infer the performance of any 

 one of these operations taken singly to be essentially easier or more 

 difficult than the performance of any other ; that is to say, the facility 

 of constructing the unit a is the same as that of constructing the 

 unit gf ; but when we consider combinations of more than one operation 

 the case is different. The combinations of the operations a and £ taken 

 two and two together are a 2 , a£, and £ 8 ; the combination a 2 is unknown, 

 «f is the unit of water, and £ 2 the unit of oxygen. ISTow, there is only 

 one way in which the unit |f 2 can be produced, namely by the suc- 

 cessive performance of two operations £. Similiarly, there is only 

 one way in which a 2 may be produced. But there are two ways in 

 which the unit may be produced, namely by first performing the 

 operation £ on the unit of space and then the operation a, in which 

 case the unit a% is the result ; and also by first performing the opera- 

 tion a and then the operation which results in the combination £a. 

 These two results (so far as our present purpose is concerned) are 

 identical, as follows from the commutative law ag — ga demonstrated 

 in Part I.* We hence say that the " facility of production " of the 

 unit ag is twice that of the respective units a 2 and £ 2 . The ternary 

 combinations of a and gf are a 3 , a 2 £ , a£ 2 , and £ 3 ; a 3 and a 2 ^ are unknown, 

 a£ 2 is the unit of binoxide of hydrogen, and £ 3 is the unit of ozone. On 

 these principles the respective "facility of production" of these units 

 is — 



a 3 ... 1 

 a 9 £ ... 3 

 at ... 3 



Again, the ternary combinations of the operations a and v are a 3 , 

 unknown ; a z u, the unit of ammonia ; av 2 , the unit of nitrogen ; v s , un- 

 known. The respective "facilities of production " of these units are — 



a 3 ... 1 

 aV ... 3 

 a v 2 ... 3 



v s . . . 1. 



* " Phil. Trans..," part ii, 1876, p. 796. 



