of Chemical Operations. 429 



Now taking the equation 



we have similarly 



;«(%-iy%-i)=p, 



an event in which a is constant, and which occurs in two ways 

 by the substitution of lfor% — thatis, by the operation (^—1). 

 Reasoning as before, we have : — 



Symbol of the unit of chlorine a XXi 



„ „ hydrochloric acid . . a^l, 



„ „ hydrogen all. 



Now the symbol 1 which appears in the symbols of hydro- 

 chloric acid and of hydrogen is not the symbol of any real 

 weight, but is the symbol of an empty unit of space serving to 

 mark the place where matter is not, but has been, and may be 

 again. The explicit introduction of this symbol into the 

 symbol of the unit of hydrogen limits the number of the ope- 

 rations x ( or of an 7 operation which may be substituted for %) 

 which may be performed upon a, the unit of hydrogen, to 

 two. Thus the operations co or ft (which may be substituted 

 for ^) may be performed once and twice upon the unit of 

 hydrogen, but no more. Hence we have : — 



Symbol of the unit of hydrogen all, 



„ „ hydriodic acid acol, 



„ „ iodine acoco ; 



but we have no means of making aw 3 . 



Now in the symbol a 2 /c, the symbol of the two combined 

 units of hydrogen, which (regarded purely as the symbol of 

 the weight of the combined hydrogen) is a 2 , becomes, by the 

 explicit introduction of the symbol 1, a 2 (1, 1, 1, 1), and the 

 symbol of marsh-gas is u 2 k (1, 1, 1, 1). In this case four 

 successive substitutions of ^ for 1 are possible, by which the 

 following units are constructed : — 



" 2 «(X> X ; !> !)> 



a K (X> XiXi 1 ) 

 v%? Xi Xi X)") 



a 2 k 



which are the symbols of the four chlorine derivatives of 

 marsh-gas. But we have no means of constructing the unit 

 a 2 tcx 5 . (Part II. Section III. (12).) 



Again, the unit of nitrogen uv 2 is derived from the unit of 

 hydrogen by the substitution of v for 1 in that unit; and we 

 have : «(!>!) hydrogen, 



a(v, 1) (unknown), 

 a(r, v) nitrogen. 

 Phil Mag. S. 5. Vol. 7. No. 45. June 1879. 2 K 



