52 Messrs. J. A. Wanklyn and R. R. P. Davey on 



Although the usual arithmetical meaning may be given to the 

 signs, such as + and — , still on inspecting the following equa- 

 tions it will be seen that a new interpretation must be given of 

 the combination of symbols. 



xy = x-\-y (where xy means x "jointly" with y), 



x 



- = t r— y. 



y J 



This introduction of a second signification imparts great appa- 

 rent profundity, if not confusion, in the mathematical portion 

 of the calculus. Thus, because " the symbol 1, regarded as a 

 numerical symbol, possesses the property given in the equation 



xl=x " (i. e. xl meaning x multiplied by 1), 



" symbol 1 is selected as the chemical symbol of no weight re- 

 garded as a component of a compound weight." The author, 

 however, is not satisfied with the above proof that 1 shall equal 

 ; and fearful that his readers should mistake an inference for 

 an assumption, he adds, " If, in the equation xy=x + y, y=l 9 

 #l = #-j-l ; whence since x = xl and x— x = 0, we infer that 



0=1." 



In fact if 1 is assumed to equal 0, we can obtain such equa- 

 tions as the above (xl=x-\-l), from which the necessary infer- 

 ence shall not differ greatly from the original assumption. This 

 may serve as^a sufficient illustration of the algebra of the ' Che- 

 mical Calculus/ 



On page 795 we are startled by the following statement : — 

 " No uniform meaning has hitherto been attached to the sym- 

 bols + and — in chemistry, notwithstanding their constant use. 

 The prevalent opinion seems to be in favour of the use of the 



symbol + as the symbol of mechanical mixture A similar 



uncertainty prevails in the use of the symbol of identity. The 

 symbol = is sometimes employed in chemistry as the symbol of 

 numerical equality, at other times as the symbol of chemical 

 transmutation." 



These extracts afford a not unfair sample of the kind of rea- 

 soning to be met with in this paper. We reply to them (although 

 at the risk of being considered tedious), that although the one 

 side of an equation may be the other side which has undergone 

 transmutation, yet it is not the = which expresses the trans- 

 mutation, but the different arrangement of the symbols ex- 

 presses the transmutation. And similarly the +, although it is 

 often written between things in mechanical mixture, does not 

 express such mixture, but is always used by chemists in its 

 strictly algebraical sense. 



