830 Sm B. C. BEODIE ON THE CALCULUS OF CHEMICAL OPERATIONS, 



the most varied character, and consequently a very high degree of probability is 

 attached to it. For we cannot but believe that if any chemical substance could exist, 

 in the symbol of which the index of x. should not be of the form mx, among the great 

 variety of known substances some one such substance would have been discovered, 

 and that the reason why the weight »" is never distributed in the chemical changes with 

 which we are acquainted is that this weight is a simple weight, and that x=l. 



It is to be observed that the weight to be given to an argument of this kind may 

 become veiy small, if the observations on which it is founded are few, and made exclu- 

 sively on one class of substances. Thus, for example, if the course of chemical inquiry 

 had been such as to make us acquainted only v(dth the following substances : olefiant gas, 

 methyl, ethyl, butylene, oxide of ethylene, glycol, alcohol, ether, acetic acid, and other 

 substances of which the symbols can be expressed by the factor k', and of which the 

 symbols are aV, «"«?, a'«f , a'«f , «'«% a'«!f , aXI, a'«f $, a'xT, a'«f f , and the like, 

 where z^2x, we should, by similar reasoning, have concluded that the symbols of the 

 compounds of carbon could be expressed by the prime factor x,, of which the absolute 

 weight w(«i)=:12, and that x, was the symbol of a simple weight, a result which would 

 not have been justified by a more extended experience. 



We are able to bring to bear upon the symbol of carbon certain arguments of a very 

 general application, and which are derived from direct experiment. If we compare the 

 chemical equations into which enter the symbols of the units of volume of those elements 

 of which the density can be experimentally determined, it will be perceived that, putting 

 A as the smallest weight of the element which is in any case formed in the decomposition 

 of the unit of any chemical substance, and V as the density of the element, either A =V, 



as in the case of mercury, or A=— , as in the case of hydrogen, chlorine, iodine, bromine, 

 nitrogen, oxygen, sulphur, selenium, or A=-, as in the case of phosphorus and arsenic. 



The truth of the above observation will be seen on inspecting the follovring equations, 

 which have already been interpreted. 



I. A=V. Mercury : — 



II. A= . Hydrogen, chlorine, iodine, bromine, nitrogen, oxygen, sulphur, selenium: — 



2au=u -\-u<i)^, 

 2a|3 = a -\-ot,(i^, 

 2a|=2a+f2, 



2afl =2a+92, 

 2uX =2a+X2, 

 2a2»i=3a+aA 



