Sir B. C. Brodie on the Calculus of Chemical Operations, fyc. 229 



• 

 these factors in that, like the numerical symbol 1, they are inca- 

 pable of partition as well as of division, which is a consequence of 

 the condition xy=-x + y. ~ 



The symbol of the unit of a chemical substance, expressed as a 

 function of the simple weights of which it consists, is identical with 

 the symbol of a whole number expressed by means of its prime factors, 

 a n , &"*, c n 2. ... A general method is given for discovering the 

 prime factors of chemical symbols. 



Section VI. is on the construction of chemical equations from 

 experimental data. 



Section VII. On the expression of chemical symbols by means of 

 prime factors in the actual system of chemical equations. The object 

 of this section is to prove that the units of weight of chemical sub- 

 stances are integral compound weights, and to discover the simplest 

 expression for the symbols which, is consistent with this assump- 

 tion. 



Such an expression cannot he effected unless some one symbol 

 be determined from external considerations. The unit of hydrogen, 

 therefore, is assumed to consist of one simple weight, its symbol 

 being expressed by one prime factor, a, which is termed the modulus 

 of the symbolic system. This assertion is the expression of an hy- 

 pothesis which may be proved or disproved by facts, and the con- 

 sequences of which are here traced. 



The symbols of the elements are considered in three groups : — 

 1 . The symbols of the elements of which the density in the gaseous 

 condition can be experimentally determined, and which form with 

 one another gaseous combinations. 2. The symbols of carbon, 

 boron, and silicon. 3. The symbols of other elements, which are 

 determined with a certain probability by the aid of the law of 

 Dulong. 



For the method of constructing these symbols, which depends 

 upon the solution in whole numbers of certain simple indeterminate 

 equations, we must refer to the memoir itself. 



The following symbols (p. 230) may serve as an illustration of the 

 general results. 



Prime factors. 



Absolute weight 

 in grammes. 



Kelative weight. 



a 



0-089 



1 



I 



0-715 



8 



X 



1-542 



17-25 



V 



0-581 



6-5 







1-305 



15 



R 



0-536 



G 



