1866.] 



Chemical Operations, S^c, 



137 



as the symbol of the absence of a weight, this symbol being identical 

 with x—x. The symbol (.r + a?) is the symbol of two weights collectively 

 considered, and as constituting a whole. 



The symbols xi/ and - are selected as the symbols of compound weights, 



and it is proved that with this interpretation these symbols are subject to 

 the commutative and distributive laws, 



and also to the index law. 



Section III. treats of the properties and interpretation of the chemical 

 symbol 1, which is selected as the symbol of the subject of chemical opera- 

 tions, namely, the unit of space. With this interpretation the chemical 

 symbol 1 has the property of the numerical symbol 1 given in the equa- 

 tion x\=x. 



Section IV. Chemical symbols are here shown to be subject to a special 

 symbolic law, given in the equation 



xy—cc-{-y. 



This property, by which chemical symbols are distinguished from the 

 symbols employed in other symbolic methods, is termed the " logarithmic'* 

 property of these symbols. A consequence of this property is that 0=1, 

 and that any number of numerical symbols may be added to a chemical 

 function without affecting its interpretation as regards weight. 



Section V. relates to the special properties of the symbols of simple 

 weights, which are termed prime factors, from their analogy to the prime 

 factors of numbers. These symbols differ, however, from these factors in 

 that, like the numerical symbol 1, they are incapable 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 factor, 5"^, c^'a. . . . A 

 general method is given for discovering the prime factors of chemical 

 symbols. 



Section YI. is on the construction of chemical equations from experi- 

 mental data. 



Section YII. 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 substances are 

 integral compound weights, and to discover the simplest expression for the 

 symbols which is consistent with this assumption. 



Such an expression cannot be effected unless some one symbol be de- 

 termined 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. 



