228 Royal Society .— 



weights," " identical weights/' "a compound weight," "a simple 

 weight," and "an integral compound weight." 



The unit of a chemical substance is denned as that weight of the 

 substance which at 0° Centigrade and 760 millims. pressure, and in 

 the condition of a perfect gas, occupies the volume of 1000 cubic 

 centimetres. This volume is termed the unit of space. 



Section II. The second section treats of symbolic expression in che- 

 mistry. A " chemical operation " is defined as an operation of which 

 the result is a weight. These operations are symbolized by letters, 

 x, y, &c. An interpretation is assigned to the symbols + and — as 

 the symbols of aggregation and segregation — that is, of the mental ope- 

 rations by which groups are formed. The symbol = is selected as the 

 symbol of chemical identity ; the symbol as the symbol of the 

 absence of a weight, this symbol being identical with x—x. The 

 symbol (x-\-x) is the symbol of two weights collectively considered 

 and as constituting a whole. 



The svmbols xy and - are selected as the symbols of compound 



y 



weights ; and it is proved that with this interpretation these symbols 

 are subject to the commutative and distributive laws 



xy—yx t 



^(y+yi)=^3/+' y yi» 



and also to the index law 



xPx q =x p+ *. 



Section III. treats of the properties and interpretation of the che- 

 mical symbol 1, which is selected as the symbol of the subject of che- 

 mical operations, namely, the unit of space. With this interpreta- 

 tion the chemical symbol 1 has the property of the numerical symbol 

 1 given in the equation xl=x. 



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

 special symbolic law, given in the equation 



xy—x+y. 



This property, by which chemical symbols are distinguished from 

 the symbols employed in other symbolic methods, is termed the " lo- 

 garithmic" property of these symbols. A consequence of this pro- 

 perty 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 



