82 PROCEEDINGS OF THE CANADIAN INSTITUTE. 



that a formula leaves much to be understood or to be discovered 

 about the units involved. Besides, it is difficult to an elementary 

 arithmetician to understand it so well as to be able to use it with 

 intelligence. 



These defects appear to me to be due to the want of a systematic 

 notation for units. By a notation for a unit 1 mean something 

 different from a name; the latter merely designates, the former shows 

 the dependence of the unit upon more fundamental units. The 

 chemical notation for a substance expresses the manner in which the 

 substance is made up of the elementary substances ; while its name, 

 however derived, serves merely as a distinguishing mark. And just 

 as the chemical notation for a substance may be used as a name for the 

 substance, so the notation for a physicM,! unit may serve as a name 

 for that unit. 



In a work,. about to be published, on Physical Arithmetic, I make 

 use of a notation for units, and I show how the notation can be ap- 

 plied in the reasoning out of problems. The analysis of a quantity 

 upon which I proceed is threefold, namely, numerical value, unit 

 and, when necessary, descriptive phrase. For example, the letter x 

 as used in geometry, denotes not only a number and a unit, but also 

 a particular direction. 



The progi'ess of physical science has made us familiar with the 

 idea of a system of units, and as specimens we have the centimetre- 

 gramme-second system, and the foot-pound-second system. There is 

 however no systematic notation for the units whether of the genei'al 

 system or of the particular systems. The notation which I propose 

 is the logical extension of existing notation, and is in harmony with 

 both the English language and the established notation of mathe- 

 matics. The nature of the notation will be seen from the table 

 appended. 



We require letters to denote the fundamental units of length, 

 time, mass, and temperature. Let L denote any unit of length, T 

 any unit of time, M any unit of mass, and any iinit of tempera- 

 ture. They are the units corresponding to the numerical values 1, t, 

 m, d The lettei-s S, V, F, W, P, Q in the same manner stand for 

 names. 



When a unit depends directly upon two units, as S upon L long 

 and L broad, the relation of the independent units is expressed by 

 means of by. When a unit depends directly upon one unit and 



