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 I 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 asa name for the 
substance, so the notation for a physical 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 progress 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 general 
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 6 any unit of tempera- 
ture. They are the units corresponding to the numerical values 1, t, 
m,@ The letters 8, 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 
