84 PROCEEDINGS OF THE CANADIAN INSTITUTE. 
The C. G. S. system is ovtained by substituting centimetre for L, 
second for T, and gramme for M. For @ the degree centigrade is 
used. Thus the unit of velocity is centimetre per second, and that 
of acceleration is centimetre per second per second. Many of those 
who study dynamics to pass examinations never attain to the idea of 
acceleration ; they can grasp the idea of velocity, but they cannot 
discriminate the idea of velocity from it. Even some of those who 
write on dynamics show by their use of centimetre per second or 
foot per second as a unit for expressing an acceleration, either that 
they have not grasped the distinction, or that they do not see the 
importance of a distinctive notation. It must, however, be admitted 
that the author has the printer to reckon with; and the latter 
supposes, not unnaturally, that the repetition of the per second is a 
mistake. 
In the C. G. S. System F is the dyne and W the erg. The nota- 
tion for the unit of heat is gramme of water by degree centigrade ; 
it is sometimes called the gramme-degree. The latter is a name formed 
after the manner of compounds, while the former is a notation ex- 
pressing the nature of the dependence. 
From the notation for a unit we can derive its dimensions, or the 
multiplier for changing from one set of fundamental units to another. 
Take for example the unit of force. Let 1 L new = L old, m M 
new — M old, and t T new= T old. From an inspection of the 
manner in which the units enter into the notation for the unit of 
force, we derive 
m 1t~” F new = F old. 
Properly speaking, the dimensions are the indices of m /t; in the 
above case 1, 1, and —2, while m1t~’ is the multipher for chang- 
ing from one unit to another. From the notation for a unit we can 
infer the multiplier; but from the multiplier we cannot infer the 
notation. 
By means of the notation we readily see what ideas or units are 
equivalent to one another. For example, 
1 erg = gm by cm. per sec. per sec. by cm.; 
therefore | erg per cm = gm by cm per seg per sec, and | erg per 
gm = cm. per sec. per sec. by cm. Thus the unit of force is eqni- 
valent to erg per cm, and erg per gm expresses the idea of potential. 
The rule is to change by into per, or per into by, when removing a 
unit from one side to the other. 
