&4 PROCEEDINGS OF THE CANADIAN INSTITUTE. 



The C. G. S. system is obtained by substituting centimetre for L, 

 second for T, and gramme for M. Foi- the degree centigrade is 

 used. Thus the unit of velocity is centimetre per second, and that 

 of accelei'ation 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 Avho 

 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 

 svippose.s, not unnaturally, that the repetition of the per second is a 

 mistake. 



In the 0. Gr. S. System F is the di/ne 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 1 t-2 F new = F old. 

 Properly speaking, the dimensions are the indices of m I t ; in the 

 above case 1,1, and — 2, while m 1 t^- is the multiplier 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 1 erg per cm = gm by cm per sec per sec, and 1 erg per 

 gra = cm. per sec. per sec. by cm. Thus the unit of force is equi- 

 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 fi'om one side to the other. 



