114 On the Suppressed Dimensions of Physical Quantities. 



To these we may add certain units in which both electrical 

 and thermal quantities occur. 

 Thus, using the relations : — 



Thermoelectric height x temperature =E.M.F., 

 or Specitic heat of electricity x temperature = E.M.F,, 



n X current X time = heat, 

 or Jn = E.M.F., 

 we get the following results : — 



Symbol. 



Thermoelectric height . . 

 Specific heat of electricity 

 Coefficient of Peltier effect 

 Geometrical capacity . . 



} 



kt 



n 



^ K 



[L^M^-T-^K-^^^-i] 

 [L-iM^TK-i^] 



[L?MiT-V'^- 



[L] 



In conclusion, then, I think it would be well to introduce 

 symbols for what I have called secondary fundamental units 

 instead of suppressing their dimensions, for the following 

 reasons : — 



(1) We thereby generalize the method of determining by 

 dimensional equations the relation between a change in the 

 magnitude of the units and in the number of which a given 

 quantity is expressed. 



(2) In the case of the electrical and magnetic units the 

 method indicates clearly the cause of the difference be- 

 tween the dimensions in terms of M, L, and T of the same 

 quantity in the two systems. 



(3) It indicates that the dimensions of different quantities 

 in the same system, which are apparently the same with re- 

 spect to M, L, T, really are or may be different, as their 

 dimensions with respect to K or jx are different ; 



e.g. ['B] = [L-^M4T->Ki] 

 [g] = [L-^M^T-iK-^]. 



(4) It suggests an explanation of the artificial and unin- 

 telligible character of the electric and magnetic units. If the 

 dimensions of K and jju were known, they would probably be 

 simplified. 



(5) Lastly, I think the symbols are thus made to express 

 the limits of our knowledge and ignorance on the subject 

 more exactly than if we arbitrarily assume that some one of 

 the quantities involved is an abstract number. 



