252 Mr. W. Williams on the Relation of Dimensions 



tive geometrical or trigonometrical meaning, its insertion 

 or suppression implies the insertion or suppression of a 

 concrete quantity, and not merely a number, so that the 

 natural relations between the various quantities are affected. 

 For this reason, therefore, the " rational units," given by 

 Mr. Oliver Heaviside, in which ir is primarily associated with 

 the radial and circuital fluxes of the field, will alone be used 

 in what follows. 



The relations made use of in deducing the dimensions of 

 electromagnetic quantities are of three kinds. 



I. Relations between quantities of the same kind, either 

 purely electrical or purely magnetic. — These are : — 

 (a) Electrical. 



1. D=*E. 



•2.C=|., ^ 



3. e = Surface-integral of D. 



4.C = |. D . 



5. E = Line-integral of E. 



Where D = electric displacement ; k = specific inductive capa- 

 city ; E = electrical force; C = electric current; e — quantity 

 of electricity ; C = current density ; E = electromotive force 

 or voltage of a closed circuit. 



(b) Magnetic. 





1. 



B =/xH. 



2. 





3. 



m = Surface-integral of B. 



4. 



°H-*- 



5. E TO = Line-integral of H. 



B = magnetic induction; jj, = specific magnetic capacity; 

 H = magnetic force ; m — quantity of magnetism. Mr. Oliver 

 Heaviside designates E m the Gaussage of a closed magnetic 

 circuit to correspond with E, the Voltage of the corresponding 

 electrical one, C m and C m being the magnetic currents. 



II. Relations between quantities of different kinds. — These 

 relations are embodied in the two laws of circuitation: 



(a) Circuitation H = C = E TO = ^-.6; 



