INTRODUCTION XXXIX 



Electric Field Intensity is measured by the ratio of the force on a quantity 

 of electricity at a point to the quantity of electricity. The dimensional 

 formula is therefore the ratio of the formulae for force and electric quantity or 

 [MLr-*/MWT- x K?] or [M*L-*T- l K.-*~\. 



Electric Potential and Electromotive Force. — Change of potential is propor- 

 tional to the work done per unit of electricity in producing the change. The 

 dimensional formula is the ratio of the formulae for work and electrical quantity 

 or [MIJT- 2 /M*DT- l K } >2 or \_A0DT~ 1 A'-*]. 



Capacity of an Insulated Conductor is proportional to the ratio of the quan- 

 tity of electricity in a charge to the potential of the charge. The dimensional 

 formula is the ratio of the two formulae for electric quantity and potential or 

 [MWT- l KyMWr- l K-*\ or [LA]. 



Specific Inductive Capacity is the ratio of the inductive capacity of the sub- 

 stance to that of a standard substance and therefore is a number. 



Electric Current is quantity of electricity flowing past a point per unit of 

 time. The dimensional formula is the ratio of the formulae for electric quan- 

 tity and for time or \_M^DT- X K^/T\ or [M l >DT- 2 K>J 



Electrical Conductivity, like the corresponding term for heat, is quantity per 

 unit area per unit potential gradient per unit of time. The dimensional formula 

 is [Af^r- 1 A"*/ L 2 (M>L>T- 1 A"*/ L)T~\ or [J" 1 A]. 



Resistivity is the reciprocal of conductivity. The dimensional formula is 



Conductance of any part of an electric circuit, not containing a source of 

 electromotive force, is the ratio of the current flowing through it to the difference 

 of potential between its ends. The dimensional formula is the ratio of the for- 

 mulae for current and potential or [_M^L'T~ i K^/M^L^T~ l K~^\ or \_LT~ 1 K~\. 



Resistance is the reciprocal of conductance. The dimensional formula is 

 [L-TA-i]. 



Exs. — Find the factor for converting quantity of electricity expressed in ft.-grain-sec. units 

 to the same expressed in c.g.s. units. The formula is [mUU~ l k¥], in which m= 0.0648, 

 / = 30.48, t = 1, k = 1; the factor is 0.0648* x 30.483, or 42.8. 



Find the factor required to convert electric potential from mm-mg-sec. units to c.g.s. units. 

 The formula is [mUU~ l k~X], in which m = 0.001, / = 0.1, / = 1, k = 1; the factor is o.ooij 

 X o.ii, or 0.01. 



Find the fail or required to convert electrostatic capacity from ft.-grain-sec. and specific 

 inductive capacity 6 units to c.g.s. units. The formula is {Ik} in which / = 30.48, k = 6; the 

 factor is 30.48 x 6, or 182.88. 



ELECTROMAGNETIC SYSTEM 



Many of the magnetic quantities are analogues of certain electric quantities. 

 The dimensions of such quantities in the electromagnetic system differ from 

 those of the corresponding electrostatic quantities in the electrostatic system 

 only in the substitution of permeability jx for A. 



