On the Dimensions of Electromagnetic Units. 323 



Then 



C= ^ 



R + r- ^"^ 



G + 

 and 



C.=Cx 



E 



Gf + X -r, (j^X G + A' 



R + ^'H- 7^-^— 



RG + G« + rGr + ?'.«* 

 Also, substituting R for x, 



^ ER 



RG+ai' + rG + rR 



If A' and R are large compared to r, the denominators of 

 the above fractions will be practically identical ; and the ap- 

 proximation will be still closer if, as would usually occur in 

 practice, x is not very different from R. 



The sensitiveness of the method is practically the same as 

 that obtained in the ordinary " substitution"" process of deter- 

 mining, but has the small advantage over the latter of not 

 requiring a knowledge of the resistance of the galvanometer. 



XXXVIII. On the Dimensions of Electromagnetic Units. 

 By Prof. G. F. Fitzgerald, F.R.S.'' 



SOME attention has lately been called to the question of 

 the dimensions of electromagnetic units, but the follow- 

 ing obvious suggestion seems to have escaped notice. 



The electrostatic system of units may be described as one 

 in which electric inductive capacity is assumed to have zero 

 dimensions and the electromagnetic system as one in which the 

 magnetic inductive capacity is assumed to have zero dimensions. 

 Now if we take a system in which the dimensions of both these 

 quantities are the same, and of the dimensions of a slowness, 



i. e. the inverse of a velocity, hp , the two systems become 



identical as regards dimensions, and differ only by a numerical 

 coefficient just as centimetres and kilometres do. There seems 

 a naturalness in this result that justifies the assumption that 

 these inductive capacities are really of the nature of a slow- 

 ness. It seems possible that they are related to the reciprocal 

 of the square root of the mean energy of turbulence of the sether. 



* Communicated by the Physical Society : read February 23, 1889. 



Y2 



