A DIRECT COMPARISON OF ELECTROSTATIC 



In the electromagnetic system we have a force equal to the product of two 

 currents multiplied by the ratio of two lines. The unit of current in this 

 system therefore varies as the square root of the unit of force; and the unit 

 of electrical quantity, which is that which is transmitted by the unit current 

 in unit of time, varies as the unit of time and as the square root of the unit 

 -f force. 



The ratio of the electromagnetic unit to the electrostatic unit is therefore 

 that of a certain distance to a certain time, or, in other words, this ratio is a 

 velocity; and this velocity will be of the same absolute magnitude, whatever 

 standards of length, time, and mass we adopt. 



The electromagnetic value of the resistance of a conductor is also a quantity 

 of the nature of a velocity, and therefore we may express the ratio of the two 

 electrical units in terms of the resistance of a known standard coil; and this 

 expression will be independent of the magnitude of our standards of length, 

 time and mass. 



In the experiments here described no absolute measurements were made, 

 either of length, time, or mass, the ratios only of these quantities being in- 

 volved ; and the velocity determined is expressed in terms of the British Asso- 

 ciation Unit of Resistance, so that whatever corrections may be discovered to 

 be applicable to the absolute value of that unit must be also applied to the 

 velocity here determined. 



A resistance-coil whose resistance is equal to about 28 '8 B. A. units would 

 represent the velocity derived from the present experiments in a manner inde- 

 |>endent of all particular standards of measure. 



The importance of the determination of this ratio in all cases in which 

 electrostatic and electromagnetic actions are combined is obvious. Such cases 

 occur in the ordinary working of all submarine telegraph-cables, in induction- 

 coils, and in many other artificial arrangements. But a knowledge of this ratio 

 is, I think, of still greater scientific importance when we consider that the 

 velocity of propagation of electromagnetic disturbances through a dielectric medium 

 depends on this ratio, and, according to my calculations*, is expressed by the 

 very same number. 



The first numerical determination of this quantity is that of Weber and 

 Kohlrauscht, who measured the capacity of a condenser electrostatically by 



* "A Dynamical Theory of the Electromagnetic Field," Philosophical Transactions, 1865. 

 t Pogg, Ann. Aug. 1856, Bd. xcix. p. 10. 



