Relations between Electrical Measurements. 511 



and therefore 



r=J|B. . ...... (22) 



To reduce a resistance measured in electromagnetic units to 

 its electrostatic value, we must divide by v 2 . 



T 



The dimensions of r are j, or the reciprocal of a velocity. 



39. Electric Resistance in Electrostatic Units is measured by 

 the Reciprocal of an Absolute Velocity. — We have seen from the 

 last paragraph that the dimensions of r establish this proposi- 

 tion ; but the following independent definition, due to Professor 

 W. Thomson, assists the mind in receiving this conception as a 

 necessary natural truth. Conceive a sphere of radius k, charged 

 with a given quantity of electricity Q. The potential of the 



sphere, when at a distance from all other bodies, will be — (40, 



K 



41, and 47). Let it now be discharged through a certain resist- 

 ance, r. Then, if the sphere could collapse with such a velocity 

 that its potential should remain constant (or, in other words, 

 that the ratio of the quantity on the sphere to its radius should 

 remain constant, during the discharge), the time occupied by 

 its radius in shrinking the unit of length would measure the 

 resistance of the discharging conductor in electrostatic measure, 

 or the velocity with which its radius diminished would measure 

 the conducting-power (50) of the discharging conductor. Thus 

 the conducting-power of a few yards of silk in dry weather 

 might be an inch per second, in damp weather a yard per 

 second. The resistance of 1000 miles of pure copper wire, T ^ 

 inch in diameter, would be about 0*00000141 of a second per 

 metre, or its conducting-power one metre per 0*00000141 of a 

 second, or 708980 metres per second. 



40. Electrostatic Measure of the Capacity of a Conductor.—*. 

 The electrostatic capacity of a conductor is equal to the quantity 

 of electricity with which it can be charged by the unit electro- 

 motive force. This definition is identical with that given of 

 capacity measured in electromagnetic units (26). Let s be the 

 capacity of a conductor, q the electricity in it, and e the electro- 

 motive force charging it ; then 



q = se (23) 



From this equation we can see that the dimension of the quantity 

 s is a length only. It will also be seen that 



s=v% (24) 



where S is the electromagnetic measure of the capacity of the 

 conductor with the electrostatic capacity s. 



