ON STANDARDS OF ELECTRICAL RESISTANCE. 151 
dimensions of 7 establish this proposition ; but the following independent de- 
finition, due to Professor W. Thomson, assists the mind in receiving this con- 
ception as a necessary natural truth. Conceive a sphere of radius /, charged 
‘vith a given quantity of electricity, Q. The potential of the sphere, when 
at a distance from all other bodies, will be : (40, 41, and 47). Let it now 
be discharged through a certain resistance, 7, Then if the sphere could col- 
lapse with such a velocity that its potential should remain constant, or, in 
other words, that the ratio of the quantity on the sphere toits radius should 
remain constant, during the discharge, then 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 re- 
sistance of 1000 miles of pure copper wire, 54; inch in diameter, would be 
about 000000141 of a second per metre, or its conducting power one metre 
per 000000141 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 electromotive force. This definition is identical 
with that given of capacity measured in electromagnetic units (26). Lets 
be the capacity of a conductor, q the electricity in it, and ¢ the electromotive 
force charging it ; then ; 
SRE eka eK seth hn nash ake fi b¥ inci EEE 
From this equation we can see that the dimension of the quantity s is a 
length only. It will also be seen that 
Syl. dori’ odes (24) 
where § is the electromagnetic measure of the capacity of the conductor with 
the electrostatic capacity, s. 
The capacity of a spherical conductor in an open space is, in electrostatic 
measure, equal to the radius of the sphere—a fact demonstrable from the 
fundamental equation (17). 
Experimentally to determine s, the capacity of the conductor in electro- 
static measure, charge it with a quantity, qg, of electricity, and measure in any 
unit its potential (47) or tension (49), ¢. Then bring it into electrical con- 
nexion with another conductor whose capacity, s,, is known. Measure the 
potential, ¢,, of s and s, after the charge is divided between them; then 
g=v=(sts,), 
and hence ete “ts, ert ake he BX atc ai bag 
1 
In this measurement we do not require to know ¢ and ¢, in absolute measure, 
since the ratio of these two quantities only is required. We must, how~- 
ever, know the value of s,, and hence we must begin either with a spherical 
conductor in a large open space, whose capacity is measured by its radius, 
or with some other form of absolute condenser alluded to in the following 
paragraph. 
41. Absolute Condenser. Practical Measurement of Quantity.—As soon as 
the electromotive force of a source of electricity is known in electrostatic 
measure, the quantity which it will produce in the form of charge on simple 
forms is known by the laws of electrical distribution experimentally proved 
