CAPACITY AND RESIDUAL CHARGE OF DIELECTRICS. 
Ill 
really all parts of a continuous magnitude. Suppose now our condenser be submitted 
to a periodically varying electromotive force, that 
Xi = A cos 2^t, 
then 
yt = A |k COS2^i + j" COSj9 {t — w) [r//(w) + /S]c?(y| 
= A |k cos ni^ + cos [ cos (w) do) + sin [ sin (w) 
[ -0 Jo J 
The effect of residual charge is to add to the capacity K the term j" cob pcoxjj (o)) do), 
whilst the term sin^)^ sin cZw will have the effect of conductivity as regards 
the phases of the currents into the flask. Thus the nature of the effect will depend 
upon the form of the function xfj (w). An idea may be obtained by assuming a form 
for \p {(o), say \p (w) = —, where m is a proper fraction. This is a fair approximation 
to the truth. Then 
cos^jftji// (&)) doi = r (l — m) cos (1 — m) 7r/2/_p^“®, 
Jo 
[ sin (w) do) = r (1 — m) sin (1 — rn) 7r/2/p^~“. 
If m is near to unity, capacity is almost entirely affected ; otherwise the effect is 
divided between the two, and dissipation of energy will occur. It is interesting to 
consider what sort of conductivity a good insulator such as light flint glass, according 
to this view of capacity, residual charge, and conduction, would have at ordinary 
temperatures if we could measure its conductivity after very short times of electrifica¬ 
tion ; if, in fact, we could extend the practice used for telegraph cables and specify 
that the test of insulation should be made after the one hundred millionth of a second 
instead of after one minute, as is usual for cables. The capacity of light flint 
measured with alternating currents with a frequency of two millions a second is 
practically the same as when measured in the ordinary way; that is, its capacity will 
be 67. Its index of refraction is 1’57 or [jd = 2*46, or, say, 2*5. We have then to 
account for 4*2 in a certain short time. The current is an alternating current, and 
we may assume as an approximation that it will be the residual charge which comes 
out in one-sixth of the period which produces this effect on the capacity; therefore 
(•1/12 X105 
\p (w) dcD = |-y X capacity of the flask as ordinarily measured. The capacity 
• 0 
of a fairly thin flask may be taken to be 1 / 1,000 microfarad to 2 / 1,000 microfarad ; 
rl,12xl0« ■ . _ 
hence we may take xjj (w) doj to be 10 “® farad ; if xfj (w) were constant during 
J 0 
this time its value must be 12 X 10® X 10~® = ohms~^ about. The value of xp (co) 
