Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

DISCHARGE OF AN AIR CONDENSER, WITH A DETERMINATION OF "v." 163
Now y//l depends on S'/S, and m,,, etc. are all finite and less than 1,;
(- - 1) S
L = (li + m2, +...)+ (- - m,
where m is of the order of the arithmetical mean of rnm,, mnl, etc.,.. L'= li 4-:I,2 +... + SThus in the case of a large number of turns, if S,/S is small the equations
already used are correct if L' be 1/nth of the whole self-induction, for we may neglect
the term 81-n/S compared with the sum lI + mn + etc.
There is now the correction for resistance to be considered. In the case of a simple
circuit
X2=T{J 1 R)2}
X, being the uncorrected value; thus we may put
X = 1 (1 - k').
Now so far as the inductance of the circuit is concerned,
X2= (1 - 1k).
And in the more important cases both k" and k' are small.
Therefore = -1 (1 - k" - k),
where k" has the value already found from Table IV.,
In some of tbe exyerinments X, is about 27r x 103,
= 200 x 109, L = 5 x 109,
R 1
X0L - 50 approximately,
and the correction is negligible.
if the period be 1/120 second as in other experiments,;. — 27r x 12 x 102= 7-2 x 102 approximately,
R 1
X0L =.0 approximately,
and k' = 400 1600 which is also negligible.
21 —2