Variable Mutual Inductances. 167 
obtained for K = 10*06 mfds. and M = 0626 6 millihenry, 
whence the frequency was found to be 2004 ~ per sec. 
With another condenser (a carefully calibrated subdivided 
one), capacities of 1-000, 0*900, ; 800, 0-701, 0*601, and 
0*551 gave 
n = 1999, 2005, 2009, 2001, 2004, and 2001 — per sec. 
respectively; the variable M was not, however, so accurately 
readable in this case. 
In this method it is very important that the insulation 
resistance S of the condenser shall be high. If the leakage 
is not negligible, equation (14) becomes 
it* • b . 
1-fSK* 
_ S(l-SKa) 
(17) 
Putting the real part equal to zero we have 
l/(l +j p 2 S 2 & 2 )=0, 
showing that an exact balance can only occur when 
p 2 S 2 K 2 =oo . In practice the insulation resistance of a good 
mica condenser is quite high enough to give a good balance ;; 
even a good paraffined paper condenser will work fairly well, 
but an ordinary one gives only a minimum deflexion on the 
galvanometer *. 
The application of this null method to the high frequencies 
used in wave telegraphy is made difficult by reason of the 
coexistence of two frequencies in the waves used. 
Appendix. 
Scale of Excentric-Coil Variable Mutual Inductance. 
The problem of finding the mutual inductance between 
two circles (thin circular coils) not in the same plane and 
whose axes are parallel has not yet been solved, as far as I 
know. For any particular case the result may be calculated 
by quadratures as follows. 
* This may, however, be due more to absorption than leakage. 
