632 PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 
is increased as the capacity increases from zero. For a certain capacity the 
increase is at its maximum; for a certain capacity still greater there is neither 
increase nor decrease, for still higher capacities the intensity of the tone is 
diminished. As we go down the scale of frequency, the capacity for which a 
particular note is sensibly increased, and that for which it is most increased, 
increases ; so that the capacity which increases a certain low note most will be 
great enough to diminish a high one practically as much as if the condenser 
were short circuited. This explains the main part at least of the phenomena 
observed. 
Experiment— 
Let €,, &, €& denote the values of €, when the neighbouring coil is open, 
closed simply, and closed through a condenser whose capacity is X microfarads. 
Then— 
_1-2pX4+9Xt? 
(1) &3= DD a 
1 q 
(2) = = 7 & a ’ 
where 
p=am'10" , g=(b+ en?)n210-” ; 
r=d+en?, s= (f+ gn?)n?210-” ,t=(h+ hn? +n!)n210-” 
Where again 
a =—N ; i NR?2 ; 
v=S4% g=L(LN—-M?), 
c= N77, h= has; 
a=K?, k=L?8? + N?R?2+2M?RS , 
Leal Bem /=(LN—M?)?. 
If X, denote the value of X for which €,=, , 
Xy ” ” = & , 
then 
__ 2(pr—s) pe grt 
(3) o— "grt > 0 ~Dgs—pi) 
The values of these functions are as follows :-— 
pr—s=M?Ln'10-”’, 
(4) qr—t= M2? {(2L.N—M?)n?—2RS}n'10-”, 
qs—pt=M? {N(LN—M?)n?—S(LS + 2NR)} 2°10°” 
I take the case where 
L=‘2 (earth-quad.), R=70 (ohms), N=-004 (earth-quad.), S=3 (ohms) 
