PROFESSOR CHRYSTAL ON THE DIFFERENTIAL TELEPHONE. 633 
In point of fact, the coil with which the experiment was most striking had 
ereater constants than these; but as its constants do not happen to be so 
accurately known to me at present, and as the general features of the experi- 
mental results were the same in both cases, I have taken the case whose 
details I know best. 
It will be seen that the functions in (4) are positive in the case considered 
for values of n* down almost to the lower limit of hearing. Hence, throughout 
the range of audibility, X, and X,’ are positive, and X,’ > X,. 
Now we may write 
oe gat 
= (ep TE 
dé; . : 
so that when X=0, or X=00, = is negative. 
ae 
aXot X—gy,X*; 5 
Hence the values 
Xn= Xo— of Xo(Xo—K) » (<K) , 
Kg Xt nl SRG Ka) 9. Xa) i, 
correspond to minimum and maximum values of &, 
These results contain the whole of the mathematical theory. The following 
table is calculated roughly for the above values of L, N, R, S, and will give a 
clear idea of the progression of the different quantities, as we proceed up or 
down the scale of audible notes. &, 
and 100, microfarads respectively.* 
, &; correspond to capacities of 1, 10, 
.pprox. 
ee g, Ss £3 f", o"; X, xX’, Xe, xX, 
Se nekO? +1 de) 14:6 teil ea 10:9 5217 — — = 
e 106 | 2:2 4:5 2-1 21 15 333 375 250 500 — 
is 107 25 60 25 088 82 32°4 35°6 24°9 46°3 
g” {108 025 062 ‘016 090 063 3°16 3°39 2°51 4:27 
& 109 0025 0062 009 0063 0062 316 339 252 ‘427 
bt 7101) 00025 00062 00068 00062 00062 0316 0339 0252 0427 
g#®§ |104; -000025) -000062) -000062); 000062; -000062 00316 00339 00252 00427 
* To avoid all possibility of misconception, I may repeat that the above table is calculated on the 
supposition that the amplitude of the disturbing electromotive force is independent of 7. 
parison for the present purpose goes by horizontal rows. 
If it be desired to compare vertically, and an approximation to the case of a telephone sender be 
contemplated, then the values of €,, €,, &, &c. must be multiplied by the respective values of n?. 
The com- 
Thus 
the values of €,, become 11, 22, 25, 25, 25, 25, 25, those of &, 15, 45, 60, 62, 62, 62, 62; so that the 
quality (i.e, the ratios of (he iatensibies - the tones of different pitch) saad be ‘little altered by 
telephonic transmission in the two cases, if we except very low notes. 
conclusions of Hatmuourz (Telephon und Klangfarbe, Wied. Ann. N. F. v. p. 448). 
The same remark does not apply to the case where a condenser is introduced, a case not con- 
VOL, XXIX. PART II. 
eae 
This agrees with the general 
