OF ELECTKIC SIGNALS THEOIJGH STJBMAEINE CABLES. 
1011 
Table XV. — Speeds and Amplitudes for various lengths. 
1. 
2. 
3. 
4. 
Number of beats 
per minute =N. 
Observed amplitude 
reduced to percentage. 
Product of number of beats 
into square of length 
Product of number of beats- 
into square of length corrected 
for battery and galvanometer 
=Nx(L+160)2. 
L = 1500...| 
130 
92 
73 
60 
2-5 
5 
10 
12-5 
297 
207 
162 
135 
X 106 
>> 
ft 
364 X 106 
254 „ 
198 „ 
165 „ 
132 
0 
429 
X 106 
508 X 106 
112 
1-2 
364 
431 
100 
1-8 
325 
385 
92 
2-7 
299 
354 
L=1802...^ 
84 
3 
273 
323 
72 
39 
234 
277 
60 
59 
195 
231 
50 
9-2 
162 
192 
40 
14-8 
130 
154 
/ 
100 
0 
480 X 106 
553 X 106 
80 
1-5 
384 
443 
60 
3 
288 
332 
L=2192..J 
40 
7-5 
192 
221 
36 
9-4 
173 
199 
30 
12-7 
144 
166 
18 
28-6 
86 
ft 
100 
ft 
Appendix. 
Eeceived January 14, 1863. 
Section I. — Effect of conduction across the sheath of an insulated wire^ or of uniformly 
imperfect insulation on the permanent received current. 
The author is indebted to Professor W. Thomson for the substance of the following 
theory. 
Consider a cable extending infinitely in one direction from an origin O. 
Let the distance of any point P from the origin be called x. 
Let i denote the resistance of the unit length of the sheath to conduction across it, 
i. e. the measure of the insulation. 
Let m denote the resistance of the unit length of the wire to conduction along it. 
Let the potential at O be called V, and the potential at any point P be called V^,. 
Let the strength of the current entering at O be called Q, and the strength of the 
current at P be called Q,. Then it is not dififtcult to prove that 
Q,-Qr"^^r, 
(1.) 
V,-Vr'^^T, 
(2.) 
Q — ^ 
{imy 
( 3 .) 
MDCCCLXII. 
6 T 
