or ELECTEIC SIGNALS THEOIJGH SIJBMAEINE CABLES, 
1008 
duce the various amplitudes in any one length of cable ; thus we see that if an ampli- 
tude or variation in the received current of 1 per cent, will suffice for distinct signals, 
twice as many signals can be sent through any given cable as if an amplitude of 7 per 
cent, is required, or four times as many as if an amplitude of 25 per cent, is required. 
The latter amplitude is probably necessary for hand signalling, but our experiments 
have shown that less than 1 per cent, is sufficient when a proper compensation is made. 
The coincidence between theory and observation places it beyond doubt that the curve 
truly expresses the relation between the speeds and amplitudes for straight as well as 
for coiled cables ; and if the amplitude at any one speed through any one straight cable 
were known, the amplitude at any other speed through any other cable of the same 
materials might be calculated from the curve with certainty; but unfortunately this 
fact is wanting. There is no proof that the absolute amplitude observed through the 
coiled .cable would remain unaltered if the cable were extended; on the contrary, it is 
very generally believed that it is easier to signal through a straight than a coiled cable ; 
and if this be so, the amplitude would increase as the cable was laid. Although, there- 
fore, the constants for the mathematical theory might easily be calculated from the 
values of the coordinates of the curve given by the observations, these constants would 
probably be inapplicable to straight cables. 
Assuming, however, for a moment the identity of a coiled and extended cable, it may 
be interesting to calculate the amplitudes which would correspond to the rates of signal- 
ling recorded for various cables. 
For the Red Sea cable the amplitude is found by taking the ordinate corresponding 
to the abscissa given by the product of the square of the length into twice the number 
of dots per minute. The speed giving the same amplitude through any other cable of 
different dimensions, but of equal length, is obtained by a simple proportion. 
The author has been informed that ten words per minute have been sent through 
640 knots of the Red Sea cable, but that seven words was the more usual speed. The 
former would correspond to an amplitude of 20 per cent, for the dots*, the latter to 
about 35 per cent. IT word per minute was sent through the Atlantic cable and 
received by a relay ; this speed would correspond to an amplitude of about 8 per 
cent. ; 2-4 words per minute (the ordinary rate of signalling from Newfoundland 
having been forty-one dots per minute) were received through the same cable by 
Professor Thomson’s galvanometer ■|’, corresponding to an amplitude of little more than 
1 per cent. 
Ninety dots per minute, the speed of the message sent by the perforated paper, would, 
* Seventeen dots per word. 
t An instrument similar to that used in this research : the observer could therefore follow every change 
in the received current, and disentangle the meaning of signals which would have produced only hopeless 
confusion on a relay, or other instrument with a fixed zero. 
MDCCCLXII. 6 X 
