Y

(I)

regards knowledge of electricity, to such as those assumed in hydrodynamics when water is treated as if incompressible, or the velocity of sound in it considered infinitely great, which re

(7)

(6)

II

quires instantaneous effects to be propagated through the whole mass of the water, on a disturbance being made in any part of it). After the interval a, the current very rapidly rises, and after

5)

(2)

(1)

about 4a more, attains to half its full strength. After 10a from the commencement, it has attained so nearly its full strength, that the farther increase would be probably insensible. The full strength is theoretically reached only after an infinite time has passed. The first (1) of the smaller curves represents the rise and fall of the current in the remote instrument when the end operated on is put in connexion with the ground after having been for a time a in connexion with the battery; the second (2) represents similarly the effect of the battery for a time 2a; the third (3) for a time 3a and so on. The curve (II) derived from the primary curve (I) by differentiation (exhibiting in fact the steepness of the primary curve at its different points, as regards the line of abscissas), represents the strength of current at different times through the remote end of the wire, consequent upon putting a very intense battery in communication with the end from which the signal is sent, for a very short time, and then instantly putting this end in communication with the ground. Thus, relatively to one another, the curves (I) and (II) may be considered as representing the relative effects of putting a certain battery in communication for the time a, and a battery of ten or

1

twenty times as many cells for a time a or

10

to guess what might be called "the retardation," which in the observations between Greenwich and Brussels was found to be about th of a second, I should say it corresponded to four or five times a, but this must depend on the kind of instrument used, and the mode of making and breaking contacts with the battery which was followed.

Equation of principal curve (I).

y= 10a - 20a (e− e* + ea − e1o + &c.), where e=
— (2)x/α ;

a being half the side of one of the squares.

If y = f(x) denote the equation of the principal wave, and if f(x) be supposed to vanish for all negative values of x, the series of derived curves are represented by the equations

I think clearly the right way of making observations on telegraph retardations would be to use either Weber's electro-dynamometer, or any instrument of suitable sensibility constructed on the same principle, that is adapted to show deflections experienced by a moveable part of a circuit, in virtue of the mutual electrodynamic force between it and the fixed part of the same circuit, due to a current flowing for a very short time through the circuit. Such an instrument, and an ordinary galvanometer, (showing impulsive deflections of a steel needle,) both kept in the circuit at the remote end of the telegraph-wire from that at which the signal is made, would give the values of y'da, and

2

[y'de, and [yda (or the area),

0

for any of the curves; and the ratio of the time a of the diagrams to the time during which the battery was held in communication with the wire, might be deduced. The method will lose sensibility if the battery be held too long in communication, but will be quite sufficiently precise if this be not more than ten or twenty times a. I believe there will be no difficulty in applying the method to telegraph-wires of only twenty or thirty miles long, where no retardation would be noticed by ordinary observation. Before, however, planning any observations of this kind with a view to having them executed, I wished to form some estimate of the probable value of a certain element,-the number of electrostatical units in the electro-magnetic unit of electrical quantity,which I hoped to be able to do, from the observation of th of a second as the apparent retardation of signals between Greenwich and Brussels. I therefore applied to the Astronomer Royal for some data regarding the mode of observation on the indications of the needle, and the dimensions and circumstances of insulation of the wire; and he was so good as to send me immediately all the information that was available for my purpose. This has enabled me to make the estimate, and so has convinced me that a kind of experiment which I proposed in a paper on Transient Electric Currents in the Philosophical Magazine for June 1853, [Art. LXII. Vol. I. above], and which I hope to be able before long to put in practice, will be successful in giving a tolerably accu

rate comparison of the electro-statical and electro-dynamic units; and, with a further investigation of the specific inductive capacity of gutta-percha, which will present no difficulty, will enable me to give all the data required for estimating telegraph retardations, without any data from telegraphic operations. This experiment [which I made about five years after the date of the present Article. See "Electrostatics and Magnetism," Art. XVIII.] is simply to put two plane-conducting discs in communication with the two poles of a Daniell's battery (or any other battery of which the electro-motive force is known in electro-magnetic units), and to weigh the attraction between them.*

It would be easy at any time to make a plan for observing telegraph indications by means of either Weber's electro-dynamometer, or an instrument constructed on the same principle, or by measuring thermal effects of intermittent currents, which could be put in practice by any one somewhat accustomed to make observations, and which would give a tolerably accurate determination of the element of time, even in cases where the observable retardation is considerably less than 1th of a second. A single wire in a submarine cable would, as far as regards the physical deductions to be made from this determination, be to be preferred to one of a number of different wires, insulated from one another under the same sheathing. I have little doubt but the Varna and Balaklava wire will be the best yet made for the purpose.

thanth

Without knowing exactly what the "retardation" may be, in terms of the element of time "a" of the diagrams, we may judge what the retardation, if similarly estimated, would be found to be in other cables of stated dimensions. Thus, if the retardation in 200 miles of submarine wire between Greenwich and Brussels be 1th of a second, the retardation in a cable of equal and similar transverse section, extending half round the world (14,000 miles), would be

H [Here follow, in the original Article, some elaborate estimates and calculations founded on too imperfect data to be worth re-publication now, They are referred to in §§ 316 and 317 of "Electrostatics and Magnetism." W. T. Apr. 3, 1883.]

and in the telegraphic cable (400 miles) between Varna and Balaklava, of which the electro-statical capacity per unit of length may be about one-half greater than in the other, while the conducting power of the wire is probably the same, the retardation may be expected to be

The rate at which distinct signals could be propagated to the remote end would perhaps be one signal in about a quarter of an hour in the former case, and nearly two signals in a second in the latter.

ART. LXXIV. ON THE ELECTRO-STATICAL CAPACITY OF A LEYDEN PHIAL AND OF A TELEGRAPH WIRE INSULATED IN THE AXIS OF A CYLINDRICAL CONDUCTING SHEATH.

[Phil. Mag., June supplement, 1855.]

[ELECTROSTATICS AND MAGNETISM, Article III.]