Fig. 2.

Now it is quite true that we need not fear any great deviation of density extending through so large a portion of the earth, for that would displace the centre of gravity to a sensible extent, which would become perceptible in the measurements of latitude; but a local deviation might produce a smaller but yet sensible amount of error; thus if AC' (fig. 2) represent a sphere of 100 miles diameter, the attraction of this on

1 dg the point A will= ; where 80 D

D is the earth's mean density, d that of the small sphere, and g the total attraction at A. If, therefore, d should be changed to d', the

B

attraction at A, or the apparent mean density, will be altered in the

d'-d
80d

proportion of 1:1+ ; which might be a sensible quantity

1 500,000

without producing any sensible effect on the true mean density, or on the position of the centre of gravity, since the bulk of AC' would be only about of that of the earth. Now we know little or nothing of the density of the matter a few miles below the surface; only we are sure, from the discordant lengths of the pendulum in different latitudes, and even in the same latitude under different meridians, that the local deviations are indeed sensible, yet of so small an amount as hardly to affect this inquiry, and that the error from this cause can never even approach 1 per mille. The Cavendish experiment may therefore be considered as practically free from error of this kind; and as regards errors arising from manipulation or instrumental causes, their probable amount may be determined in the ordinary way from the variation of the results. But if the Cavendish, why may not the Huttonian experiment equally be considered free from error? Because in the former we are dealing with disturbing masses whose amount is exactly known, whereas in the latter, while we may approximately measure the mass of the mountain above the surface, we do not know how much may be added or abstracted

below; and we have no right to assume that the mountain is merely a detached mass resting upon the general surface; it will almost certainly have roots differing in density from the surrounding country, as has been ably shown by Mr. Airy in the Philosophical Transactions for 1855, page 101.

Fig. 3.

A

In the case of the pendulum experiment the uncertainty is somewhat greater; thus, let AB represent the Harton pit, and let BC be a sphere of lead (supposed to lie at its foot) of a diameter equal to AB (i. e. about mile); the density of this being about double the mean density of the earth and about quadruple that of the neighbouring country, its excess of attrac

B

attraction at A will be only of this, and the difference of its attrac

tion on the two stations will therefore be

g 23625'

being only a little

less than the whole quantity observed by Mr. Airy. We may indeed be pretty sure that there is no such mass of lead, or mineral of nearly equal density, at the foot of the Harton shaft, yet it is quite conceivable that there should be, within the sphere BC, an excess of density amounting to of that of lead, or about 1·4; and this would

produce a difference of effect on A and B amounting to

D*
d

g

144,000'

and

would alter the value of to 2.384, and that of Et to 5.96,

approaching considerably nearer to Baily's determination. Further, there must doubtless be a small latitude allowed to the assumed density of the upper strata, the average of which, within the limits that would affect the pendulum, may not be exactly the same as in the immediate vicinity of the pit; supposing it to be 2-4 instead of 2·5, E will be reduced to 5·72, being nearly identical with Baily's value.

If it should be objected that so large a variation of density as that. assumed above (1·4), though possible, is not likely; the same effect

*Ratio of mean density of the earth to that at the surface.
Earth's mean density.

might be produced by a smaller rate of change through a greater space; thus an addition of about 0.5 to the specific gravity of a sphere of 1 mile in diameter, or of 0.33 to one of 10 miles diameter, would have nearly the same effect, and it cannot be contended that these are improbably large.

Should the experiment ever be repeated, it would be desirable to swing the pendulum at one (at least) intermediate station between the top and bottom of the shaft, by which means any error of this kind might be approximately eliminated. In the mean time I think there are hardly sufficient grounds for impugning the correctness of the value of E (5.67) deduced by the late Francis Baily from his carefully conducted repetition of the Cavendish experiment.

IV. "On Practical Methods for rapid Signalling by the Electric Telegraph." By Prof. W. THOMSON, F.R.S. Received November 14, 1856.

I am at present engaged in working out various practical applications of the formulæ communicated some time ago in a short article on the "Theory of the Electric Telegraph" (Proceedings, May 17, 1855), and I hope to be able very soon to lay the results in full before the Royal Society. In the mean time, as the project of an Atlantic Telegraph is at this moment exciting much interest, I shall explain shortly a telegraphic system to which, in the course of this investigation, I have been led, as likely to give nearly the same rapidity of utterance by a submarine one-wire cable of ordinary lateral dimensions between Ireland and Newfoundland, as is attained on short air or submarine lines by telegraphic systems in actual use.

Every system of working the electric telegraph must comprehend (1) a plan of operating at one extremity, (2) a plan of observing at the other, and (3) a code of letter-signals. These three parts of the system which I propose will be explained in order,-I. for long submarine lines, and II. for air or short submarine lines.

I. Proposed telegraphic system for long submarine lines.

1. Plan of operating.-This consists in applying a regulated gal

vanic battery to give, during a limited time, a definite variation of electric potential determined by theory, so as to fulfil the condition of producing an electric effect at the other extremity, which, after first becoming sensible, rises very rapidly to a maximum, then sinks as rapidly till it becomes again, and continues, insensible.

The principle followed is that pointed out by Fourier, by which we see, that, when the wire is left with both ends uninsulated after any electrical operations whatever have been performed upon it, the distribution of electric potential through it will very quickly be reduced to a harmonic law, with an amplitude falling in equal proportions during equal intervals of time. Unless the electric operations fulfil a certain condition, this ulterior distribution is according to the simple harmonic law (that is, is proportional to the sine of the distance from either extremity, the whole length being reckoned as 180°). The condition which I propose to fulfil is, that the coefficient of the simple harmonic term in the expression for the electrical potential shall vanish. Then, according to Fourier, the distribution will very much more quickly wear into one following a double harmonic law (that is, the sine of the distance from one extremity, the whole length being reckoned as 360°). In this state of electrification the two halves of the wire on each side of its middle point, being symmetrically and oppositely electrified, will discharge into one another, as well as into the earth at their remote extremities; each will be like a single wire of half-length, with the simple harmonic distribution; and the wire will, on the whole, be discharged as fast as a wire of half the length, or four times as fast as a wire of the whole length, after an ordinary electrification. There is considerable latitude as to the mode of operating so as to fulfil this condition, but the theoretical investigation is readily available for finding the best way of fulfilling it in practice. The result, as I have tested by actual calculation of the electric pulse at the remote end, is most satisfactory. The calculations, and curves exhibiting the electric pulse in a variety of cases, will, I trust, very soon be laid before the Royal Society.

The time and law of operations being once fixed upon, a mechanical contrivance of the simplest kind will give the means of directing a regulated galvanic battery to perform it with exactness, and to any stated degree (positive or negative) of strength. Complete

plans of all details I have ready to describe when wanted, and shall very soon be able to state exactly the battery power required for a cable of stated dimensions.

2. Plan of observation for receiving a message.—The instrument which I propose is Helmholtz's galvanometer, with or without modification. The time of vibration of the suspended magnet, and the efficiency of the copper damper, will be so arranged, that during the electric pulse the suspended magnet will turn from its position of equilibrium into a position of maximum deflection, and will fall back to rest in its position of equilibrium. The possibility of fulfilling these conditions is obvious from the form of the curve I have found to represent the electric pulse. The observer will watch through a telescope the image of a scale reflected from the polished side of the magnet, or from a small mirror carried by the magnet, and he will note the letter or number which each maximum deflection brings into the middle of his field of view.

3. Code of letter-signals.-The most obvious way of completing a telegraphic system on the plans which have been described, is to have the twenty-six letters of the alphabet written on the scale of which the image in the suspended mirror is observed, and to arrange thirteen positive and thirteen negative strengths of electric operation, which will give deflections, positive or negative, bringing one or other of these letters on the reflected scale into the centre of the field of view. But it would be bad economy to give the simple signals to rare letters, and to require double or triple signals for double and triple combinations of frequent occurrence. Besides, by the plans which I have formed, it will, I believe, be easy to make much more than thirteen different positive and thirteen different negative strengths of electric operation, giving unmistakeably different degrees of deflection; and if so, then many of the most frequent double and triple combinations, as well as all the twenty-six letters of the alphabet singly, might be made by simple signals. But it is also possible (although I believe highly improbable), that in practice only three or four, or some number less than thirteen, of unmistakeably different deflections could be produced in the galvanometer at one end by electric operations performed on the other extremity. If so, the whole twenty-six letters could not each have a simple signal, and double signals would have to be chosen for the less frequent letters.