SN, and SP. Let the semiaxes of the equator be expressed by the relations

a2=k2(1+i); b2=k2(1—i),

where i is a very small quantity whose square is to be neglected. Then the coordinates x, y, z of any point, as S, are proportional to

(1+i) cos w: (1−i) sin w: tan 6.

k2

Substitute these in (6), (7), (8), and we get finally the following results for the angles between the lines in question:

c2

MSP=-i sin & sin 20(1+ sin2 + k2 cos2 4.

In the figure of the earth, as determined in the paper in the 'Memoirs of the Royal Astronomical Society' for 1860, there is a difference of a mile between the greatest and least radii of the equator. Although this seems but a small departure from the form of a circle, yet i=52"-33 (in parts of radius unity), and the angles expressed above become somewhat large quantities. Supposing S to be on a meridian midway between the greatest and least radii of the equator, the angle between the "meridian" and the "north line" is 52"-33 sin ; and the defect of MSP from a right angle is about double this quantity. So large an angle as this should be detected by firstrate geodetic observations, though it would require a somewhat long measurement of meridian and parallel. It is to be remembered that, SM, SN being directed towards the north, and SP towards the minor axis of the equator, SM lies between SP and SN.

And in an ellipsoidal earth the direction of the principal sections of the surface (that is, of maximum and minimum curvature) are no longer coincident with meridians, north lines, or parallels. Supposing that S is not in a very high latitude, one of the lines of curvature, as SR through S, will lie somewhere in the direction of SP, and the second line of curvature will be perpendicular to SR. It may be shown that the angle

an expression which does not hold in high latitudes; for in the vicinity of the umbilics, the lines of curvature are approximately confocal conics having the umbilics as foci. The defect

of RSN from a right angle might, with the value of i we have been supposing, amount to some degrees without going to any high latitudes.

It appears, then, that it would not do to take the longitudeequations which we have used for the determination of a spheroidal figure for the earth also for the determination of an ellipsoidal figure. The only thing that can be done under the circumstances is to take simply the longitude-arc between Bombay and Vizagapatam, as these points are nearly in the same latitude, and to reduce it according to the expression for the length of an arc of parallel on the surface of an ellipsoid, given in the before-mentioned paper on the Figure of the Earth, page 43.

Then, with fifty-one equations I get the following:

u=-0.4903; v = +0.2842; w=+0·3599; z=-0.1067.

From these quantities the following values finally result:

a=20926629;

b=20925105;

c=20854477.

If by the word "ellipticity" of an ellipse we mean the ratio of the difference of the semiaxes to half the sum of the same, the ellipticities of the two principal meridians of the earth are

This

The longitude of the greater axis of the equator is 8° 15' west of Greenwich-a meridian passing through Ireland and Portugal and cutting off a portion of the north-west corner of Africa; in the opposite hemisphere this meridian cuts off the north-eastern corner of Asia and passes through the southern island of New Zealand. The meridian containing the smaller diameter of the equator passes through Ceylon on the one side of the earth and bisects North America on the other. position of the axis, brought out by a very lengthened calculation, certainly agrees very remarkably with the physical features of the globe-the distribution of land and water on its surface. On the ellipsoidal theory of the earth's figure, small as is the difference between the two diameters of the equator, only 3000 feet, the Indian longitudes are better represented than on the spheroidal; but there is still left at Madras and Mangalore an attraction or disturbance of the plumb-line seawards.

As to the relative evidence for the two figures presented in this paper, the sum of the squares of the residual corrections to the astronomical observations is, of course, less in the ellipsoid than in the spheroid; but the difference is certainly small. The radius of curvature perpendicular to the meridian in India, in latitude 15° say, is, on the spheroid, 20930972 feet, whereas on the ellipsoid it is 20932877; and this last is distinctly more in harmony with the Indian Longitude Observations.

Ordnance Survey Office, Southampton,
June 15, 1878.

THE

XIII. On Telephony. By W. SIEMENS*.

HE surprising performances of the telephones of Bell and Edison rightly claim in a high degree the interest of natural philosophers. The solution (facilitated by it) of the problem of the conveyance of tones and the sounds of speech to distant places promises to give mankind a new means of intercourse and culture which will essentially affect their social relations and also render substantial service to science; and hence it seems fitting that the Academy should draw these exceedingly promising discoveries into the sphere of its contemplations.

The possibility of reproducing mechanically not merely tones, but also noises and spoken sounds, at great distances is given theoretically by Helmholtz's path-opening investigations, which elucidated the essential nature of shades of tone and the sounds of speech.

If, as he has demonstrated, noises and sounds are only distinguished from pure tones by the fact that the latter consist of simple, the former of a plurality of series of undulations, superposed to one another, of the sonorific medium, and if the noises of speech (Sprachgeräusche) may be conceived as irregular vibrations with which the vocal sounds begin or end, then it is also possible to reproduce mechanically a certain succession of such vibrations at distant localities. Indeed practical life has in this, as is frequently the case, outrun science. The hitherto too little regarded so-called "speaking telegraph," consisting of two membranes stretched by a strong and at the same time extremely light thread or fine wire which is fastened to their centres, effects a perfectly distinct transmission of speech to a distance of several hundred metres. The threads or wires can

Translated from the Monatsbericht der königlich preussischen Akademie der Wissenschaften zu Berlin, January 1878, pp. 38-53.

be supported at any number of points by elastic threads of a few inches length, and also, with similar elastic fastenings at the angles, from any number of angles, without the apparatus losing the capability of conveying with perfect distinctness and correctness completely toneless whispered speech-a performance which previously no electric telephone could accomplish. Although this "speaking telegraph," or, more correctly, "thread telephone," possesses no practical value (since its working is still limited to short distances and is interrupted by wind and rain), yet it is most deserving of notice, because it proves that stretched membranes are fitted to take up, almost completely, all the air-vibrations by which they are struck, and to reproduce in another place all speech-sounds and noises when mechanically put into similar vibrations.

Reis, as is well known, was the first to endeavour to operate the conveyance of tones by electric currents instead of a stretched thread. He made use of the vibrations of a membrane exposed to sound-waves to produce closing contacts of a galvanic series. The current-waves hereby generated traversed, at the other end of the conduction, the coil of an electromagnet, which, provided with a suitable resonancearrangement, again produced approximately the same tones by which the membrane, struck by the sound-waves, had been set vibrating. This could only be done very imperfectly, since the contact-arrangements only became effective with the greater vibrations of the membrane, and could only imperfectly render even these.

Bell appears first to have had the happy thought to let the vibrating membrane itself call forth the currents serving for the transmission of its vibrations-making it of soft iron, and placing its centre opposite and very near to the end of a steel magnet wound round with insulated wire. By the vibrations of the membrane the attraction between the plate and the magnet, and therewith the magnetic potential of the wireenveloped end of the bar-magnet, were alternately augmented and diminished; by this, in the wire of the coil and in the conduction, currents were produced which, with the minuteness of the vibrations of the plate, generated electrical sine vibrations corresponding to the vibrations of the mass of air, which were thus in a condition to call forth again membraneand air-vibrations in a similar apparatus at the other extremity of the conduction. The result was unaffected by the circumstance that, as Du Bois-Reymond* has pointed out, in the receiving membrane the phases and ratios of amplitude of the partial tones are different from those in the emitting membrane. * Archiv für Physiologie, 1877, pp. 573, 582,

An essentially different path was struck out by Edison (as it appears, simultaneously with Bell). He uses a galvanic series, which sends a constant current through the conduction.

At the sending end a layer of powdered graphite, which is gently pressed between two metal plates insulated one from the other, is inserted in the circuit. The upper plate is fastened to the vibrating membrane, and presses the graphite powder more or less together in correspondence with the airvibrations. By this the resistance of the graphite to conduction is correspondingly varied, and thereby sinusoid variations, equivalent to the air-vibrations, are produced in the intensity of the current passing through the conducting line. As receiving-apparatus, Edison uses no membrane, but another and quite peculiar contrivance. It is based on the experience that the friction between a piece of metal and a paper band saturated with a conducting fluid and pressed against the metal is diminished when a current passes through the paper to the metal. I have verified this remarkable phenomenon for the case in which the direction of the current is such that hydrogen is separated at the metal plate, or when the metal is not oxidizable. Hence the lessening of the coefficient of friction by the current evidently proceeds from electrolytically generated gases deposited on the plate of metal. Surprising, however, remains the almost instantaneous rapidity with which the effect takes places even with very feeble currents.

Now Edison attaches the metal plate, pressed against the moist paper, to a sounding-board, and draws the moist paper, which is carried over a roller, under the metal piece by continual rotation of the roller. If now the metal piece and the roller (also of metal) be inserted in the galvanic circuit, the variations produced in the current by the greater or less pressure of the graphite powder effect equivalent variations of the friction-coefficient between the metal plate attached to the sounding-board and the paper, whereby the former is put into corresponding vibrations, which are communicated to the sounding-board, and through this to the air.

Edison's telephone is very remarkable on account of the novelty of the expedients employed in it; but it is obviously not yet complete for practical use; while Bell's telephone has, in its remarkably simple form, been widely spread in a short time, especially in Germany; and already much material of experience has been accumulated for judging of its usefulness. Its principal defect consists in the feebleness of the reproduced sounds, which, in order to be distinctly understood, require the sound-aperture to be pressed to the ear, and at the other end an immediate speaking into it. Per