produce the standard sound is found to be 7.4 × 10−8 C.G.S., or 7.4 × 10-7 amperes, for telephone T1.

The results obtained by the method of the revolving magnet are collected into the accompanying table. The "wooden coil" is of smaller dimensions than the "ebonite coil," the mean radius being only 3.5 centim. The number of convolutions is 370.

The method of the revolving magnet seemed to be quite satisfactory so far as it went, but it was desirable to extend the determinations to frequencies higher than could well be reached in this manner. For this purpose recourse was had to magnetized tuning-forks, vibrating with known amplitudes. If, for the moment, we suppose the magnetic poles to be concentrated at the extremities of the prongs, a vibrating-fork may be regarded as a simple magnet, fixed in position and direction, but of moment proportional to the instantaneous distance between the poles. Thus, if the magnetic axis pass perpendicularly through the centre of the mean plane of the inductor-coil, the situation is very similar to that obtaining in the case of the revolving magnet. The angle o in (2) is no longer variable, but such that sin p=1 throughout. On the other hand m varies harmonically. If I be the mean distance between the poles, 28 the extreme arc from rest to rest traversed by each pole during the vibration, mo the mean magnetic moment,

m/m。=1+2ß/l . sin pt,

The formula corresponding to (5) is thus derived from it by simple introduction of the factor 28/1.

The forks were excited by bowing, and the observation of amplitude was effected by comparison with a finely divided scale under a magnifying-glass. It was convenient to observe the extreme end of a prong where the motion is greatest, but the double amplitude thus measured must be distinguished from 26. In order to allow for the distance between the resultant poles and the extremities of the prongs, the measured amplitude was reduced in the ratio of 2 to 3. The observation of the magnetic moment at the magnetometer is not embarrassed by the diffusion of the free polarity.

In order to explain the determination more completely, I will give full details of an observation with a fork c of frequency 256. The distance between the middles of the prongs was 875 inch, and the double amplitude of the vibration at the end of one of the prongs was '09 inch. Thus 28 is reckoned as 06 inch. The inductor-coil was the ebonite coil already described, and the sound was judged to be of the standard distinctness when, for example, B=15 inches, or C=15.5 inches, and the added resistance was 1000 ohins, so that R=1100 × 109. The quantities required for the computation of (5) as extended are

X

and they give for the current corresponding to the standard sound 9.8 x 10-8 c.G.s., or 9.8 × 10-7 amperes.

A summary of the results obtained with forks of pitch c, c', e', g', c", e", g" is annexed. As the pitch rose, the difficulties of observation increased, both on account of the less duration of the sound and of the smaller amplitudes available for measurement. In one observation with telephone T2 at pitch c", the resistance, estimated at 11 ohms, was that of the coil, telephone, and leads only. No trustworthy result was to be expected under such conditions, but the number is included in order to show how small was the influence of self-induction, even where it had every opportunity

of manifesting itself. If we bring together the numbers* derived with the revolving magnet and with the forks, we obtain in the case of T1:—

It would appear that the maximum sensitiveness to current occurs in the region of frequency 640; but observations at still higher frequencies would be needed to establish this conclusion beyond doubt. Attention must be paid to the fact that the sounds were not the least that could be heard, and that before a comparison is made with the numbers given by other experimenters there should be a division by 2, if not by 3. But this consideration does not fully explain the difference between the above table and that of Ferraris already quoted, from which it appears that in his experiments a current of 5 × 10-9 amperes was audible.

It is interesting to note that the sensitiveness of the telephone to periodic currents is of the same order as that of the galvanometer of equal resistance to steady currents †, viz. that the currents (at pitch 512) just audible in the telephone would, on commutation, be just easily visible by a deflexion in the latter instrument. But there is probably more room for further refinements in the galvanometer than in the telephone.

If we compare the performances of the two telephones T1 and T2, we find ratios of sensitiveness to current ranging from 13 to 30; so that T2 shows itself inferior in a degree beyond what may be accounted for by the resistances. It is singular that an experiment of another kind led to the opposite conclusion. The circuit of a Daniell cell A was permanently closed through resistance-coils of 5 ohms and of 1000 ohms. The two telephones in series with one another and with a resistance-box C were placed in a derived circuit where was

* The observations recorded were made with my own ears. Mr. Gordon obtained very similar numbers when he took my place.

+ See, for example, Ayrton, Mather, and Sumpner, Phil. Mag. vol, xxx. p. 90, 1890, "On Galvanometers."

also a scraping contact-apparatus B, as indicated in the figure. The adjustment was made by varying the resistance in C until the sound was just easily audible in the telephone under trial. Experiments conducted upon this plan showed that T1 was only about five times as sensitive to current as T2.

1

It was

1000

B

noticed, however, that the sounds, though as equal as could be estimated, were not of the same quality, and in this probably lies the explanation of the discrepancy between the two methods of experimenting. In the latter the original sound is composite, and the telephone selects the most favourable elements-that is, those nearly in agreement with the natural pitch of its own plate. In this way the loudness of the selected sound becomes a question of the freedom of vibration of the plate, an element which is almost without influence when the sound is of pitch far removed from that of the proper tone of the telephone. There was independent reason for the suspicion that T, had not so well defined a proper pitch as was met with in the case of some other telephones.

P.S.-Measurements with the electro-dynamometer have been made by Cross and Page of the currents used in practical telephony. The experiments were varied by the employment of several transmitters, and various vowel sounds were investigated. The currents found were of the order 2 × 10-4 amperes.

XXXIV. An Attempt at a Quantitative Theory of the Telephone. By Lord RAYLEIGH, Sec. R.S.†

THE

HE theory of the telephone cannot be said to be understood, in any but the most general manner, until it is possible to estimate from the data of construction what its sensitiveness should be, at least so far as to connect the magnitude of the vibratory current with the resulting condensations and rarefactions in the external ear-passage.

* Electrical Review, Nov. 14, 1885. I owe this reference to Mr. Swinburne.

+ Communicated by the Author, having been read at the Oxford Meeting of the British Association.