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complete. This view is still further confirmed by the production of beats from the excitation of separate ears. There must be a deeper action than that considered by Helmholtz, a kind of interference in the sensorium itself instead of, or rather, in addition to, the interference of vibrations in the inner ear.

III. Intensity of Sound as related to Amplitude of Vibration. In the ordinary statement that the intensity of sound is proportioned to the square of the amplitude of vibration, a proposition that has of late been clearly recognized as applying in any case only to sounds of the same pitch, the complexity of the relation between the intensity of the vibration exciting the ear, and the resulting sensation has been universally lost sight of. Probably, though not certainly, the Psychophysic Law of Fechner applies to intensity-variations, and the sensation certainly does not increase as rapidly as the exciting cause. Hence, in strictness, we cannot assume the ordinary statement to be accurately true except in applying it to objective sound. It is a mechanical rather than an aural measure of the intensity, that we assume.

Also in the diminution of intensity with increase of distance, the sensation must diminish less rapidly than the law of inverse squares would lead us to suppose.

IV. On a Musical Application of the Principle of Fatigue. In the so-called "Voix celeste" stop in cabinet organs a tremolo is produced by calling into play two sets of reeds just out of unison with each other, which make slow beats with each other and with the notes produced on other stops in use at the same time. Besides this, there is a remarkable strengthening of the whole body of tone from the instrument. This seems to arise from the increased average intensity of the sensation due to the alternate increase and decrease of sound, which, however, with the slow beats used, is not so great as to become harsh and painful.

ON A PROPOSED METHOD FOR ASCERTAINING THE LEAST NUMBER of
VIBRATIONS NECESSARY TO DETERMINE PITCH. By Prof. CHAS.
R. CROSS, Mass. Institute of Technology, Boston, Mass.
[ABSTRACT]

THE methods hitherto used for this purpose are all of them defective for the reason that the vibrations produced are complex in their nature instead of being pendular. In the method proposed

pendular vibrations are employed. Two magnetic-telephones are connected up with each other in the usual manner, and a circuitmaking wheel with a single radial metallic strip is interposed, so that by the rotation of the wheel the circuit shall remain closed for a short interval, which can be determined by the rapidity of rotation. If the sound of a tuning-fork giving pendular vibrations is transmitted through the circuit a greater or less number of these vibrations, or even a fractional part of a single one, can be caused to act upon the ear. Suitable precautions are taken to avoid the production of extraneous sounds in the circuit itself. A properly adjusted microphone transmitter with an induction coil may be substituted for the magneto-transmitter, the circuit-making wheel being placed in the secondary circuit.

UPON A GENERATOR IN USE AT CORNELL UNIVERSITY FOR PRODU

CING OXYGEN AND HYDROGEN GAS BY MEANS OF THE DYNAMO

MACHINE. By Prof. Wм. A. ANTHONY, Cornell University,
Ithaca, N. Y.

[ABSTRACT.]

THE generator which forms the subject of this paper has now been in use for more than three years at the Cornell University with such good results that it is deemed worth while to give some account of it. The generator consists of twelve cells, each cell being essentially a U tube of white earthen ware with suitable openings for introducing the electrodes and for replenishing the fluid. The electrodes are of platinum foil 2 X 5 inches, attached to the ends of lead tubes which serve at the same time for conveying the current and delivering the gas. The openings are stopped by paraffined corks, and the tubes from the several cells are connected to the general delivery tubes (of lead) in the same way. twelve cells are connected electrically in series.

The

In an experiment to determine the maximum amount of gas to be obtained by the power at command (about 5 H. P.) the result was as follows:

Amount of both gases evolved in three hours 544.8 litres, or .00226 grms. per cell per second. This would correspond to 24.49

ampères, while a large tangent galvanometer indicated 25.22. The discrepancy is not surprising as the amount of gas was determined by measuring the rise of the gasholders, four feet in diameter, in which the gas was collected, a measurement not calculated to give very great accuracy.

The E. M. F. employed was 123.08 volts, and the energy employed 3104.08 watts.

The useful energy represented by the gases generated was 429 watts, and the efficiency 13.8 per cent. This is a small efficiency, but it is evident that it might be much increased for the same apparatus by using less energy per second, and producing gas less rapidly. In another experiment in which only three-fourths as much gas per hour was obtained, the usual rate of running the apparatus, the efficiency was twenty-four per cent. The resistance of the cells might be much diminished and their efficiency increased by using in place of the U tube, a vessel with a porous partition extending to near the bottom. The part of the partition above the liquid could be glazed; but even if it were not, there would be no appreciable mixture of the gases through it, since it would be always wet.

DETERMINATION

OF THE

COEFFICIENT OF EXPANSION OF THE

SPECULUM METAL USED FOR ROWLAND'S GRATINGS. By Prof.
WM. A. ROGERS, Harvard Observatory, Cambridge, Mass.

[ABSTRACT.]

THE Coefficient of the speculum metal cast by Mr. Brashear with the components given by Professor Rowland, and determined in this paper, was derived from a half yard and half meter bar prepared for Professor Wead of Michigan University.

The comparisons were made as follows;

(a) With the steel screw of dividing engine.
(b)* *With bronze meter R2

(c)* With steel meter R

*See Proceedings American Academy Vol. XVIII, p. 382.

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The absolute coefficient of this particular piece of metal is therefore 17.99 for each degree Centigrade.

ADDITIONAL OBSERVATIONS CONFIRMING THE RELATION:

METRE DES ARCHIVES IMPERIAL YARD +3.37027 INCHES. By Prof. WILLIAM A. ROGERS, Harvard Observatory, Cambridge, Mass.

[ABSTRACT.]

SINCE the determination of the relation between the yard and the meter, communicated to the Association at the Minneapolis Meeting, additional data bearing upon the subject have been obtained. It will be remembered that the relation was derived from a yard and meter laid off upon a bar of bronze having the same form and dimensions in cross section as the Imperial yard.

A

B

C

Representing the yard by the line AB, and the meter by the line AC, the operation consisted:

(a) In the determination of the length of AC in terms of the Metre des Archives, A, through a comparison with a meter upon copper traced and standardined by Tresca and with a meter upon brass belonging to the Stevens Institute and compared with Type I of the International Bureau of Weights and Measures at Breteuil by Dr. Benoit.

(b) In the determination of the length of AB in terms of the Imperial Yard through comparisons with "Bronze 11" belonging to the United States Coast Survey and with a yard upon brass belonging to the Stevens Institute which has been compared directly with the Imperial Yard by Mr. Chaney, Warden of the Imperial Standards.

(c) The determination of BC in terms of either AB or AC. Under these divisions the following additional data have been obtained:

(a) In my paper Studies in Metrology, Proceedings of the American Academy, Vol. XVIII, p. 382, the following relations are given:

From a comparison of the bronze metre R and the steel meter R1 with the Tresca metre T, designating the metre des Archives by A, we have:—

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From a comparison of the metres R1 and R2 with the Stevens Institute Meter designated CS,

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The values of the coefficient of expansion for the bars T, CS, R1 and R, were found as given on page 380, viz.:

For T, coefficient for 1°C. = 16.18μ.

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The length of the meter CS was derived from the provisional relation communicated by Dr. Pernet, viz. :

CS at 0°C. +310.0μ = A。.

The coefficient of expansion of this metal determined at Breteuil had not been communicated at the time of the publication of my paper. It was, therefore, necessary to use the value given above, viz., 17.60μ in the reduction to 16.67° C. or to 62.0° Fahr.

In February last, I received from Dr. Pernet not only the exact observed relation between C S and Type I of the Bureau, but also the adopted value of the coefficient for this bar. The following are the relations communicated:

CS310.7

Coefficient of CS

Ao

17.71 for each degree C.

Substituting these values for those originally employed, we have the following relation between R2 and A.:

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