and not the first for a, on account of its being faulty, we get

The criterion of areas applied to those experiments gives very close results. The approximately true areas are given by the formula

and the real areas are found by assuming the curve to be

which gives for the area between the curve and axes, taking the limits for y of first and last experiment,

In all the experiments given in this paper there is one special point to which I wish to draw attention; and that is that only two observations are taken to find the necessary constants; if these had been calculated for each pair of observations and the means taken, better agreement with theory would doubtless have been obtained; but such a procedure is apt to throw doubts on a theory, as to which, if it were true, one observation should be as good as another for determining the constants, unless large errors were suspected.

Before selecting those observations which were to be taken for the constants, the first few were laid off graphically, and those which seemed to be the most regular were chosen.

Influence of Temperature.-Chemical decompositions are all more or less influenced by heat, the effect being an acceleration of the rate of change; but it is very probable there is a point at or below which temperature no change can take place, as in the many cases where an acid has not action on a body at the ordinary temperature, while on heating to about 100° C. change goes on briskly.

The relation of the rate of change to the temperature and the point of zero action are possible to be discovered by the foregoing experiments in a simple manner.

It has been shown that the rate of change is expressed by the equation

dy dt

and if it be proportional to an unknown function of the temperature f(), 0 being degrees Centigrade above the zeropoint, so that

integrating,

dy_

=—μf(0)y3,

dt

1

writing it in the usual form,

b=y(a+t),

b and a being determined experimentally. If for a second experiment under exactly the same conditions, but temperature differing by n° C., the equation is found to be

but it does not follow that is also equal to this ratio, unless

a α

the value for y when t=0 is the same in each case.

A number of experiments were made to determine ƒ(0); but as the temperatures ranged only from 18° to 22° C., and they are rather incomplete, I refrain from giving them fully; the results, however, seemed to indicate that ƒ(0)=02, or that the rate of change varies as the square of the temperature from the zero-point; and on this hypothesis the point of no action was found to range from +2° C. to -2° C., or about the temperature at which the solution would become ice.

In conclusion, I may state that the following experiments were made. An increase in the amount of H2SO4 accelerates the change, still obeying the law. Ferrous chloride, in presence of HCl, is oxidized by KClO3, at 18° C., approximately according to the law y(a+t)=b, the discrepancies in this case being caused by the difficulty of accurately determining the iron by permanganate in presence of free hydric chloride. Ferrous sulphate in hydric sulphate is only very slowly acted on by potassic nitrate in the cold, probably being too near the zero-point.

I hope soon to give the results of some experiments on the rates of change for the various chlorates, as potassic against sodic chlorate, and possibly get some relation between the dynamical equivalences of those salts.

Glasgow, August 1878.

L. Phenomena of Binaural Audition.-Part II. By SILVANUS P. THOMPSON, D.Sc., B.A., Professor of Experimental Physics in University College, Bristol*.

1.

N a paper read before Section A of the British Associa

the

communicated the discovery of two phenomena: first, the existence of an interference in the perception of sound; secondly, an apparent localization of simple sounds at the back of the head when led to the two ears in such a manner that the vibrations reached the ears simultaneously in opposite phases. The present paper recapitulates the former experiments, and gives some further account of the phenomena and of new methods of experimentation.

2. The existence of an interference in the perception of * Communicated by the Author.

+ Rep. Brit. Assoc. Plymouth, 1877, p. 37; Phil. Mag. October 1877,

p. 274.

sounds was demonstrated by leading separately to the ears with india-rubber pipes the sounds of two tuning-forks struck in separate apartments, and tuned so as to "beat" with one another-the "beats" being very distinctly marked in the resultant sensation, although the two sounds had had no opportunity of mingling externally, or of acting jointly on any portion of the air-columns along which the sound travelled. The experiment succeeded even with vibrations of so little intensity as to be singly inaudible.

3. The apparent localization at the back of the head of sounds whose vibrations reach the ears in opposite phases being a subjective phenomenon, was announced by the author as the result of the concurrent testimony of several independent witnesses. Its existence was demonstrated by leading separately to the two ears the sound of two unison tuningforks, one of which was slightly loaded to make its phase change slowly relatively to the other. The "beats" were described as being not "silences," as ordinarily observed when the difference of phase is half a complete vibration, yet as being "most distinctly heard, and seeming to be taking place within the cerebellum." Referring to this attempt to ascertain the effect of bringing to the two ears waves of equal pitch and intensity, but differing in phase, the author stated that a fuller series of experiments was in course of completion. The sequel of the present paper records with what result those experiments have been made.

4. The telephone of Graham Bell, introduced into this country at the Meeting at Plymouth, where the former paper was read, furnishes a new instrument peculiarly adapted for researches of this nature. Both the phenomena recapitulated above have been reobserved by a considerable number of independent experimenters, confirming the results announced by the author. Thus it was announced by Professor Graham Bell, in a lecture before the Society of Arts, November 28, 1877 *, that these two phenomena had been discovered by Sir William Thomson when experimenting at Glasgow with the telephone.

One important advantage of the Bell telephone as an instrument of research is that the phase of vibration can be inverted at will, by reversing the connexions of the receiving-instrument, so that the currents traverse the coil in a reversed direction, the motion of the vibrating disk being consequently also executed in a reverse sense. Using two systems of telephones to bring to the ears two sounds capable of yielding interferencebeats, interference in the resulting perception of the sounds is

* Vide Journal of the Society of Arts, vol. xxvi. No. 1306, p. 22 (Nov. 30, 1877).

very clearly recognized. I have not been able hitherto, however, to devise any crucial experiment to decide whether the interference is an interference of the sensations, or whether it is to be attributed to the physical conveyance of the sounds through the bones of the skull, and their mechanical interference.

5. Phenomena of Localization.-Almost all persons who have experimented with the Bell telephone, when using a pair of instruments to receive the sounds, one applied to each ear, have at some time or other noticed the apparent localization of the sounds of the telephone at the back of the head. Few, however, seemed to be aware that this was the result of either reversed order in the connexion of the terminals of the instrument with the circuit, or reversed order in the polarity of the magnet of one of the receiving-instruments. When the two vibrating disks execute similar vibrations, both advancing or both receding at once, the sound is heard as usual in the ears; but if the action of one instrument be reversed, so that when one disk advances the other recedes, and the vibrations have opposite phases, the sound apparently changes its place from the interior of the ear, and is heard as if proceeding from the back of the head, or, as I would say, from the top of the cerebellum. So distinctly marked is the apparent localization, that it has been regularly employed, I am informed, by Professor D. E. Hughes to ascertain whether a pair of receiving-telephones are rightly adjusted or not.

6. My recent experiments have been directed to determining how this apparent localization is affected by variations of the sounds in respect of (a) pitch, (b) phase, (c) intensity, (d) quality, and whether it is to be accounted as a physical, physiological, or psychological phenomenon. I have made, finally, a few experiments on the binaural estimation of combinational tones.

appa

(a) After employing the simple sounds of tuning-forks of various pitches, and conveying their vibrations to the two ears in opposite phases by three distinct methods, I find the rent locality of the sound (the acoustic "image") to occupy an invariable position near the top of the cerebellum. These three methods are:-First, employing two india-rubber tubes of equal length, armed with either glass funnels or box resonators, in front of which two tuning-forks are held, difference of phase being obtained by rotating one fork round on its axis, or by loading it to obtain a continuously varying phase. Secondly, by employing one tuning-fork, but having a branching tube to the ears, and making the lengths of the two branches differ by half a wave-length. Thirdly, by emPhil. Mag. S. 5. Vol. 6. No. 38. Nov. 1878.

2 C