On

consonant intervals, the periods of silence, or the periods of great diminution of sound, are a fraction of the periods of sound, or of the periods of maximum intensity of sound. To test this opinion I combined the sinusoids corresponding to the two tones of various smallest consonant intervals. taking as the residual duration of the sound, not the time from maximum to maximum of vibration (as in the deduction of the durations from the smallest consonant intervals), but the interval of time during which much diminished intensity of sound exists, as shown in the combined curves, I found that the durations of the sonorous sensations were thus reduced, on the average, about, whereas the reduction in time should be only to make these durations agree with those determined by the rotating perforated disks. The explanation suggested is therefore not tenable.

For the period of much diminished intensity of sound I took that length (in time) of the resultant curve which is bounded, at each end, by an amplitude of vibration maxima amplitudes of the curve. We here are in doubt as to the relative intensities of the sensations given by two sound-vibrations whose amplitudes are 2: I, and whose energies are as 4: 1. We at once face an obstacle which, from our want of knowledge, is insurmountable for, assuming that either the law of Weber, or the formula of Fechner deduced from it, correctly gives the relations existing between the intensity of a stimulus and its corresponding sensation, we cannot apply either of these laws, because we do not know the absolute energies of the soundvibrations whose sensations are to be compared. Thus, if we adopt the law of Weber, with the least perceptible difference in the sensation of two sounds equal to of their energy, as given by the experiments of Volkmann *, we find that if 1 and 4

* In the investigations on this subject of which I have knowledge, the experimenters have used either noises, or sounds of complex composi tion mingled with noise, and the ways in which they have determined the relative energies of sounds, or noise-producing vibrations, are open to criticism. I do not know of similar experiments made with simple sounds or tones. I would suggest that the problem of determining the difference in the energies of two simple sounds to give a perceptible difference in the sensations they cause may be solved as follows:-A fork or rod is vibrated with a constant amplitude, and this amplitude is accurately measured with a micrometer-microscope. A second fork, or rod, placed alongside of the first fork or rod, has a much smaller amplitude of vibration, which can be varied, and is also measured with a microscope. The second fork differs from the first slightly in pitch, so that, say, three beats per second are given. The amplitude of the secord, or of the first fork, is varied till the perception of beats just vanishes, or just appears, while the ear is kept at a fixed distance from the forks.

are the absolute energies of the sound-vibrations, we get for the ratio of their corresponding intensities of sensations 1:26; but if the absolute energies of the sounds are 10 ard 40 (and their ratio is also 1: 4), we get for their relative sensations 1: 1:48. Or, what is the same, on the curve expressing the law of Weber, or of Fechner, the ratio of the sensations of two sounds as given by their corresponding ordinates depends on the number of units in the abscissas forming the ratio of the energies of these sounds.

Professors Cattell and Fullerton, from extended experiments "On the Perception of Small Differences", very carefully made and skilfully reduced, have formed the opinion that neither the law of Weber nor Fechner's formula is correct, and à priori considerations lead them to the opinion that it is probable that the sensation is directly as the stimulus. If the sensation increases directly as the stimulus, then we can obtain the relative sensations of two sounds whose relative energies are known. Adopting this relation, we have 1 : 4 as the ratio of the maximum sensation in the periods taken

If we take for the relative intensities of the sound-giving vibrations the ratio of the squares of the amplitudes of the forks, the least perceptible difference in sensation corresponding to the differences in the energies of the sounds may be computed. As example, suppose the second fork has of the amplitude of vibration of the first. Then the energy of the maximum sounds of the beats will be 20+12=441, and the energy of the minimum sound of the beating will be 20-12-361, 441 and =the ratio of the stimuli giving the least perceptible difference 361 in sensation. Sound-vibrations of different amplitudes and of different pitch will have to be experimented with, and the fork giving the greater amplitude of vibration should, in successive experiments, be lower in pitch, and then higher in pitch, than the fork giving the lesser amplitude of vibration, for reasons set forth in my research (1) "On the Obliteration of the Sensation of one Sound by the simultaneous action on the ear of another more intense and lower sound; (2) On the Discovery of the Fact that a Sound even when intense cannot obliterate the sensation of another Sound lower than it in pitch" (Phil. Mag. Dec. 1876; 'Nature,' Aug. 10, 1876). Such a research will be difficult and tedious, and will require many precautions in arranging the experiments.

Any one may readily observe the phenomena described by sounding a fork with long amplitude of vibration, and, gradually bringing up to the ear a second fork with a small amplitude of vibration, giving with the first three beats per second. As the latter fork gradually approaches the ear the beats become stronger, reaching a maximum of intensity, and then diminishing till, at a certain distance of the fork from the ear, they vanish in the more intense sensation of the more intense sound, to reappear when the faintly vibrating fork has been brought closer to the ear.

Publications of the University of Pennsylvania,' Philosophical Series, No. 2, May 1892,

288

Mr. J. Daniel on the Polarization upon a

for those of much diminished sound to the maximum sensation in the periods of much increased sound, as given by the measurements of the amplitudes of the resultant curves of the smallest consonant intervals.

In explanation of the facts and laws given in this paper I have no hypothesis to offer. It appears to me that the present condition of our knowledge of audition demands that we should ascertain more facts relating to it before we frame hypotheses on the mechanism and action of the apparatus of hearing.

XXIV. A Study of the Polarization upon a Thin Metal Partition in a Voltameter.—Part II. By JOHN DANIEL.

IN

N this paper two questions will be discussed: first, the passage of ions through a gold-leaf partition in a voltameter; second, the minimum current-strength at which the ions are deposited visibly upon the partition for various electrolytes. This will be called the "critical current." This paper is a continuation of the work done last spring in Berlin in the quantitative measurement of the polarization upon metal partitions ranging in thickness from 0001 millim. to 02 millim. for various current-strengths in a 30-per-cent. H2SO voltameter. In those experiments there was development of gas nor polarization on a gold-leaf partition (0001 millim. thick) for the highest current used, which was four tenths to five tenths ampere.

no

The present apparatus consists essentially of a glass voltameter vessel with platinum electrodes separated by the metal partition under investigation, so that there is no path for the current except through this partition; an accurate currentmeasurer, and a strong, steady battery. The voltameter consists of an outer glass jar 8 centim. high, 8 centim. wide, and 8 centim. long; and a glass jar 8 centim. high, 5 centim. wide, and 5 centim. long, placed inside the first jar. A platinum kathode suspended by a platinum wire is placed inside the inner jar, and a similar electrode serves as anode in the larger jar, though a copper anode was sometimes used when the electrolyte was CuSO4. A hole 2 centim. in diameter was bored in one side of the smaller jar.

*Communicated by Prof. O. J. Lodge, D.Sc., F.R.S.

Glass

plates 4 centim. wide, 6 centim. long, and 1 millim. thick were bored with a hole 15 centim. in diameter. Powdered sealing-wax was placed around the edge of this hole, melted, and the gold-leaf secured to the melted sealing-wax.

This plate was then securely and perfectly (i. e. with no possible chance for leakage) sealed upon the side of the inner jar so that the gold-leaf was over the hole almost centrally. The voltameter was then carefully filled, keeping the liquid inside and outside on the same level so as not to break the gold-leaf partition, and was then ready for use.

To measure the current, a Thomson No. VI. Composite Electric Balance (No. 106), and a Weston double-scale ammeter No. 598, ranging from 0 to 1.5, reading directly to 01 ampere and estimated to 001, and from 0 to 150, reading to amperes and estimated to 01, were used in series with the voltameter. The two instruments were found to agree so well that the Weston ammeter was used alone for most of this work as it was much more convenient to read.

The battery consisted of 25 Accumulator Company "23 M" type accumulators, 350 ampere-hours capacity, 50 volts E.M.F. The current-strength was adjusted to any desired value by resistance in series, which could be varied at pleasure between zero and 12,000 ohms. For sealing-wax, pure rosin and bees-wax (without colouring-matter), mixed in such proportion as to give a low melting-point, was used. The gold-leaf used was bought in Nashville, and is known to the trade as "XX." It is about 0001 millim thick.

Careful selection was made of such parts of the gold-leaf as were found, by holding up to the light, to be free from small holes. It has already been observed, in Part I. of this paper, that when CuSO4 was used as the electrolyte and the currentstrength was over 3 ampere, Cu was deposited on the rim of the gold-leaf, which was necessarily larger than the hole in the glass plate. In this work it was found necessary to remove this gold quite close up to the edge of the hole by scraping it off, as was first tried, or by covering it carefully with sealing-wax, which was found both easier and better. This was accomplished by melting the sealing-wax over the gold with a hot brass hammer of peculiar shape made for the purpose. The wax could thus be made to flow quite close to the edge of the hole. This left only that part of the gold exposed which was immediately over the hole. To neglect this was in all cases to reduce the critical current, the deposit of the cation appearing first on that part of the gold-leaf which was nearest the anode and farthest from the opening.

Passage of the Ions through the Gold-leaf Partition.

To test this, CuSO, solution (17 per cent. i. e. 1 gram CuSO4 to 5 cub. centim. H2O) was used in the outside vessel (anode side of the voltameter), and H2SO, (30 per cent. solution, sp. gr. 1.23) in the inside vessel (kathode side of the voltameter). These solutions being separated by the gold-leaf partition, the appearance of the ions upon the electrodes and upon the partition, when the current was closed, was roted. The first method of observation was to close the circuit upon the voltameter, read the currentstrength by the ammeter, and at stated intervals weigh the Cu deposited on the kathode. This gave Table I., where it may be seen that the amount of Cu deposited was very small at first, not more than 2 per cent. or 3 per cent. the first hour, but increased rapidly with the time.

This did not settle the question as to whether the current caused the copper to pass through the gold-leaf partition

or not.

The second method was to set up two exactly similar voltameters at the same time, close the circuit on one leaving the other open, and at stated intervals weigh the Cu deposited on the kathode of the vol.ameter through which the current had passed, and at the same time make a quantitative analysis of the solution on the kathode side of both the open and the closed voltameters. This was done by extracting 10 cub. centim. from each with a pipette, and depositing the Cu electrolytically in two similar platinum crucibles conrected in series. Equilibrium was maintained in the voltameter by adding 10 cub. centim. of the 30 per cent. H2SO4 solution to replace the 10 cub. centim. thus removed. Knowing the volume of solution in each voltam eter, these analyses were sufficient to determine the total amount of Cu that had passed through the partition during the same interval for each voltameter. Table II. gives the results.

The

Here it was observed that imperceptible differences in the specimens of gold-leaf were sufficient to cause enough difference in the diffusion to leave the question unsettled. amount passing the partition of the open voltameter was as often greater as it was less than that of the closed voltameter. It was now evidently necessary to test one and the same goldleaf partition for diffusion with circuit open and closed successively. This leads to the third method shown in Table III.

It is thought that this is entirely free from objection or serious error, and leads to the conclusion that the current does not sensibly affect the diffusion of CuSO4 and H2SO,