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current of any magnitude at low temperatures, but at high temperatures it does.
Chromic chloride solution.
If the E.M.F. of the cell be measured on a potentiometer, or by means of a ballistic galvanometer and condenser, by either of which methods the cell is not called on to produce a current, it is found that the E.M.F. at all temperatures is approximately volt, and that the E.M.F. is slightly less at the boiling-point of water than at the ordinary temperature.
The explanation of the results is not difficult. The cell polarizes very rapidly at low temperatures, and the opposing E.M.F. of polarization increases so rapidly and so largely that almost at the moment of connexion the effective E.M.F. becomes zero. The cell behaves like a condenser which is connected to a battery through a very high resistance. Such a condenser would discharge itself when its plates were connected, but when they were isolated again it would slowly become charged by the battery through the high resistance.
At the high temperature the polarization is very largely reduced, and the cell will produce a continuous current.
Another interesting feature of the cell is that it may be used as the mechanism of a heat-engine for the production of work, and we can trace in it the complete cycle of Carnot. Let the cell be placed in a hot chamber, and work may be derived from it until all the CrCl or the tin is used. Then let the cell be placed in a cold chamber, it will give up heat, and becomes restored to its original chemical condition.
Measurements of the electromotive force of two cells are
given in the following tables. The first cell contained tinamalgam, and the second cell contained a tin rod. Both cells had not been used for producing current within the 24 hours immediately preceding the measurements.
Connexion was made and a current allowed to flow for 1 minute, and then the cell was allowed to rest for 1 minute :
These results showed that the cell had polarized, and was only slowly recovering its electromotive force.
When a solution of the green chromic chloride at the ordinary temperature has silver nitrate added to it, only twothirds of the chlorine is precipitated. This, according to the theory of ionisation, indicates that only two atoms out of three act as negative ions, the other atom apparently being part of the positive ion. On the other hand, if a solution of chromic chloride near 100° be treated with silver nitrate, the whole of the chlorine may be precipitated. This indicates that at the higher temperature all the chlorine atoms behave as negative ions.
Taking this into account, the Grotthus chain representing
the action of the cell about 15° must be as follows:
Pt | ClCrCl | CICrCl2 | CICrCl2 | Sn,
becoming, after connexion,
Pt,ClCr | C1,ClCr | Cl2CICr | Cl2Sn.
This view of the action leaves the ion ClCr polarizing the cell. Now if a depolarizer acts so as to remove this ion, the cell will go on producing a current. The excess of chromic chloride might perform this function, forming with this ion chromous chloride :
CrCl + CrCl3=2CrCl2.
The behaviour of the cell shows that this does not take place readily.
A similar view of the action in the cell at about 100° indicates the presence of chromium ions as the polarizing agent. At this temperature there is not much polarization; so that it appears the following chemical change takes place readily: Cr+ 2CrCl3=3CrCl2.
XLIII. Some Acoustical Experiments. By CHARLES V. BURTON, D.Sc., Demonstrator in Physics, University College, London*.
I. Subjective Lowering of Pitch.
YEAR or two ago, in the physical laboratory of Bedford College, London, the professor, Mr. Womack, called my attention to the fact that a tuning-fork which was being used by a student appeared to rise perceptibly in pitch as the vibration died away. It then occurred to me that the effect observed might be a subjective one that one result of increasing the intensity of a musical note without changing its frequency, might be to depress the pitch as estimated by ear. To determine this point I have made experiments upon myself, and on others whose perception of musical intervals was known to be reliable.
2. Let a tuning-fork mounted on a resonance-box be strongly excited by bowing, and immediately let the open end of the resonance-box be brought very close to one ear, the other ear being preferably closed. After a second or so, let the fork and box be moved away from the ear and held at arm's length, then brought close to the ear again, and so on, backwards and forwards, two or three times. If there is any * Communicated by the Physical Society: read March 22, 1895.
subjective depression of pitch accompanying increase of loudness without change of frequency, the fork will appear to be lower in pitch when close to the ear and higher when further away, the effect becoming less marked as the vibration gradually dies down. This is what observation shows to be actually the case, and it is evidently nothing of the nature of a Doppler effect with which we are here concerned. In the first place, the motion of the fork from one position to the other may be made quite slow; and in the second place, the difference of pitch is observed, not between the fork approaching and the fork receding, but between the nearer and further positions of the fork.
3. In some of these observations a fork giving the note d (256 complete vibrations per second) has been used, the effect with forks of higher pitch being less marked. When the vibration was made as strong as possible by means of bowing, the lowering of pitch was found to amount to a full semitone (15:16). Mr. Womack, Prof. Ramsay, and Dr. G. F. McCleary, who repeated the experiment, all agreed pretty nearly with my estimate: in each case the greatest apparent flattening observed was as much as a semitone.
With a large fork giving e (one octave lower) the effect was more striking. In this case the fork with its resonance-box was too unwieldy to be moved bodily to and fro, so it was allowed to stand on a table while the observer's head was lowered so as to bring one ear opposite to the opening of the resonance-box at a distance of a few inches. Thus the fork was heard with great intensity, while on raising the head through half a metre or so the loudness was greatly diminished. Here the lowering of pitch due to the greatest intensity of vibration which I could excite in the fork amounted usually to a minor third (56) or even more. Thus, repeating the experiment on different days, I have estimated the interval sometimes as rather more and sometimes as rather less than a minor third. Mr. Womack heard something between a minor and a major third; Professor Ramsay a full tone; Dr. McCleary more than a minor third.
4. Before saying more concerning the observations, it will be convenient to mention a physiological theory by which I have attempted to account for the observed effects. Helmholtz's discussion of the vibration of the basilar membrane in the cochlea is applicable only to infinitesimal amplitudes, inasmuch as all his equations of motion are linear, and though the introduction of terms of higher order would have made the investigation very lengthy and an exact solution impossible, it is not difficult to see on general grounds what
modification of the sense of pitch is to be expected from increased loudness. If the basilar membrane may be regarded as being stretched with a finite tension in the direction of its breadth, and as having no appreciable tension in the perpendicular direction, then Helmholtz shows that it will be vibrationally equivalent to a series of strings stretched side by side and unconnected with one another. For shortness, I shall speak of the membrane as if it actually consisted of such separate strings, and thus, following Helmholtz's theory, we are to suppose that a disturbance of given period reaching the ear excites the strongest resonance in those strings whose natural period is most nearly the same. Now when a string is vibrating freely with finite amplitude, the period of its vibrations is shorter than if the amplitude were infinitesimal; and we are accordingly led to enquire whether a periodic force of considerable intensity would not excite the maximum resonance in those strings whose natural period for some finite vibration-amplitude was most nearly the same.
5. As sufficiently representative of our case we may take a system with one degree of freedom, in which the positional force contains a term proportional to the cube of the displacement from equilibrium, as well as one proportional to the first power*, the equation of motion being accordingly written
F=mx+kx+hx 1 +
where F is the external force impressed on the system, a is the displacement from the equilibrium position, and m, k, h, a are real constants.
If we take F to be a simple harmonic function of the time whose character has been maintained long enough for the whole motion to have become periodic, the value of a will be expansible in a Fourier's series in which the constant coefficients have to be determined. But the expressions thus obtained are very unwieldy; and it will therefore be more convenient to treat a instead of F as a simple harmonic function of the time. It is not easy to say definitely which assumption corresponds most nearly with the actual case, and from what follows I think it will be evident enough that whichever case we consider the general conclusions would be much the
* Terms of even degree would imply that the free vibrations were not symmetrical with respect to the equilibrium position, and would therefore be absent in the case of a stretched string, which we have supposed to agree pretty nearly with the physiological case.