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2. Glowing gases can be obtained of a temperature below 150° C. (cold flames).

3. Sodium salts emit light in flames only as a consequence of chemical processes.

4. Metallic sodium heated in neutral gases emits light only as a consequence of chemical processes.

5. The assumption that gases can emit light by mere elevation of their temperature is a hypothesis demanded neither on experimental nor theoretical grounds.

These conclusions, which go to the root of spectrum analysis, are, it must be admitted, of the most serious importance. I am not satisfied that they are warrantable, and wish to direct attention to the following points:

(I.) The fifth, and in all probability the first, conclusion (supra) of Pringsheim is contradicted by the experiment with iodine vapour which I have already described (p. 252).

(II.) The second conclusion of Pringsheim is unwarrantable, for the reasons stated in the first part of this paper. It may be that a certain disulphide air-flame can be obtained having an average temperature below 150° C. This tells us nothing of the temperature of the molecules of CO, and SO2 which are formed in the flame. Theory, on the other hand, would assign to them a very high temperature if the heat produced in their birth is assumed to be stored in them for an instant. The ready inflammability of the mixture only points to the relatively great distance at which the combining molecules of CS, may be apart, and to the interpolation of a large number of non-burning molecules which tend enormously to lower the average temperature of the flame. (III.) Pringsheim's third and fourth conclusions are undoubtedly the most serious. Metallic sodium, he says, heated in neutral gases emits light only as a consequence of chemical processes. This conclusion is reached only by indirect evidence. In the first place, I would remark on the fact that according to Pringsheim (loc. cit. p. 444) the admission of carbon dioxide to the hot porcelain tube, in which the sodium spectrum has been developed by the action of hydrogen on sodium compounds, does not destroy the spectrum, while air does so immediately. Why is this? Hot sodium vapour and carbon dioxide are quite incompatible; surely CO2 and air ought both to extinguish the spectrum; both are powerful oxidizing agents to sodium. The important experiments are those with the movable iron or nickel boat, and in these another difficulty with CO, appears. After withdrawing the

iron boat from the hot part of the tube filled with CO2, the spectrum does not fade to the degree anticipated but acquires a stationary intensity. This is attributed to the lingering of sodium vapour, which attacks the sodium silicate with which the interior of the tube has become coated in previous experiments. A "reciprocal" reaction is said to take place: the sodium vapour attacks the silicate, liberating other sodium vapour, a process at first rapid but gradually attaining equilibrium. After this the process goes on steadily, sodium liberating sodium. This seems to me to be a very extraordinary assumption, and more a robbing of Peter to pay Paul than the picture of a chemical equilibrium. We are to suppose that a film of sodium silicate-at the most, liquid-in contact with sodium vapour, and above all in an oxidizing atmosphere of carbon dioxide, is constantly giving and taking sodium atoms so as to keep up the chemical action which Pringsheim demands for the development of the sodium spectrum. Such a state of things will be, I imagine, as surprising to chemists as it is novel. It is true that dissociation phenomena are pictured as involving a constant in-and-out movement of the products of dissociation from the compound undergoing dissociation. But if sodium acts on sodium silicate at all it will be to liberate silicon, and after that is complete we can only assume the resulting sodium oxide to react with fresh sodium at the temperature at which sodium oxide dissociates. We have no knowledge of the dissociation of sodium oxide. If, as I venture to think, Pringsheim's explanation of this point is not to be accepted, there is less difficulty in accounting for his other observations, for the sudden reduction of the intensity of the spectral effect in hydrogen when the boat is suddenly withdrawn is only important in comparison with what occurs in CO2. I do not see any cause for surprise that the intensity of the spectrum should suddenly diminish in hydrogen when the boat is withdrawn suddenly. One would expect the moving boat to drag its small atmosphere of sodium vapour with it to the cool part of the tube, and, again, one would not expect the spectrum to persist in air. I can, therefore, see no adequate grounds for the important conclusion which Pringsheim draws from these experiments, namely, that metallic sodium only gives its spectrum when undergoing chemical change.

I may summarize the views above expressed as follows:1. There is no evidence for, but much against, the supposition that sodium salts when introduced into a flame are dissociated by heat so as to liberate the metal.

2. There is great difficulty in accounting for the reduction of the metal by purely chemical processes.

3. Arrhenius's hypothesis of ionic dissociation in flames is a chemically acceptable way of accounting for the liberation of sodium when its salts are heated in flames.

4. There is no direct evidence and no decisive indirect evidence that the sodium spectrum is the direct consequence of the chemical action in which the atoms are engaged.

Postscript.

In a recent number of Wiedemann's Annalen* there is a paper by Paschen in which he shows by bolometric measurements that the invisible spectra of hot gases exhibit distinct maxima of intensity-that, in short, gases do give discontinuous spectra on being heated, independently of chemical action. On these grounds and others, some of which are similar to those explained in the foregoing paper, Paschen does not consider that Pringsheim's conclusions can be accepted.

[To be continued.]

XXIII. Researches in Acoustics.-No. IX. By ALFRED M.
MAYER, Ph.D.†
CONTENTS.

1. The Law connecting the Pitch of a Sound with the Duration of its Residual Sensation.

2. The Smallest Consonant Intervals among Simple Tones.

3. The Durations of the Residual Sonorous Sensations as deduced from the Smallest Consonant Intervals among Simple Tones.

1. On the Law connecting the Pitch of a Sound with the Duration of its Residual Sensation.

N October 1874 I published in the American Journal of Science Paper No. 6 of Researches in Acoustics, which contained an account of my attempts to establish the law connecting the pitch of a sound with the duration of its residual sensation. The law given in that paper was the expression of the results of the first experiments, extending through several octaves, ever made on the duration of sonorous sensations.

Subsequently, in April 1875, I published in the American Journal of Science ‡ the results of similar experiments which *Vol. 50. p. 409 (1893).

+ Communicated by the Author.

The papers cited above were published in the Philosophical Magazine of May 1875, in one paper, "Researches in Acoustics, No. VI."

Madame Ema Seiler had made at my request. She made a long series of experiments with the same apparatus I had used. Her determinations, though agreeing with mine in having approximately the same variation of the residual sensation with the pitch, yet differed considerably in the absolute quantities which she found for the durations of these sensations. That the two series of observations should differ was to be expected from the known variation of the sonorous sensations among different observers; but the principal cause of the difference is to be attributed to the apparatus (fig. 3) used in these experiments. This apparatus generated sounds in addition to the one to be specially observed, so that the determinations were difficult to make except by one whose hearing was peculiarly trained and naturally gifted in the power of excluding other sound-sensations from the one alone to be studied. In the ability to analyse composite sounds Madame Seiler was noted; and I had no doubt at the time of the publication of her results that they were more worthy than mine to form the basis of a physiological law. This I stated in my paper of 1875, and the experiments described in the present paper, made with improved methods, show that the opinion then entertained was correct.

That there is a physiological law which gives the relation between the pitch of a sound and the duration of its residual sensation is shown by the numerous experiments contained in this paper. But those published in 1874 and 1875 sufficed to establish that fact; yet those experiments have never been repeated by physiologists.

I have waited nineteen years in the hope that others would make similar experiments, so that the combination of the results of various experimenters would give an expression of the law which might be regarded as general and accepted as expressing the average residual sensations of sounds.

It is true that Professor C. R. Cross and H. M. Goodwin published a series of similar experiments in "Some considerations regarding Helmholtz's Theory of Consonance" (Proc. Amer. Acad., Boston, June 1891). They obtained the smallest consonant intervals of simple sounds by blowing sheets of air across the mouths of resonators. The reciprocals of the differences of the frequency of the vibrations forming the intervals thus found are plotted in the curve CC of fig. 1. I and I' give their determinations of the durations of the residual sensations of UT, and of UT4, deduced from their observations of the coalescence of these sounds when interrupted by a perforated disk rotating between a resonator and its corresponding fork.

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