I suppose that most of those who have listened to (single-engined) aeroplanes in flight must have noticed the highly uneven character of the sound, even at moderate distances. It would seem that the changes are to be attributed to atmospheric irregularities affecting the propagation rather than to variable emission. This may require confirmation; but, in any case, a comparison of what is to be expected in the analogous propagation of light and sound has a certain interest.

One point of difference should first be noticed. The velocity of propagation of sound through air varies indeed with temperature, but is independent of pressure (or density), while that of light depends upon pressure as well as upon temperature. In the atmosphere there is a variation of pressure with elevation, but this is scarcely material for our present purpose. And the kind of irregular local variations which can easily occur in temperature are excluded in respect of pressure by the mechanical conditions, at least in the absence of strong winds, not here regarded. The question is thus reduced to refractions consequent upon temperature variations.

The velocity of sound is as the square root of the absolute temperature. Accordingly for 1° C. difference of temperature the refractivity (μ − 1) is 000183. In the case of light the corresponding value of (μ − 1) is 0.000294 × 0.00366, the pressure being atmospheric. The effect of temperature upon sound is thus about 2000 times greater than upon light. If we suppose the system of temperature differences to be altered in this proportion, the course of rays of light and of sound will be the same.

From the theoretical point of view there is little to distinguish propagation of sound in an unlimited mass of water from the corresponding case of air; of course the velocity is greater (about four times). It is probable that at a great depth the velocity increases, the effect of diminishing compressibility out-weighing increased density.

As regards absorption, it would appear that it is likely to be less in water than in air. The viscosity (measured kinematically) is less in water.

But the practical questions are largely influenced by the presence of a free surface, which must act as a nearly perfect reflector. So far the case is analogous to that of a fixed wall reflecting sound waves in air; but there is an important difference. In order to imitate the wall in air, we must suppose the image of the source of sound to be exactly similar to the original; but the image of the source of sound reflected from the free surface of water must be taken negatively, viz., in the case of a pure tone with phase altered by 180°. In practice the case of interest is when both source and place of observation are somewhat near the reflecting surface. We must expect phenomena of interference varying with the precise depth below the surface. The analogy is with Lloyd's interference bands in Optics. If we suppose the distance to be travelled very great, the paths of the direct and reflected sounds will be nearly equal. Here the distinction of the two problems comes in.

For air and wall the phases of the direct and reflected waves on arrival would be the same, and the effect a maximum.

The suggestion has been put forward (as I understand by Lt.-Col. A. C. Williams) that the action of a range-finder, adjusted for a quiescent atmosphere, may be liable to disturbance when employed upon a ship in motion, as a result of the variable densities in the air due to such motion and consequent refraction of the light. That this is vera causa must be admitted; but the question arises as to the direction and magnitude of the effect, and whether or not it would be negligible in practice. It is not to be supposed that any precise calculation is feasible for the actual circumstances of a ship; but I have thought that a simplified form of the problem may afford sufficient information to warrant a practical conclusion. For this purpose I take the case of an infinite cylinder moving transversely through an otherwise undisturbed atmosphere, and displacing it in the manner easily specified on the principles of ordinary hydrodynamics. When the motion of the fluid is known, the corresponding pressures and densities follow, and the refraction of the ray of light, travelling from a distance in a direction parallel to the ship's motion, may be calculated as in the case of astronomical and prismatic dispersion or of mirage. It is doubtless the fact that in the rear of the disturbing body the motion differs greatly from that assumed; but in front of it the difference is much less, and not such as to nullify the conclusions that may be drawn. The first step is accordingly to specify the motion, and to determine the square of the total velocity (q) on which depends the reduction of pressure.

[Note.—This paper was found in the author's writing-table drawer after his death. It is not dated, but was probably written in 1917. It was no doubt withheld in the hope of making additions.]

I owe my knowledge of this subject, as well as beautiful specimens, to Prof. S. Leduc of Nantes. His work on the Mechanism of Life gives an account of the history of the discovery and a fairly detailed description of the modus operandi. “According to Prof. Quincke of Heidelberg, the first mention of the periodic formation of chemical precipitates must be attributed to Runge in 1885. Since that time these precipitates have been studied by a number of authors, and particularly by R. Liesegang of Düsseldorf, who in 1907 published a work on the subject, entitled On Stratification by Diffusion.” In 1901 and again in 1907 Leduc exhibited preparations showing concentric rings, alternately transparent and opaque, obtained by diffusion of various solutions in a layer of gelatine.

“The following is the best method of demonstrating the phenomenon. A glass lantern slide is carefully cleaned and placed absolutely level. We then take 5 c.c. of a 10 per cent. solution of gelatine and add to it one drop of a concentrated solution of sodium arsenate. This is poured over the glass plate whilst hot, and as soon as it is quite set, but before it can dry, we allow a drop of silver nitrate solution containing a trace of nitric acid to fall on it from a pipette.

At intervals during the past year I have tried a good many experiments in the hope of throwing further light upon the origin of these figures, especially those due to the passage of a small blow-pipe flame, or of hot sulphuric acid, across the surface of a glass plate on which, before treatment, the breath deposits evenly. The even deposit consists of a multitude of small lenses easily seen with a hand magnifier. In the track of the flame or sulphuric acid the lenses are larger, often passing into flat masses which, on evaporation, show the usual colours of thin plates. When the glass is seen against a dark ground, and is so held that regularly reflected light does not reach the eye, the general surface shows bright, while the track of the flame or acid is by comparison dark or black. It will be convenient thus to speak of the deposit as bright or dark—descriptive words implying no doubtful hypothesis. The question is what difference in the glass surface determines the two kinds of deposit.

In Aitken's view (Proc. Ed. Soc. p. 94, 1893; Nature, June 15, 1911), the flame acts by the deposit of numerous fine particles constituting nuclei of aqueous condensation, and in like manner he attributes the effect of sulphuric (or hydrofluoric) acid to a water-attracting residue remaining in spite of washing. On the other hand, I was disposed to refer the dark deposit to a greater degree of freedom from grease or other water-repelling contamination (Nature, May 25, 1911), supposing that a clean surface of glass would everywhere attract moisture. It will be seen that the two views are sharply contrasted.

The ideal form of Helmholtz resonator is a cavernous space, almost enclosed by a thin, immovable wall, in which there is a small perforation establishing a communication between the interior and exterior gas. An approximate theory, based upon the supposition that the perforation is small, and consequently that the wave-length of the aërial vibration is great, is due to Helmholtz, who arrived at definite results for perforations whose outline is circular or elliptic. A simplified, and in some respects generalised, treatment was given in my paper on “Resonance.” In the extreme case of a wavelength sufficiently great, the kinetic energy of the vibration is that of the gas near the mouth as it moves in and out, much as an incompressible fluid might do, and the potential energy is that of the almost uniform compressions and rarefactions of the gas in the interior. The latter is a question merely of the volume S of the cavity and of the quantity of gas which has passed, but the calculation of the kinetic energy presents difficulties which have been only partially overcome. In the case of simple apertures in the thin wall (regarded as plane), only circular and elliptic forms admit of complete treatment. The mathematical problem is the same as that of finding the electrostatic capacity of a thin conducting plate having the form of the aperture, and supposed to be situated in the open.

The project of a stricter treatment of the problem, in the case of a spherical wall and an aperture of circular outline, has been in my mind more than 40 years, partly with the hope of reaching a closer approximation, and partly because some mathematicians have found the former method unsatisfactory, or, at any rate, difficult to follow.

With all its advantages, the division of labour, so much accentuated in modern times, tends to carry with it a regrettable division of information. Much that is familiar to theorists and experimenters in laboratories percolates slowly into the workshop, and, what is more to my present purpose, much practical knowledge gained in the workshop fails to find its way into print. At the moment I am desirous of further information on two matters relating to the working of glass in which I happen to be interested, and I am writing in the hope that some of your readers may be able to assist.

Almost the only discussion that I have seen of the cutting of glass by the diamond is a century old, by the celebrated W. H. Wollaston (Phil. Trans. 1816, p. 265).

In his recent paper on the Photometry of Lights of Different Colours Mr H. Ives remarks:—“No satisfactory theory of the action of the flicker photometer can be said to exist. What does it actually measure? We may assume the existence of a ‘luminosity sense’ distinct from the colour sense.… If, for instance, there exists a physiological process called into action both by coloured and uncoloured light, a measure of this would be a measure of a common property.”

Very many years ago it occurred to me that the adjustment of the iris afforded just such a “physiological process”. The iris contracts when the eye is exposed to a bright red or to a bright green light. There must therefore be some relative brightness of the two lights which tends equally to close the iris, and this may afford the measure required. The flicker adjustment is complete when the iris has no tendency to alter under the alternating illumination.

This question was brought home to me very forcibly, when in 1875 I fitted the whole area of the window of a small room with revolving sectors after the manner of Talbot. The intention was to observe, more conveniently than when the eye is at a small hole, the movements of vibrating bodies. The apparatus served this purpose well enough; but incidentally I was much struck with the remarkably disagreeable and even painful sensations experienced when at the beginning or end of operations the slits were revolving slowly so as to generate flashes at the rate of perhaps 3 or 4 per second.

I regret that I overlooked Prof. Bayliss's letter in Nature of October 17, in which he made an appeal for my opinion. But, if I rightly understand, the question at issue seems to be mainly one of words. Can we properly speak of the propagation of sound through an incompressible fluid? I should answer, Yes. There may be periodic motion and periodic variation of pressure; the fact that there are no variations of density seems immaterial. Consider plane waves, corresponding with a pure tone, travelling through air. In every thin layer of air—and thin means thin relatively to the wavelength—there are periodic motion and periodic compression, approximately uniform throughout the layer. But the compression is not essential to the travelling of the sound. The substitution of an incompressible fluid of the same density for the gas within the layer would be no hindrance. Although there is no compression, there remain a periodic pressure and a periodic motion, and these suffice to carry on the sound.

The case is even simpler if we are prepared to contemplate an incompressible fluid without mass, for then the layer need not be thin. The interposition of such a layer has absolutely no effect, the motion and pressure at the further side being the same as if the thickness of the layer were reduced to zero. To all intents and purposes the sound is propagated through the layer, though perhaps exception might be taken to the use of the word propagation.

As regards the ear, we have to consider the behaviour of water. From some points of view the difference between air and water is much more one of density than of compressibility.