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.

Modern views respecting mechanical lubrication are founded mainly on the experiments of B. Tower, conducted upon journal bearings. He insisted upon the importance of a complete film of oil between the opposed solid surfaces, and he showed how in this case the maintenance of the film may be attained by the dragging action of the surfaces themselves, playing the part of a pump. To this end it is “necessary that the layer should be thicker on the ingoing than on the outgoing side,” which involves a slight displacement of the centre of the journal from that of the bearing. The theory was afterwards developed by 0. Reynolds, whose important memoir includes most of what is now known upon the subject. In a later paper Sommerfeld has improved considerably upon the mathematics, especially in the case where the bearing completely envelops the journal, and his exposition to be recommended to those who wish to follow the details of the investigation. Reference may also be made to Harrison, who includes the consideration of compressible lubricants (air).

In all these investigations the question is treated as two-dimensional. For instance, in the case of the journal the width—axial dimension—of the bearing must be large in comparison with the arc of contact, a condition not usually fulfilled in practice. But Michell has succeeded in solving the problem for a plane rectangular block, moving at a slight inclination over another plane surface, free from this limitation, and he has developed a system of pivoted bearings with valuable practical results.

It is singular that the explanation of some of the most striking and beautiful of optical phenomena should be still matters of controversy. I allude to the brilliant colours displayed by many birds (e.g. hummingbirds), butterflies, and beetles, colours which vary greatly with the incidence of the light, and so cannot well be referred to the ordinary operation of dyes. In an early paper, being occupied at the time with the remarkable coloured reflexions from certain crystals of chlorate of potash described by Stokes, and which I attributed to a periodic twinning, I accepted, perhaps too hastily, the view generally current among naturalists that these colours were “structurecolours,” more or less like those of thin plates, as in the soap-bubble. Among the supporters of this view in more recent times may be especially mentioned Poulton and Hodgkinson. In Poulton's paper the main purpose was to examine the history of the very remarkable connexion between the metallic colours of certain pupse (especially Vanessa urticce) and the character of the light to which the larvae are exposed before pupation. In a passage describing the metallic colour itself he remarks:

“The Nature of Effects Produced.—The gilded appearance is one of the most metal-like appearances in any non-metallic substance. The optical explanation has never been understood. It has, however, been long known that it depends upon the cuticle, and needs the presence of moisture, and that it can be renewed when the dry cuticle is moistened. Hence it can be preserved for any time in spirit.

That this work should have already reached a fourth edition speaks well for the study of mathematical physics. By far the greater part of it is entirely beyond the range of the books available a generation ago. And the improvement in the style is as conspicuous as the extension of the matter. My thoughts naturally go back to the books in current use at Cambridge in the early sixties. With rare exceptions, such as the notable one of Salmon's Conic Sections and one or two of Boole's books, they were arid in the extreme, with scarcely a reference to the history of the subject treated, or an indication to the reader of how he might pursue his study of it. At the present time we have excellent books in English on most branches of mathematical physics and certainly on many relating to pure mathematics.

The progressive development of his subject is often an embarrassment to the writer of a text-book. Prof. Lamb remarks that his “work has less pretensions than ever to be regarded as a complete account of the science with which it deals. The subject has of late attracted increased attention in various countries, and it has become correspondingly difficult to do justice to the growing literature. Some memoirs deal chiefly with questions of mathematical method and so fall outside the scope of this book; others though physically important hardly admit of a condensed analysis; others, again, owing to the multiplicity of publications, may unfortunately have been overlooked. And there is, I am afraid, the inevitable personal equation of the author, which leads him to take a greater interest in some branches of the subject than in others.”

Dear Prof. Nernst,

Having been honoured with an invitation to attend the Conference at Brussels, I feel that the least that I can do is to communicate my views, though I am afraid I can add but little to what has been already said upon the subject.

I wish to emphasize the difficulty mentioned in my paper of 1900 with respect to the use of generalized coordinates. The possibility of representing the state of a body by a finite number of such (short at any rate of the whole number of molecules) depends upon the assumption that a body may be treated as rigid, or incompressible, or in some other way simplified. The justification, and in many cases the sufficient justification, is that a departure from the simplified condition would involve such large amounts of potential energy as could not occur under the operation of the forces concerned. But the law of equi-partition lays it down that every mode is to have its share of kinetic energy. If we begin by supposing an elastic body to be rather stiff, the vibrations have their full share and this share cannot be diminished by increasing the stiffness. For this purpose the simplification fails, which is as much as to say that the method of generalized coordinates cannot be applied. The argument becomes, in fact, self-contradictory.

Perhaps this failure might be invoked in support of the views of Planck and his school that the laws of dynamics (as hitherto understood) cannot be applied to the smallest parts of bodies. But I must confess that I do not like this solution of the puzzle.

In a paper with the above title, Ehrenfest (Zeitsch. physikal. Chem. 1911, 77, 2) has shown that, as usually formulated, the principle is entirely ambiguous, and that nothing definite can be stated without a discrimination among the parameters by which the condition of a system may be defined. The typical example is that of a gas, the expansions and contractions of which may be either (α) isothermal or (β) adiabatic, and the question is a comparison of the contractions in the two cases due to an increment of pressure δp. It is known, of course, that if δp be given, the contraction |δv| is less in case (β) than in case (α). The response of the system is said to be less in case (β), where the temperature changes spontaneously. But we need not go far to encounter an ambiguity. For if we regard δv as given instead of δp, the effect δp is now greater in (β) than in (α). Why are we to choose the one rather than the other as the independent variable?

When we attempt to answer this question, we are led to recognise that the treatment should commence, with purely mechanical systems. The equilibrium of such a system depends on the potential energy function, and the investigation of its character presents no difficulty. Afterwards we may endeavour to extend our results to systems dependent on other, for example, thermodynamic, potentials.

In the problems here considered the fluid is regarded as incompressible, and the motion is supposed to take place in two dimensions.

Potential and Kinetic Energies of Wave Motion.

When there is no dispersion, the energy of a progressive wave of any form is half potential and half kinetic. Thus in the case of a long wave in shallow water, “if we suppose that initially the surface is displaced, but that the particles have no velocity, we shall evidently obtain (as in the case of sound) two equal waves travelling in opposite directions, whose total energies are equal, and together make up the potential energy of the original displacement. Now the elevation of the derived waves must be half of that of the original displacement, and accordingly the potential energies less in the ratio of 4 : 1. Since therefore the potential energy of each derived wave is one quarter, and the total energy one half that of the original displacement, it follows that in the derived wave the potential and kinetic energies are equal”.

The assumption that the displacement in each derived wave, when separated, is similar to the original displacement fails when the medium is dispersive. The equality of the two kinds of energy in an infinite progressive train of simple waves may, however, be established as follows.

Consider first an infinite series of simple stationary waves, of which the energy is at one moment wholly potential and [a quarter of] a period later wholly kinetic.

[Note.—The concluding paragraphs of this paper were dictated by my father only five days before his death. The proofs therefore were not revised by him. The figure was unfortunately lost in the post, and I have redrawn it from the indications given in the text.—Rayleigh.]

One of the most important questions in meteorology is the constitution of the travelling cyclone, for cyclones usually travel. Sir N. Shaw says that “a velocity of 20 metres/second [44 miles per hour] for the centre of a cyclonic depression is large but not unknown, a velocity of less than 10 metres/second may be regarded as smaller than the average. A tropical revolving storm usually travels at about 4 metres/second.” He treats in detail the comparatively simple case where the motion (relative to the ground) is that of a solid body, whether a simple rotation, Or such a rotation combined with a uniform translation; and he draws important conclusions which must find approximate application to travelling cyclones in general. One objection to regarding this case as typical is that, unless the rotating area is infinite, a discontinuity is involved at the distance from the centre where it terminates. A more general treatment is desirable, which shall allow us to suppose a gradual falling off of rotation as the distance from the centre increases; and I propose to take up the general problem in two dimensions, starting from the usual Eulerian equations as referred to uniformly rotating axes. The density (ρ) is supposed to be constant, and gravity can be disregarded.