Before entering upon the matters that I had intended to lay before you, it is fitting that I should refer to the loss we have sustained within the last few days in the death of Sir William Crookes, a former President of the Society during several years from 1896–1899, and a man of world-wide scientific reputation. During his long and active life he made many discoveries in Physics and Chemistry of the first importance. In quite early days his attention was attracted by an unknown and brilliant green line in the spectrum, which he succeeded in tracing to a new element named Thallium, after its appearance. Later he was able so to improve vacua as to open up fresh lines of inquiry with remarkable results in more than one direction. The radiometer, a little instrument in which light, even candlelight, or ordinary day-light, causes the rotation of delicately suspended vanes, presents problems even yet only partially solved. And his discoveries relating to electric discharge in high vacua lie near the foundation of the modern theories of electricity as due to minute charged particles called electrons, capable of separation from ordinary chemical atoms, and of moving with speeds of the order of the speed of light. One is struck not only by the technical skill displayed in experiments more difficult at the time they were made than the younger generation of workers can easily understand, but also by the extraordinary instinct whieh directed Crookes’ choice of subjects. In several cases their importance was hardly realized at the time, and only later became apparent.

In a short paper “On the Diffraction of Light by Particles Comparable with the Wave-length,” Keen and Porter describe curious observations upon the intensity and colour of the light transmitted through small particles of precipitated sulphur, while still in a state of suspension, when the size of the particles is comparable with, or decidedly larger than, the wave-length of the light. The particles principally concerned in their experiments appear to have decidedly exceeded those dealt with in a recent paper, where the calculations were pushed only to the point where the circumference of the sphere is 2.25 λ. The authors cited give as the size of the particles, when the intensity of the light passing through was a minimum, 6 μ to 10 μ, that is over 10 wave-lengths of yellow light, and they point out the desirability of extending the theory to larger spheres.

The calculations referred to related to the particular case where the (relative) refractive index of the spherical obstacles is 1.5. This value was chosen in order to bring out the peculiar polarisation phenomena observed in the diffracted light at angles in the neighbourhood of 90°, and as not inappropriate to experiments upon particles of high index suspended in water. I remarked that the extension of the calculations to greater particles would be of interest, but that the arithmetical work would rapidly become heavy.

In copying a subject by photography the procedure usually involves two distinct steps. The first yields a so-called negative, from which, by the same or another process, a second operation gives the desired positive. Since ordinary photography affords pictures in monochrome, the reproduction can be complete only when the original is of the same colour. We may suppose, for simplicity of statement, that the original is itself a transparency, e.g. a lantern-slide.

The character of the original is regarded as given by specifying the transparency (t) at every point, i.e. the ratio of light transmitted to light incident. But here an ambiguity should be noticed. It may be a question of the place at which the transmitted light is observed. When light penetrates a stained glass, or a layer of coloured liquid contained in a tank, the direction of propagation is unaltered. If the incident rays are normal, so also are the rays transmitted. The action of the photographic image, constituted by an imperfectly aggregated deposit, differs somewhat. Rays incident normally are more or less diffused after transmission. The effective transparency in the half-tones of a negative used for contact printing may thus be sensibly greater than when a camera and lens is employed. In the first case all the transmitted light is effective; in the second most of that diffused through a finite angle fails to reach the lens. In defining t—the transparency at any place—account must in strictness be taken of the manner in which the picture is to be viewed. There is also another point to be considered. The transparency may not be the same for different kinds of light.

Some two years ago I asked for suggestions as to the formation of an artificial hiss, and I remarked that the best I had then been able to do was by blowing through a rubber tube nipped at about half an inch from the open end with a screw clamp, but that the sound so obtained was perhaps more like an f than an s. “There is reason to think that the ear, at any rate of elderly people, tires rapidly to a maintained hiss. The pitch is of the order of 10,000 per second.” The last remark was founded upon experiments already briefly described under the head “Pitch of Sibilants.”

“Doubtless this may vary over a considerable range. In my experiments the method was that of nodes and loops (Phil. Mag. Vol. VII. p. 149 (1879); Scientific Papers, Vol. I. p. 406), executed with a sensitive flame and sliding reflector. A hiss given by Mr Enock, which to me seemed very high and not over audible, gave a wave-length (λ) equal to 25 mm., with good agreement on repetition. A hiss which I gave was graver and less definite, corresponding to λ = 32 mm. The frequency would be of the order of 10,000 per second, more than 5 octaves above middle C.”

The manner in which aqueous vapour condenses upon ordinarily clean surfaces of glass or metal is familiar to all. Examination with a magnifier shows that the condensed water is in the form of small lenses, often in pretty close juxtaposition. The number and thickness of these lenses depend upon the cleanness of the glass and the amount of water deposited. In the days of wet collodion every photographer judged of the success of the cleaning process by the uniformity of the dew deposited from the breath.

Information as to the character of the deposit is obtained by looking through it at a candle or small gas flame. The diameter of the halo measures the angle at which the drops meet the glass, an angle which diminishes as the dew evaporates. That the flame is seen at all in good definition is a proof that some of the glass is uncovered. Even when both sides of a plate are dewed the flame is still seen distinctly though with much diminished intensity.

The process of formation may be followed to some extent under the microscope, the breath being led through a tube. The first deposit occurs very suddenly. As the condensation progresses, the drops grow, and many of the smaller ones coalesce: During evaporation there are two sorts of behaviour. Sometimes the boundaries of the drops contract, leaving the glass bare. In other cases the boundary of a drop remains fixed, while the thickness of the lens diminishes until all that remains is a thin lamina.

In a former paper I gave solutions applicable to the passage of light through very narrow slits in infinitely thin perfectly opaque screens, for the two principal cases where the polarisation is either parallel or perpendicular to the length of the slit. It appeared that if the width (2b) of the slit is very small in comparison with the wave-length (λ), there is a much more free passage when the electric vector is perpendicular to the slit than when it is parallel to the slit, so that unpolarised light incident upon the screen will, after passage, appear polarised in the former manner. This conclusion is in accordance with the observations of Fizeau upon the very narrowest slits. Fizeau found, however, that somewhat wider slits (scratches upon silvered glass) gave the opposite polarisation ; and I have long wished to extend the calculations to slits of width comparable with λ. The subject has also a practical interest in connection with observations upon the Zeeman effect.

The analysis appropriate to problems of this sort would appear to be by use of elliptic coordinates; but I have not seen my way to a solution on these lines, which would, in any case, be rather complicated. In default of such a solution, I have fallen back upon the approximate methods of my former paper. Apart from the intended application, some of the problems which present themselves have an interest of their own. It will be convenient to repeat the general argument almost in the words formerly employed Plane waves of simple type impinge upon a parallel screen.

In an early paper Stokes showed “that in the case of a homogeneous incompressible fluid, whenever udx + vdy + wdz is an exact differential, not only are the ordinary equations of fluid motion satisfied, but the equations obtained when friction is taken into account are satisfied likewise. It is only the equations of condition which belong to the boundaries of the fluid that are violated.” In order to satisfy these also, it is only necessary to suppose that every part of the solid boundaries is made to move with the velocity which the fluid in irrotational motion would there assume. There is no difficulty in the supposition itself; but the only case in which it could readily be carried into effect with tolerable completeness is for the two-dimensional motion of fluid between coaxal cylinders, themselves made to rotate in the same direction with circumferential velocities which are inversely as the radii. Experiments upon these lines, but not I think quite satisfying the above conditions, have been made by Couette and Mallock. It would appear that, except at low velocities, the simple steady motion becomes unstable.

But the point of greatest interest is not touched in the above example. It arises when fluid passing along a uniform or contracting pipe, or channel, arrives at a place where the pipe expands. It is known that if the expansion be sufficiently gradual, the fluid generally speaking follows the walls, or, as it is often expressed, the pipe flows full; and the loss of velocity accompanying the increased section is represented by an augmentation of pressure, approximately according to Bernoulli's law.

Among the little remembered writings of that remarkable man H. F. Talbot, there is an optical note in which he describes the behaviour of fused nitre (nitrate of potash) as observed under the polarizing microscope. The experiments are interesting and easily repeated by any one who has access to a suitable instrument, by preference one in which the nicols can be made to revolve together so as to maintain a dark field in the absence of any interposed crystal.

“Put a drop of a solution of nitre on a small plate of glass, and evaporate it to dryness over a spirit-lamp; then invert the glass, and hold it with the salt downwards and in contact with the flame. By this means the nitre may be brought into a state of fusion, and it will spread itself in a thin transparent film over the surface of the glass.

“Removed from the lamp it immediately solidifies, and the film in cooling cracks irregularly. As soon as the glass is cool enough, let it be placed beneath the microscope (the polariness being crossed, and the field of view consequently dark).”

I have found it better to use several drops spread over a part of the glass. And instead of inverting the plate in order to melt the nitre, I prefer to employ the flame from a mouth blow-pipe, caused to play upon the already heated salt. The blow-pipe may also be used to clean the glass in the first instance, after a preliminary heating over the flame to diminish the risk of fracture. Further security is afforded by keeping down the width of the strip, for which half an inch suffices.

Recent investigations, especially the beautiful work of Wood on “Radiation of Gas Molecules excited by Light”, have raised questions as to the behaviour of a cloud of resonators under the influence of plane waves of their own period. Such questions are indeed of fundamental importance. Until they are answered we can hardly approach the consideration of absorption, viz. the conversion of radiant into thermal energy. The first action is upon the molecule. We may ask whether this can involve on the average an increase of translatory energy. It does not seem likely. If not, the transformation into thermal energy must await collisions.

The difficulties in the way of answering the questions which naturally arise are formidable. In the first place we do not understand what kind of vibration is assumed by the molecule. But it seems desirable that a beginning should be made ; and for this purpose I here consider the case of the simple aerial resonator vibrating symmetrically. The results cannot be regarded as even roughly applicable in a quantitative sense to radiation, inasmuch as this type is inadmissible for transverse vibrations. Nevertheless they may afford suggestions.

The action of a simple resonator under the influence of suitably tuned primary aerial waves was considered in Theory of Sound, § 319 (1878). The primary waves were supposed to issue from a simple source at a finite distance c from the resonator.

Recent researches have emphasized the importance of a clear comprehension of the operation under various conditions of a group of similar unit sources, or centres, of iso-periodic vibrations, e.g. of sound or of light. The sources, supposed to be concentrated in points, may be independently excited (as probably in a soda flame), or they may be constituted of similar small obstacles in an otherwise uniform medium, dispersing plane waves incident upon them. We inquire into an effect, such as the intensity, at a great distance from the cloud, either in a particular direction, or in the average of all directions. For convenience of calculation and statement we shall consider especially sonorous vibrations; but most of the results are equally applicable to electric vibrations, as in light, the additional complication being merely such as arises from the vibrations being transverse to the direction of propagation.

If the centres, supposed to be distributed at random in a region whose three dimensions are all large, are spaced widely enough in relation to the wave-length (λ) to act independently, the question reduces itself to one formerly treated, for it then becomes merely one of the composition of a large number (n) of unit vibrations of arbitrary phases. It is known that the “expectation” of intensity in any direction is n times that due to a single centre, or (as we may say) is equal to n. The word “expectation” is here used in the technical sense to represent the mean of a large number of independent trials, or combinations, in each of which the phases are redistributed at random.

As is well known, the pressure of radiation, predicted by Maxwell, and since experimentally confirmed by Lebedew and by Nichols and Hull, plays an important part in the theory of radiation developed by Boltzmann and W. Wien. The existence of the pressure according to electromagnetic theory is easily demonstrated, but it does not appear to be generally remembered that it could have been deduced with some confidence from thermodynamical principles, even earlier than in the time of Maxwell. Such a deduction was, in fact, made by Bartoli in 1876, and constituted the foundation of Boltz-mann's work. Bartoli's method is quite sufficient for his purpose; but, mainly because it employs irreversible operations, it does not lend itself to further developments. It may therefore be of service to detail the elementary argument on the lines of Carnot, by which it appears that in the absence of a pressure of radiation it would be possible to raise heat from a lower to a higher temperature.

The imaginary apparatus is, as in Boltzmann's theory, a cylinder and piston formed of perfectly reflecting material, within which we may suppose the radiation to be confined. This radiation is always of the kind characterised as complete (or black), a requirement satisfied if we include also a very small black body with which the radiation is in equilibrium. If the operations are slow enough, the size of the black body may be reduced without limit, and then the whole energy at a given temperature is that of the radiation and proportional to the volume occupied. When we have occasion to introduce or abstract heat, the communication may be supposed in the first instance to be with the black body.

The idea that the passage of heat from solids to liquids moving past them is governed by the same principles as apply in virtue of viscosity to the passage of momentum, originated with Reynolds (Manchester Proc., 1874); and it has been further developed by Stanton (Phil. Trans., Vol. cxc. p. 67, 1897; Tech. Rep. Adv. Committee, 1912–13, p. 45) and Lanchester (same Report, p. 40). Both these writers express some doubt as to the exactitude of the analogy, or at any rate of the proofs which have been given of it. The object of the present note is to show definitely that the analogy is not complete.

The problem which is the simplest, and presumably the most favourable to the analogy, is that of fluid enclosed between two parallel plane solid surfaces. One of these surfaces at y = 0 is supposed to be fixed, while the other at y = 1 moves in the direction of x in its own plane with unit velocity. If the motion of the fluid is in plane strata, as would happen if the viscosity were high enough, the velocity u in permanent régime of any stratum y is represented- by y simply. And by definition, if the viscosity be unity, the tangential traction per unit area on the bounding planes is also unity.

Let us now suppose that the fixed surface is maintained at temperature 0, and the moving surface at temperature 1. So long as the motion is stratified, the flow of heat is the same as if the fluid were at rest, and the temperature (θ) at any stratum y has the same value y as has u.

In a recent paper on Æolian Tones I had occasion to determine the velocity of wind from its action upon a narrow strip of mirror (10·1 cm. × 1·6 cm.), the incidence being normal. But there was some doubt as to the coefficient to be employed in deducing the velocity from the density of the air and the force per unit area. Observations both by Eiffel and by Stanton had indicated that the resultant pressure (force reckoned per unit area) is less on small plane areas than on larger ones; and although I used provisionally a diminished value of C in the equation P = CpV2 in view of the narrowness of the strip, it was not without hesitation. I had in fact already commenced experiments which appeared to show that no variation in C was to be detected. Subsequently the matter was carried a little further; and I think it worth while to describe briefly the method employed. In any case I could hardly hope to attain finality, which would almost certainly require the aid of a proper wind channel, but this is now of less consequence as I learn that the matter is engaging attention at the National Physical Laboratory.

According to the principle of similitude a departure from the simple law would be most apparent when the kinematic viscosity is large and the stream velocity small. Thus, if the delicacy can be made adequate, the use of air resistance and such low speeds as can be reached by walking through a still atmosphere should be favourable.