For distinctness of conception the material of the particles may be supposed to be uniform and non-magnetic, but of dielectric capacity different from that of the surrounding medium; at the same time the results at which we shall arrive are doubtless more general. The smallness is, of course, to be understood as relative to the wave-length of the vibrations.

When the particles are spherical, the problem is simple, as their orientation does not then enter. If the incident light be polarized, there is no scattered ray in the direction of primary electric vibration, or if the incident light be unpolarized there is complete polarization of the light scattered at right angles to the direction of primary propagation. The consideration of elongated particles shows at once that a want of symmetry must usually entail a departure from the above law of polarization and may be one of the causes, though probably not the most important, of the incomplete polarization of sky-light at 90° from the sun. My son's recent experiments upon light scattered by carefully filtered gases reveal a decided deficiency of polarization in the light emitted perpendicularly, and seem to call for a calculation of what is to be expected from particles of arbitrary shape.

As a preliminary to a more complete treatment, it may be well to take first the case of particles symmetrical about an axis, or at any rate behaving as if they were such, for the calculation is then a good deal simpler.

Modern improvements in optical methods lend additional interest to an examination of the causes which interfere with the absolute homogeneity of spectrum lines. So far as we know these may be considered under five heads, and it appears probable that the list is exhaustive:

1. (i) The translatory motion of the radiating particles in the line of sight, operating in accordance with Doppler's principle.

2. (ii) A possible effect of the rotation of the particles.

3. (iii) Disturbance depending on collision with other particles either of the same or of another kind.

4. (iv) Gradual dying down of the luminous vibrations as energy is radiated away.

5. (v) Complications arising from the multiplicity of sources in the line of sight. Thus if the light from a flame be observed through a similar one, the increase of illumination near the centre of the spectrum line is not so great as towards the edges, in accordance with the principles laid down by Stewart and Kirchhoff; and the line is effectively widened. It will be seen that this cause of widening cannot act alone, but merely aggravates the effect of other causes.

There is reason to think that in many cases, especially when vapours in a highly rarefied condition are excited electrically, the first cause is the most important. It was first considered by Lippich and somewhat later independently by myself.

The experiments now to be described originated in an accidental observation. Some old lantern-plates, from which the gelatine films had been cleaned off a few years before (probably with nitric acid), being required for use, were again placed in dilute nitric acid to ensure cleanliness. From these plates a gas-flame burning over the dish was seen reflected with colour, of which the cause was not obvious. On examination in daylight a dry plate was observed to be iridescent, but so slightly that the fact might easily escape attention. But when the plate was under water and suitably illuminated, the brilliancy was remarkably enhanced. Upon this question of illumination almost everything depends. The window-shutter of one of the rooms in my laboratory has an aperture about 4 inches square. In front of this the dish of water is placed and at the bottom of the dish a piece of dark-coloured glass. In the water the plate under observation is tilted,so as to separate the reflexions of the sky as given by the plate and by the glass underneath. In this way a dark background is ensured. At the corners and edges of the plate the reflected light is white, then follow dark bands, and afterwards the colours which suggest reflexion from a thin plate. On this view it is necessary to suppose that the iridescent film is thinnest at the outside and thickens towards the interior, and further, that the material constituting the film has an index intermediate between those of the glass and of the water.

In response to the request for comments on this work, I may say that I have read these papers with interest.

The experiments recorded relate directly to the air pressures at various distances in the close neighbourhood of the surface of a long board parallel to the current of air in a wind channel. Three series of such pressures, and deduced air velocities,- were obtained at different distances (A, B, C) from the leading edge. Major Taylor suggests that these experiments should be repeated and extended at the National Physical Laboratory, and in this recommendation I fully concur, as it is of importance to improve our imperfect comprehension of the character of “skin-friction.”

From the air pressure measurements the author deduces by calculation the actual force exercised upon the board, and in the second paper corrects, as far as possible, some deficiencies in the first. These calculations are a little difficult to follow as approximations are introduced whose validity is difficult to estimate, at any rate, without the instinct which familiarity with the subject matter may bring with it. For example, at some points, the problem is treated as if it were two-dimensional, which the actual dimensions of the board do not seem to justify.

Without undervaluing the interest of connecting the forces experienced by the various parts of the board with the air pressures in its neighbourhood, I am inclined to prefer—or at any rate to recommend as alternative—direct measurements of the forces on the board, more as in Zahm's experiments.

The general use of Pitot's tubes for measuring the velocity of streams suggests hydrodynamical problems. It can hardly be said that these are of practical importance, since the action to be observed depends simply upon Bernoulli's law. In the interior of a long tube of any section, closed at the further end and facing the stream, the pressure must be that due to the velocity (υ) of the stream, i.e. ½ρυ2 being the density. At least, this must be the case if viscosity can be neglected. I am not aware that the influence of viscosity here has been detected, and it does not seem likely that it can be sensible under ordinary conditions. It would enter in the combination ν/υl, where ν is the kinematic viscosity and l represents the linear dimension of the tube. Experiments directed to show it would therefore be made with small tubes and low velocities.

In practice a tube of circular section is employed. But, even when viscosity is ignored, the problem of determining the motion in the neighbourhood of a circular tube is beyond our powers. In what follows, not only is the fluid supposed frictionless, but the circular tube is replaced by its two-dimensional analogue, i.e. the channel between parallel plane walls. Under this head two problems naturally present themselves.

The first problem proposed for consideration may be defined to be the flow of electricity in two dimensions, when the uniformity is disturbed by the presence of a channel whose infinitely thin non-conducting walls are parallel to the flow.

In his interesting address on spectroscopic methods, Prof. Michelson falls into a not uncommon error when he says that, in order to obtain a pure spectrum, “two important modifications must be made in Newton's arrangement. First, the light must be allowed to pass through a very narrow aperture, and, secondly, a sharp image of this aperture must be formed by a lens or mirror.”

Both these modifications were made by Newton himself, and with a clear understanding of their advantages. In Opticks, Exper. 11, we read:—“In the Sun's Light let into my darkened Chamber through a small round hole in my Window—shut, at about 10 or 12 feet from the Window, I placed a Lens, by which the Image of the hole might be distinctly cast upon a sheet of white Paper, placed at the distance of six, eight, ten, or twelve Feet from the Lens.…For in this case the circular Images of the hole which comprise that Image…were terminated most distinctly without any Penumbra, and therefore extended into one another the least that they could, and by consequence the mixture of the Heterogeneous Rays was now the least of all.”

The subject of this lecture has received the attention of several generations of mathematicians and experimenters. Over a part of the field their labours have been rewarded with a considerable degree of success. In all that concerns small vibrations, whether of air, as in sound, or of water, as in waves and tides, we have a large body of systematized knowledge, though in the case of the tides the question is seriously complicated by the fact that the rotation of the globe is actual and not merely relative to the sun and moon, as well as by the irregular outlines and depths of the various oceans. And even when the disturbance constituting the vibration is not small, some progress has been made, as in the theory of sound waves in one dimension, and of the tidal bores, which are such a remarkable feature of certain estuaries and rivers.

The general equations of fluid motion, when friction or viscosity is neglected, were laid down in quite early days by Euler and Lagrange, and in a sense they should contain the whole theory. But, as Whewell remarked, it soon appeared that these equations by themselves take us a surprisingly little way, and much mathematical and physical talent had to be expended before the truths hidden in them could be brought to light and exhibited in a practical shape. What was still more disconcerting, some of the general propositions so arrived at were found to be in flagrant contradiction with observation, even in cases where at first sight it would not seem that viscosity was likely to be important.

It is known that “when a thin transparent film is backed by a perfect reflector, no colours should be visible, all the light being ultimately reflected, whatever the wave-length may be. The experiment may be tried with a thin layer of gelatine on a polished silver plate.” An apparent exception has been described by R. W. Wood: “A thin film of collodion deposited on a bright surface of silver shows brilliant colours in reflected light. It, moreover, scatters light of a colour complementary to the colour of the directly reflected light. This is apparently due to the fact that the collodion film “frills,” the mesh, however, being so small that it can be detected only with the highest powers of the microscope. Commercial ether and collodion should be used. If chemically pure ether obtained by distillation is used, the filmdoes not frill, and no trace of colour is exhibited. Still more remarkable is the fact that if sunlight be thrown down upon the plate at normal incidence, brilliant colours are seen at grazing emergence, if a Nicol prism is held before the eye. These colours change to the complementary tints if the Nicol is rotated through 90°, i.e. in the scattered light, one half of the spectrum is polarized in one plane, and the remainder in a plane perpendicular to it.”

I have lately come across an entirely forgotten letter from Rowland in which he describes a similar observation. Writing to me in March 1893, he says:—“While one of my students was working with light reflected from a metal, it occurred to me to try a thin collodion film on the metal.