AS in former volumes, the papers here included embrace a wide range of subjects. In Optics, Arts. 149, 150 deal with the reflexion of light at a twin plane of a crystal and, besides revealing unexpected peculiarities respecting polarization, explain some remarkable phenomena observed by Prof. Stokes. Attention may also be called to Art. 185 in which it is shown that the light found by Jamin to be reflected from water at the polarizing angle is to be attributed to a film of grease, and to Art. 157 “On the Limit to Interference when Light is radiated from moving Molecules.”

Several papers treat of capillary questions. In Art. 170 Plateau's “Superficial Viscosity” is traced to greasy contamination of water surfaces. The theory of Surface Forces is expounded in Arts. 176, 186, 193, and attention is called to T. Young's remarkable estimates of molecular magnitudes.

The relative densities of Hydrogen and Oxygen and the composition of Water are the subjects of Arts. 146, 153, 187.

In Acoustics the most important paper is probably that on Bells (Art. 164). The modes of vibration and the corresponding partial tones of a large number of bells are there recorded.

The next volume will bring the Collection down to about the present time and, it is hoped, may be ready in about a year.

§ 1. A general statement of the principles of the undulatory theory, with elementary explanations, has already been given under Light [Enc. Brit. Vol. xiv.], and in the article on Ether the arguments which point to the existence of an all-pervading medium, susceptible in its various parts of an alternating change of state, have been traced by a master hand; but the subject is of such great importance, and is so intimately involved in recent optical investigation and discovery, that a more detailed exposition of the theory, with application to the leading phenomena, was reserved for a special article. That the subject is one of difficulty may be at once admitted. Even in the theory of sound, as conveyed by aerial vibrations, where we are well acquainted with the nature and properties of the vehicle, the fundamental conceptions are not very easy to grasp, and their development makes heavy demands upon our mathematical resources. That the situation is not improved when the medium is hypothetical will be easily understood. For, although the evidence is overwhelming in favour of the conclusion that light is propagated as a vibration, we are almost entirely in the dark as to what it is that vibrates and the manner of vibration. This ignorance entails an appearance of vagueness even in those parts of the subject the treatment of which would not really be modified by the acquisition of a more precise knowledge, e.g., the theory of the colours of thin plates, and of the resolving power of optical instruments.

As a step towards a better understanding of the action of fog upon light, it seems desirable to investigate what the phenomena would be in the simplest case that can be proposed. For this purpose we may consider the atmosphere and the material composing the fog to be absolutely transparent, and also make abstraction from the influence of obstacles, among which must be included the ground itself.

Conceive a small source of radiation, e.g. an incandescent carbon filament, to be surrounded by a spherical cloud, of uniform density, or at any rate symmetrically disposed round the source, outside of which the atmosphere is clear. Since by hypothesis there is no absorption, whatever radiation is emitted by the source passes outward through the external surface of the cloud. The effect of the cloud is to cause diffusion, i.e. to spread the rays passing through any small area of the surface (which in the absence of the cloud would be limited to a small solid angle) more or less uniformly over the complete hemisphere.

Whether the total radiation passing outwards through the small area on the external surface of the cloud is affected by the existence of the cloud depends upon the circumstances of the case. If it be laid down that the total emission of energy from the source is given, then the presence of the cloud makes no difference in respect of the energy passing any element of the spherical area.

In a former communication to the Society (March 6, 1882) [Art. 82, vol. II. p. 92] I made some remarks upon the extraordinary influence of apparent magnitude upon the visibility of objects whose ‘apparent brightness’ was given, and I hazarded the suggestion that in consequence of aberration (attending the large aperture of the pupil called into operation in a bad light) the focussing might be defective. Further experiment has proved that in my own case at any rate much of the effect is attributable to an even simpler cause. I have found that in a nearly dark room I am distinctly short-sighted. With concave spectacles of 36 inches negative focus my vision is rendered much sharper, and is attended with increased binocular effect. On a dark night small stars are much more evident with the aid of the spectacles than without them.

In a moderately good light I can detect no signs of short-sightedness. In trying to read large print at a distance I succeeded rather better without the glasses than with them. It seems therefore that the effect is not to be regarded as merely an aggravation of permanent short-sightedness by increase of aperture.

The use of spectacles does not however put the small and the large objects on a level of brightness when seen in a bad light, and the outstanding difference may still be plausibly attributed to aberration.

In connection with the experimental results of Professor Hughes, I have recently been led to examine more minutely the chapter in Maxwell's Electricity and Magnetism (vol. II. ch. xiii.), in which the author calculates the self-induction of cylindrical conductors of finite section. The problems being virtually in two dimensions, the results give the ratio L: l, where L is the coefficient of self-induction, and l the length considered. And since both these quantities are linear, the ratio is purely numerical. In some details the formulæ, as given by Maxwell, require correction, and in some directions the method used by him may usefully be pushed further. The present paper may thus be regarded partly as a review, and partly as a development of Maxwell's chapter.

The problems divide themselves into two classes. In the first class the distribution of the currents is supposed to be the same as it would be if determined solely by resistance, undisturbed by induction; in particular the density of current in a cylindrical conductor is assumed to be uniform over the section. The self-induction calculated on this basis can be applied to alternating currents, only under the restriction that the period of the alternation be not too small in relation to the other circumstances of the case. If this condition be not satisfied, the investigation must be modified so as to include a determination of the distribution of current.

It is well known that an electro-magnet, interposed in the circuit of an alternate current machine, diminishes the effect far more than in a degree corresponding to the resistance of the additional wire. This behaviour of an electro-magnet may be exhibited to an audience in an instructive manner, by use of a helix wound with two contiguous wires (such as are commonly used for large instruments), one of which is included in the circuit of a De Meritens machine and a few incandescent lamps. If the circuit of the second wire be open, the introduction of a few stout iron wires into the helix causes a very marked falling off in the incandescence. On closing the second circuit, currents develope themselves in it of such a kind as to compensate the self-induction, and the lights recover their brilliancy. Even without iron, the effect of closing the second circuit is perceptible, provided the degree of incandescence be suitable.

An arrangement suitable for illustrating the same phenomenon with currents of small intensity was described in Nature for May 23, 1872.

In electrical work it is often necessary to use coils of such proportions that their constants cannot well be obtained from the data of construction, but must be determined by electrical comparison with other coils whose proportions are more favourable. A method for comparing the galvanometer constants of two coils, i.e. of finding the ratio of magnetic forces at their centres when they are traversed by the same current, is given in Maxwell's Treatise, vol. II. § 753.

I have used a slight modification of Maxwell's arrangement which is perhaps an improvement, when the coils to be compared are of copper and therefore liable to change their resistance pretty quickly in sympathy with variations of temperature. The coils are placed as usual approximately in the plane of the meridian so that their centres and axes coincide, and a very short magnet with attached mirror is delicately suspended at the common centre. If the current from a battery be divided between the coils, connected in such a manner that the magnetic effects are opposed, it will be possible by adding resistance to one or other of the branches in multiple arc to annul the magnetic force at the centre, so that the same reading is obtained whichever way the battery current may circulate. The ratio of the galvanometer constants is then simply the ratio of the resistances in multiple arc.

To obtain this ratio in an accurate manner, the two branches already spoken of are combined with two other resistances of german silver, so as to form a Wheatstone's balance.

In the reaction against the arbitrariness of prismatic spectra there seems to be danger that the claim to ascendancy of the so-called diffraction spectrum may be overrated. On this system the rays are spaced so that equal intervals correspond to equal differences of wave-length, and the arrangement possesses indisputably the advantage that it is independent of the properties of any kind of matter. This advantage, however, would not be lost, if instead of the simple wave-length we substituted any function thereof; and the question presents itself whether there is any reason for preferring one form of the function to another.

On behalf of the simple wave-length, it may be said that this is the quantity with which measurements by a grating are immediately concerned, and that a spectrum drawn upon this plan represents the results of experiment in the simplest and most direct manner. But it does not follow that this arrangement is the most instructive.

Some years ago Mr Stoney proposed that spectra should be drawn so that equal intervals correspond to equal differences in the frequency of vibration. On the supposition that the velocity of light in vacuum is the same for all rays, this is equivalent to taking as abscissa the reciprocal of the wave-length instead of the wave-length itself. A spectrum drawn upon this plan has as much (if not more) claim to the title of normal, as the usual diffraction spectrum.

In the present communication I propose to give an account of a photometric arrangement presenting some novel features, and of some results found by means of it for the reflecting power of glass and silver surfaces. My attention was drawn to the subject by an able paper of Professor Rood, who, in giving some results of a photometric method, comments upon the lack of attention bestowed by experimentalists upon the verification, or otherwise, of Fresnel's formulæ for the reflection of light at the bounding surfaces of transparent media. It is true that polarimetric observations have been made of the ratio of the intensities with which the two polarised components are reflected; but even if we suppose (as is hardly the case) that these measurements are altogether confirmatory of Fresnel's formulæ, the question remains open as to whether the actual intensity of each component is adequately represented. This doubt would be set at rest, were it shown that Young's formulæ for perpendicular incidence (to which Fresnel's reduce), viz., (µ − 1)2/(µ+ 1)2, agrees with experiment.

Professor Rood's observations relate to the effect of a plate of glass when interposed in the course of the light. He measures, in fact, the transmission of light by the plate, and not directly the reflection. No one is in a better position than myself for appreciating the advantages of this course from the point of view of experiment.

In the measurements of the efficiency of dynamos by Dr Hopkinson's ingenious method, would it not be possible to carry out the principle more fully, so as to dispense with all measurement of mechanical power, by introducing into the circuit a few storage cells which should supply the small percentage of energy wanted? In this way all the data could be observed electrically.

The present paper relates to the same subject as that entitled “On the Determination of the Ohm in Absolute Measure,” communicated to the Society by Dr Schuster and myself, and published in the Proceedings for April, 1881 [Art. 79]—referred to in the sequel as the former paper. The title has been altered to bring it into agreement with the resolutions of the Paris Electrical Congress, who decided that the ohm was to mean in future the absolute unit (109c.g.s.), and not, as has usually been the intention, the unit issued by the Committee of the British Association, called for brevity the B.A. unit. Much that was said in the former paper applies equally to the present experiments, and will not in general be repeated, except for correction or additional emphasis.

The new apparatus [fig. 0] was constructed by Messrs Elliott on the same general plan as that employed by the original Committee, the principal difference being an enlargement of the linear dimensions in the ratio of about 3: 2. The frame by which the revolving parts are supported is provided with insulating pieces to prevent the formation of induced electric currents, and more space is allowed than before between the frame and those parts of the ring which most nearly approach it during the revolution. It is supported on three levelling screws, and is clamped by bolts and nuts to the stone table upon which it stands.

Introduction

The first impression upon the mind of the reader of the above title will probably be, that the subject has long since been exhausted. The explanation of these colours, as due to interference, was one of the first triumphs of the Wave Theory of Light; and what Young left undone was completed by Poisson, Fresnel, Arago, and Stokes. And yet it would be hardly an exaggeration to say that the colours of thin plates have never been explained at all. The theory set forth so completely in our treatises tells us indeed how the composition of the light reflected depends upon the thickness of the plate, but what will be its colour cannot, in most cases, be foretold without information of an entirely different kind, dealing with the chromatic relations of the spectral colours themselves. This part of the subject belongs to Physiological Optics, as depending upon the special properties of the eye. The first attempt to deal with it is due to Newton, who invented the chromatic diagram, but his representation of the spectrum is arbitrary, and but a rough approximation to the truth. It is to Maxwell that we owe the first systematic examination of the chromatic relations of the spectrum, and his results give the means of predicting the colour of any mixed light of known composition.