Soon after the discovery of Argon it was thought desirable to compare the percolation of the gas through indiarubber with that of nitrogen, and Sir W. Roberts-Austen kindly gave me some advice upon the subject. The proposal was simply to allow atmospheric air to percolate through the rubber film into a vacuum, after the manner of Graham, and then to determine the proportion of argon. It will be remembered that Graham found that the percentage of oxygen was raised in this manner from the 21 of the atmosphere to about 40. At the time the experiment fell through, but during the last year I have carried it out with the assistance of Mr Gordon.

The rubber balloon was first charged with dry boxwood sawdust. This rather troublesome operation was facilitated by so mounting the balloon that with the aid of an air-pump the external pressure could be reduced. When sufficiently distended the balloon was connected with a large Töpler pump, into the vacuous head of which the diffused gases could collect. At intervals they were drawn off in the usual way.

The diffusion was not conducted under ideal conditions. In order to make the most of the time, the apparatus was left at work during the night, so that by the morning the internal pressure had risen to perhaps three inches of mercury. The proportion of oxygen in the gas collected was determined from time to time.

The observations here described were made in connexion with the isolation of argon by removal of the nitrogen from air, but they may, perhaps, possess a wider interest as throwing light upon the behaviour of nitrogen itself.

According to Davy, the dissolved nitrogen of water is oxidised to nitrous (or nitric) acid when the liquid is submitted to electrolysis. “To make the experiment in as refined a form as possible, I procured two hollow cones of pure gold containing about 25 grains of water each, they were filled with distilled water connected together by a moistened piece of amianthus which had been used in the former experiments, and exposed to the action of a voltaic battery of 100 pairs…. In 10 minutes the water in the negative tube had gained the power of giving a slight blue tint to litmus paper: and the water in the positive tube rendered it red. The process was continued for 14 hours; the acid increased in quantity during the whole time, and the water became at last very sour to the taste…. The acid, as far as its properties were examined, agreed with pure nitrous acid having an excess of nitrous gas” (p. 6).

The influence of viscosity and heat conduction in modifying the propagation of sound in circular tubes of moderate dimensions has been treated by Kirchhoff in his usual masterly style, but he passes over the case when the diameter is very large. In my book on the Theory of Sound, 2nd edition, § 348, I have given a full statement of Kirchhoff's theory, and have indicated the alterations required when the boundary is supposed to take the form of two parallel planes instead of a cylindrical surface. In any case the action of the wall is supposed to be such as to annihilate variation of temperature, and tangential as well as normal motion. In connexion with the problem of the propagation of sound over water I recently had occasion to extend the analysis to the case of a layer of very great thickness; and though, as the result showed, the solution fails to answer the question which I had then in view, it is of some interest in itself. In this case the practical question differs somewhat from that proposed by Kirchhoff, who assumes not only complete periodicity with respect to time, but also a quasi-periodicity with respect to x, the direction of propagation, all the functions being supposed proportional to emx, where m is a complex constant, and not otherwise to depend upon x.

The observations here recorded were carried out by the method and with the apparatus described in a former paper, to which reference must be made for details. It must suffice to say that the globe containing the gas to be weighed was filled at 0° C., and to a pressure determined by a manometric gauge. This pressure, nearly atmospheric, is slightly variable with temperature on account of the expansion of the mercury and iron involved. The actually observed weights are corrected so as to correspond with a temperature of 15° C. of the gauge, as well as for the errors in the platinum and brass weights employed. In the present, as well as in the former, experiments I have been ably assisted by Mr George Gordon.

Carbonic Oxide

This gas was prepared by three methods. In the first method a flask, sealed to the rest of the apparatus, was charged with 80 grams recrystallised ferrocyanide of potassium and 360 c.c. strong sulphuric acid. The generation of gas could be started by the application of heat, and with care it could be checked and finally stopped by the removal of the flame with subsequent application, if necessary, of wet cotton-wool to the exterior of the flask. In this way one charge could be utilised with great advantage for several fillings.

The remarkable formula, arrived at almost simultaneously by L. Lorenz and H. A. Lorentz, and expressing the relation between refractive index and density, is well known; but the demonstrations are rather difficult to follow, and the limits of application are far from obvious. Indeed, in some discussions the necessity for any limitation at all is ignored. I have thought that it might be worth while to consider the problem in the more definite form which it assumes when the obstacles are supposed to be arranged in rectangular or square order, and to show how the approximation may be pursued when the dimensions of the obstacles are no longer very small in comparison with the distances between them.

Taking, first, the case of two dimensions, let us investigate the conductivity for heat, or electricity, of an otherwise uniform medium interrupted by cylindrical obstacles which are arranged in rectangular order. The sides of the rectangle will be denoted by α, β, and the radius of the cylinders by a. The simplest cases would be obtained by supposing the material composing the cylinders to be either non-conducting or perfectly conducting; but it will be sufficient to suppose that it has a definite conductivity different from that of the remainder of the medium.

By the principle of superposition the conductivity of the interrupted medium for a current in any direction can be deduced from its conductivities in the three principal directions.

The lecture commenced with a description of a home-made spectroscope of considerable power. The lens, a plano-convex of 6 inches aperture and 22 feet focus, received the rays from the slit, and finally returned them to a pure spectrum formed in the neighbourhood. The skeleton of the prism was of lead; the faces, inclined at 70°, were of thick plate-glass cemented with glue and treacle. It was charged with bisulphide of carbon, of which the free surface (of small area) was raised above the operative part of the fluid. The prism was traversed twice, and the effective thickness was 5½ inches, so that the resolving power corresponded to 11 inches, or 28 cm., of CS2. The liquid was stirred by a perforated triangular plate, nearly fitting the prism, which could be actuated by means of a thread within reach of the observer. The reflector was a flat, chemically silvered in front.

So far as eye observations were concerned, the performance was satisfactory, falling but little short of theoretical perfection. The stirrer needed to be in almost constant operation, the definition usually beginning to fail within about 20 seconds after stopping the stirrer. But although the stirrer was quite successful in maintaining uniformity of temperature as regards space, i.e. throughout the dispersing fluid, the temperature was usually somewhat rapidly variable with time, so that photographs, requiring more than a few seconds of exposure, showed inferiority. In this respect a grating is more manageable.

The announcement (Nature, August 10) that it is in contemplation to raise a sum exceeding £2000 for the establishment of a special photographic telescope at the Cambridge Observatory, leads me to ask whether astronomers have duly considered the facilities afforded by modern photography. At the time of my early experience of the art, thirty-five years ago, it would have been thought a great feat to photograph the Fraunhofer lines in the yellow or red regions of the spectrum, although even then the statement so commonly made that chemical activity was limited to the blue and ultrablue rays was quite unwarranted. With the earlier photographic processes the distinction was necessary between telescopes to be used with the eye or for photography. In the former case the focal length had to be a minimum for the yellow rays, in the latter for the blue rays of the spectrum.

But the situation is entirely changed. There is now no difficulty in preparing plates sensitive to all parts of the spectrum, witness the beautiful photographs of Rowland and Higgs. I have myself used “Orthochromatic” plates in experiments where it was desirable to work with the same rays as most influence the eye. The interference bands of sodium light may be photographed with the utmost facility on plates sensitised in a bath containing cyanin.

The problems in fluid motion of which solutions have hitherto been given relate for the most part to two extreme conditions. In the first class the viscosity is supposed to be sensible, but the motion is assumed to be so slow that the terms involving the squares of the velocities may be omitted; in the second class the motion is not limited, but viscosity is supposed to be absent or negligible.

Special problems of the first class have been solved by Stokes and other mathematicians; and general theorems of importance have been established by v. Helmholtz and by Korteweg, relating to the laws of steady motion. Thus in the steady motion (M0) of an incompressible fluid moving with velocities given at the boundary, less energy is dissipated than in the case of any other motion (M) consistent with the same conditions. And if the motion M be in progress, the rate of dissipation will constantly decrease until it reaches the minimum corresponding to M0. It follows that the motion M0 is always stable.

It is not necessary for our purpose to repeat the investigation of Korteweg; but it may be well to call attention to the fact that problems in viscous motion in which the squares of the velocities are neglected, fall under the general method of Lagrange, at least when this is extended by the introduction of a dissipation function.

If a point, or line, of light be regarded through a telescope, the aperture of which is limited to two narrow parallel slits, interference bands are seen, of which the theory is given in treatises on Optics. The width of the bands is inversely proportional to the distance between the centres of the slits, and the width of the field, upon which the bands are seen, is inversely proportional to the width of the individual slits. If the latter element be given, it will usually be advantageous to approximate the slits until only a small number of bands are included. In this way not only are the bands rendered larger, but illumination may be gained by the then admissible widening of the original source.

Supposing, then, the proportions of the double slit to be given, we may inquire as to the effect of an alteration in scale. A diminution in ratio m will have the effect of magnifying m times the field and the bands (fixed in number) visible upon it. Since the total aperture is diminished m times, it might appear that the illumination would be diminished m2 times, but the admissible widening of the original source m times reduces the loss, so that it stands at m times, instead of m2 times.

I have noticed a curious misapprehension, even on the part of high authorities, with respect to the application of Carnot's law to an engine in which the steam is superheated after leaving the boiler. Thus, in his generally excellent work on the steam-engine, Prof. Cotterill, after explaining that in the ordinary engine the superior temperature is that of the boiler, and the inferior temperature that of the condenser, proceeds (p. 141): “When a superheater is used, the superior temperature will of course be that of the superheater, which will not then correspond to the boiler pressure.”

This statement appears to me to involve two errors, one of great importance. When the question is raised, it must surely be evident that, in consideration of the high latent heat of water, by far the greater part of the heat is received at the temperature of the boiler, and not at that of the superheater, and that, of the relatively small part received in the latter stage, the effective temperature is not that of the superheater, but rather the mean between this temperature and that of the boiler. An estimate of the possible efficiency founded upon the temperature of the superheater is thus immensely too favourable. Superheating does not seem to meet with much favour in practice; and I suppose that the advantages which might attend its judicious use would be connected rather with the prevention of cylinder condensation than with an extension of the range of temperature contemplated in Carnot's rule.

By the experiments of Jamin and others it has been abundantly proved that in the neighbourhood of the polarizing angle the reflexion of light from ordinary transparent liquids and solids deviates sensibly from the laws of Fresnel, according to which the reflexion of light polarized perpendicularly to the plane of incidence should vanish when the incidence takes place at the Brewsterian angle. It is found, on the contrary, that in most cases the residual light is sensible at all angles, and that the change of phase by 180°, which, according to Fresnel's formula, should occur suddenly, in reality enters by degrees, so that in general plane-polarized light acquires after reflexion a certain amount of ellipticity. Although Jamin describes the non-evanescence at the polarizing angle and the ellipticity in its neighbourhood as “deux ordres de phénomènes de nature différente,” it is clear that they are really inseparable parts of one phenomenon. If we suppose the incident light polarized perpendicularly to the plane of incidence to be given, the vibration which determines the reflected light at various angles may be represented in amplitude and phase by the situation of points relatively to an origin and coordinate axes.

The copious undisturbed transmission of light by glass powder when surrounded by liquid of the same index, as in Christiansen's experiment [vol. II. p. 433], suggests the question whether the reflection of any particular ray is really annihilated when the relative refractive index is unity for that ray. Such would be the case according to Fresnel's formulæ, but these are known to be in some respects imperfect. Mechanical theory would indicate that when there is dispersion, reflection would cease to be merely a function of the index or ratio of wave-velocities. We may imagine a stretched string vibrating transversely under the influence of tension, and in a subordinate degree of stiffness, to be composed of two parts so related to one another in respect of mass and stiffness that the wave-velocity is the same in both parts for a specified wave-length. But, as it is easy to see, this adjustment will not secure the complete transmission of a train of progressive waves incident upon the junction, even when the wave-length is precisely that for which the velocities are the same.

The experiments that I have tried have been upon plate glass immersed in a mixture of bisulphide of carbon and benzole, of which the first is more refractive and the second less refractive than the glass; and it was found that the reflection of a candle-flame from a carefully cleaned plate remained pretty strong at moderate angles of incidence, in whatever proportions the liquids were mixed.

The investigation in question, which was published by Maxwell in the 12th volume of the Cambridge Philosophical Transactions only a short time before his death, has been the subject of some adverse criticism at the hands of Sir W. Thomson and of Mr Bryan. The question is indeed a very difficult one; and I do not pretend to feel complete confidence in the correctness of the view now to be put forward. Nevertheless, it seems desirable that at the present stage of the discussion some reply to the above-mentioned criticisms should be hazarded, if only in order to keep the question open.

The argument to which most exception has been taken is that by which Maxwell (Scientific Papers, ii. p. 722) seeks to prove that the mean kinetic energy corresponding to every variable is the same. In the course of it, the expression (T) for the kinetic energy is supposed to be reduced to a sum of squares of the component momenta, an assumption which Mr Bryan characterizes as fallacious. But here it seems to be overlooked that Maxwell is limiting his attention to systems in a given configuration, and that no dynamics are founded upon the reduced expression for T. The reduction can be effected in an infinite number of ways. We may imagine the configuration in question rendered one of stable equilibrium by the introduction of suitable forces proportional to displacements.

The theory of the vibrations of bells is of considerable difficulty. Even when the thickness of the shell may be treated as very small, as in the case of air-pump receivers, finger-bowls, claret glasses, &c., the question has given rise to a difference of opinion. The more difficult problem presented by church bolls, where the thickness of the metal in the region of the sound-bow (where the clapper strikes) is by no means small, has not yet been attacked. A complete theoretical investigation is indeed scarcely to be hoped for; but one of the principal objects of the present paper is to report the results of an experimental examination of several church bells, in the course of which some curious facts have disclosed themselves.

In practice bells are designed to be symmetrical about an axis, and we shall accordingly suppose that the figures are of revolution, or at least differ but little from such. Under these circumstances the possible vibrations divide themselves into classes, according to the number of times the motion repeats itself round the circumference. In the gravest mode, where the originally circular boundary becomes elliptical, the motion is once repeated, that is it occurs twice. The number of nodal meridians, determined by the points where the circle intersects the ellipse, is four, the meridians corresponding (for example) to longitudes 0° and 180° being reckoned separately.