In a recent paper on the limit to interference when light is radiated from moving molecules, it was necessary to form an estimate of the ratio of illuminations (h) at the darkest and brightest parts of a system of bands corresponding to the moment when they just cease to be visible from lack of contrast. In the comparison of uniformly illuminated surfaces, brought well into juxtaposition, h might be as great as .99; but in the case of bands, where the transition is gradual, a higher degree of contrast between the brightest and darkest parts may be expected to be necessary. In order to allow for this, I supposed that h might be estimated at 95, the intensity of the light and the angular magnitude of the bands being assumed to be suitable. But since widely different estimates have been put forward by others, I have thought it worth while to test the matter with bands that are well under control.

In the first experiments light polarized by a Nicol fell upon a slit, against which was held a somewhat stout selenite. Direct examination of the slit through an analysing Nicol revealed no colour on account of the thickness of the selenite; but when a dispersing-prism was added, the resulting spectrum was marked out into bands, whose brightness and contrast depended upon the relative orientations of the Nicols and of the selenite.

It has long been a mystery why a few liquids, such as solutions of soap and saponine, should stand so far in advance of others in regard to their capability of extension into large and tolerably durable laminæ. The subject was specially considered by Plateau in his valuable researches, but with results which cannot be regarded as wholly satisfactory. In his view the question is one of the ratio between capillary tension and superficial viscosity. Some of the facts adduced certainly favour a connexion between the phenomena attributed to the latter property and capability of extension; but the “superficial viscosity” is not clearly defined, and itself stands in need of explanation.

It appears to me that there is much to be said in favour of the suggestion of Marangoni to the effect that both capability of extension and so-called superficial viscosity are due to the presence upon the body of the liquid of a coating, or pellicle, composed of matter whose inherent capillary force is less than that of the mass. By means of variations in this coating, Marangoni explains the indisputable fact that in vertical soap films the effective tension is different at various levels. Were the tension rigorously constant, as it is sometimes inadvertently stated to be, gravity would inevitably assert itself, and the central parts would fall 16 feet in the first second of time.

The appearance of Professor Cooke's important memoir upon the atomic weights of hydrogen and oxygen induces me to communicate to the Royal Society a notice of the results that I have obtained with respect to the relative densities of these gases. My motive for undertaking this investigation, planned in 1882, was the same as that which animated Professor Cooke, namely, the desire to examine whether the relative atomic weights of the two bodies really deviated from the simple ratio 1 : 16, demanded by Prout's Law. For this purpose a knowledge of the densities is not of itself sufficient; but it appeared to me that the other factor involved, viz., the relative atomic volumes of the two gases, could be measured with great accuracy by eudiometric methods, and I was aware that Mr Scott had in view a redetermination of this number, since in great part carried out. If both investigations are conducted with gases under the normal atmospheric conditions as to temperature and pressure, any small departures from the laws of Boyle and Charles will be practically without influence upon the final number representing the ratio of atomic weights.

In weighing the gas the procedure of Regnault was adopted, the working globe being compensated by a similar closed globe of the same external volume, made of the same kind of glass, and of nearly the same weight.

The existence of a defect is probably most easily detected in the first instance by Holmgren's wool test; but this method does not decide whether the vision is truly dichromic. For this purpose we may fall back upon Maxwell's colour discs. Dichromic vision allows a match between any four colours, of which black may be one. Thus we may find 64 green + 36 blue = 61 black + 39 white—a neutral matched by a green-blue. But this is apparently not the most searching test. The above match was in fact made by an observer whose vision I have reason to think is not truly dichromic, for he was unable to make a match among the four colours red, green, blue, black. The nearest approach appeared to be 100 red = 8 green + 7 blue + 85 black, but was pronounced far from satisfactory. An observer with dichromic vision, present at the same time, made without difficulty 82 red + 18 blue = 22 green + 78 black—a bright crimson against a very dark green.

It would usually be very unsafe to conclude that a colour-blind person is incapable of making a match because he thinks himself so. But, in the present instance, repeated trials led to the same result, while other matches, almost equally forced in my estimation, were effected without special difficulty. It looked as though the third colour sensation, presumably red, was defective, but not absolutely missing.

When I was turning over in my mind the subject for this evening, it occurred to me to take as the title of the lecture, “Froth.” But I was told that a much more poetical title would be “Foam,” as it would so easily lend itself to appropriate quotations. I am afraid, however, that I shall not be able to keep up the poetical aspect of the subject very long; for one of the things that I shall have most to insist upon is that foaming liquids are essentially impure, contaminated—in fact, dirty. Pure liquids will not foam. If I take a bottle of water and shake it up, I get no appreciable foam. If, again, I take pure alcohol, I get no foam. But if I take a mixture of water with 5 per cent. of alcohol there is a much greater tendency. Some of the liquids we are most familiar with as foaming, such as beer or ginger-beer, owe the conspicuousness of the property to the development of gas in the interior, enabling the foaming property to manifest itself; but of course the two things are quite distinct. Dr Gladstone proved this many years ago by showing that beer from which all the carbonic acid had been extracted in vacuo still foamed on shaking up. I now take another not quite pure but strong liquid, acetic acid, and from it we shall get no more foam than we did from the alcohol or the water.

The nature of the question to be first considered may be best explained by a paragraph from a former paper, in which the subject was briefly treated. “There is also another kind of maintained vibration which, from one point of view, may be regarded as forced, inasmuch as the period is imposed from without, but which differs from the kind just referred to (ordinary forced vibrations) in that the imposed periodic variations do not tend directly to displace the body from its configuration of equilibrium. Probably the best-known example of this kind of action is that form of Melde's experiment in which a fine string is maintained in transverse vibration by connecting one of its extremities with the vibrating prong of a massive tuning-fork, the direction of motion of the point of attachment being parallel to the length of the string. The effect of the motion is to render the tension of the string periodically variable; and at first sight there is nothing to cause the string to depart from its equilibrium condition of straightness. It is known, however, that under these circumstances the equilibrium position may become unstable, and that the string may settle down into a state of permanent and vigorous vibration whose period is the double of that of the point of attachment.” Other examples of acoustical interest are mentioned in the paper.

In Part IV. of your “Foundations of the Kinetic Theory of Gases,” you take exception to the manner in which Van der Waals has introduced Laplace's intrinsic pressure K into the equation of virial. “I do not profess to be able fully to comprehend the arguments by which Van der Waals attempts to justify the mode in which he obtains the above equation. Their nature is somewhat as follows:—He repeats a good deal of Laplace's capillary work, in which the existence of a large, but unknown, internal molecular pressure is established, entirely from a statical point of view. He then gives reasons (which seem, on the whole, satisfactory from this point of view) for assuming that the magnitude of this force is as the square of the density of the aggregate of particles considered. But his justification of the introduction of the term a/v2 into an account already closed, as it were, escapes me. He seems to treat the surface-skin of the group of particles as if it were an additional bounding-surface, exerting an additional and enormous pressure on the contents. Even were this justifiable, nothing could justify the multiplying of this term by (ν − β) instead of by ν alone. But the whole procedure is erroneous. If one begins with the virial equation, one must keep strictly to the assumptions made in obtaining it, and consequently everything connected with molecular force, whether of attraction or of elastic resistance, must be extracted from the term Σ(Rr).”

The experiments here described are rather miscellaneous in character, but seem of sufficient interest to be worthy of record. The greater number of them have been exhibited in the course of lectures at the Royal Institution.

The Behaviour of Clean Mercury

According to Marangoni's rule, water, which has the lower surfacetension, should spread upon the surface of mercury; whereas the universal experience of the laboratory is that drops of water standing upon mercury retain their compact form without the least tendency to spread. To Quincke belongs the credit of dissipating the apparent exception. He found that mercury specially prepared behaves quite differently from ordinary mercury, and that a drop of water deposited thereon spreads over the whole surface. The ordinary behaviour is evidently the result of a film of grease, which adheres with great obstinacy.

The process described by Quincke is somewhat elaborate; but my experience with water suggested that success might not be so difficult, if only the mistake were avoided of pouring the liquid to be tried from an ordinary bottle. In the early experiments upon the camphor movements difficulty seems to have been experienced in securing sufficiently clean water surfaces. The explanation is probably to be found in the desire to use distilled water, and to the fact that the liquid would usually be simply poured from a stock bottle into the experimental vessel. No worse procedure could be devised; for the free surface in the bottle is almost sure to be dirty, and is transferred in great part to the vessel.

The idea that liquids are endowed with a viscosity peculiar to the surface is to be found in the writings of Descartes and Rumford; but it is to Plateau that its general acceptance is due. His observations related to the behaviour of a compass needle, turning freely upon a point, and mounted in the centre of a cylindrical glass vessel of diameter not much more than sufficient to allow freedom of movement. By means of an external magnet the needle was deflected 90° from the magnetic meridian. When all had come to rest the magnet was suddenly removed, and the time occupied by the needle in recovering its position of equilibrium, or rather in traversing an arc of 85°, was noted. The circumstances were varied in two ways: first, by a change of liquid, e.g., from water to alcohol; and, secondly, by an alteration in the level of the liquid relatively to the needle. With each liquid observations were made, both when the needle rested on the surface, so as to be wetted only on the under side, and also when wholly immersed to a moderate depth. A comparison of the times required in the two cases revealed a remarkable dependence upon the nature of the liquid. With water, and most aqueous solutions, the time required upon the surface was about double of that in the interior; whereas, with liquids of Plateau's second category, alcohol, ether, oil of turpentine, &c., the time on the surface was about half of the time in the interior.

The phenomenon in question is that exhibited by certain crystals of chlorate of potash, consisting of a peculiar internal coloured reflexion. The following, stated very briefly, are its leading features as described by Stokes:—

1. (1) If one of the crystalline plates be turned round in its own plane, without alteration of the angle of incidence, the peculiar reflexion vanishes twice in a revolution, viz. when the plane of incidence coincides with the plane of symmetry of the crystal.

2. (2) As the angle of incidence is increased, the reflected light becomes brighter and rises in refrangibility.

3. (3) The colours are not due to absorption, the transmitted light being strictly complementary to the reflected.

4. (4) The coloured light is not polarized. It is produced indifferently whether the incident light be common light or light polarized in any plane, and is seen whether the reflected light be viewed directly or through a Nicol's prism turned in any way.

5. (5) The spectrum of the reflected light is frequently found to consist almost entirely of a comparatively narrow band. When the angle of incidence is increased, the band moves in the direction of increasing refrangibility, and at the same time increases rapidly in width. In many cases the reflexion appears to be almost total.

Prof. Stokes has proved that the seat of the colour is a narrow layer, about a thousandth of an inch in thickness, in the interior of the crystal; and he gives reasons for regarding this layer as a twin stratum.

One of the subjects to which I propose to invite your attention this evening is the application of instantaneous photography to the illustration of certain mechanical phenomena which pass so quickly as to elude ordinary means of observation. The expression “instantaneous photography” is not quite a defensible one, because no photography can be really instantaneous—some time must always be occupied. One of the simplest and most commonly used methods of obtaining very short exposures is by the use of movable shutters, for which purpose many ingenious mechanical devices have been invented. About two years ago we had a lecture from Prof. Muybridge, in which he showed us the application of this method—and a remarkably interesting application it was—to the examination of the various positions assumed by a horse in his several gaits. Other means, however, may be employed to the same end, and one of them depends upon the production of an instantaneous light. It will obviously come to the same thing whether the light to which we expose the plates be instantaneous, or whether by a mechanical device we allow the plate to be submitted to a continuous light for only a very short time. A good deal of use has been made in this way of what is known as the magnesium flash light. A cloud of magnesium powder is ignited, and blazes up quickly with a bright light of very short duration.

Introduction

When there is interference of light, the width of the resulting bands, measured for example from darkness to darkness, is usually a function of the colour of the light employed. Thus, in the case of Fresnel's well-known interference-experiment, in which light reflected from two slightly inclined mirrors illuminates a screen, the width of the bands is proportional to the wave-length of the light. In order that a considerable number of bands may be visible, it is necessary that the light be highly homogeneous; otherwise it is impossible that the various band-systems can fit one another over the necessary range. If the light could be supposed to be absolutely homogeneous, there would be no limit to the number of observable bands: and, what is especially to be remarked, there would be nothing by which one band could be distinguished from another,—in particular there could be no central band recognizable. When, on the other hand, the light is white, there may be a central band at which all the maxima of brightness coincide; and this band, being white, may be called the achromatic band. But the system of bands is not usually achromatic. Thus, in Fresnel's experiment the centre of symmetry fixes the position of the central achromatic band, but the system is far from achromatic. Theoretically there is not even a single place of darkness, for there is no point where there is complete discordance [opposition] of phase for all kinds of light.

The question here proposed has been considered by Roiti and by Zecher. My experiments were made in ignorance of the work of these observers, and the results would scarcely be worth recording were it not that the examination seems to have been pushed further than hitherto. It may be well to say at once that the result is negative.

The interference fringes were produced by the method of Michelson as used in his important investigation respecting “The Influence of Motion of the Medium upon the Velocity of Light.” The incident ray ab meets a half-silvered surface at b, by which part of the light is reflected and part is transmitted. The reflected ray follows the course abcdefbg, being in all twice reflected in b. The transmitted ray takes the course abfedcbg, being twice transmitted at b. These rays having pursued identical paths are in a condition to form the centre of a system of fringes, however long and far apart may be the courses cd, ef.

There is here nothing to distinguish the ray ab from a neighbouring parallel ray. The incident plane wave-front perpendicular to ab gives rise eventually to two coincident wave-fronts perpendicular to bg. With a wave incident in another direction the case is different. The two emergent wavefronts remain, indeed, necessarily parallel, both having experienced an even number of reflexions (four and six).

Numerous and varied phenomena prove that the tension of a water surface is lowered by the presence of even a trace of grease. In the case of olive-oil, a film whose calculated thickness is as low as 2 micro-millimetres is sufficient to entirely alter the properties of the surface in relation to fragments of camphor floating thereupon. It seemed to me of importance for the theory of capillarity to ascertain with some approach to precision the tensions of greasy surfaces; and in a recent paper I gave some results applicable to the comparison of a clean surface with one just greasy enough to stop the camphor movements and also with one saturated with olive-oil. The method employed was that depending upon the rise of liquid between parallel plates of glass; and I was not satisfied with it, not merely on account of the roughness of the measurement, but also because the interpretation of the result depends upon the assumption that the angle of contact with the glass is zero. In the opinion of Prof. Quincke, whose widely extended researches in this field give great weight to his authority, this assumption is incorrect even in the case of pure liquids, and, as it seemed to me, is still less to be trusted in its application to contaminated surfaces, the behaviour of which is still in many respects obscure. I was thus desirous of checking my results by a method independent of the presence of a solid body.

In a preliminary notice upon this subject, I explained the procedure by which I found as the ratio of densities 15·884. The hydrogen was prepared from zinc and sulphuric, or from zinc and hydrochloric, acid, and was liberated upon a platinum plate, the generator being in fact a Smee cell, enclosed in a vessel capable of sustaining a vacuum, and set in action by closing the electric circuit at an external contact. The hydrogen thus prepared was purified by corrosive sublimate and potash, and desiccated by passage through a long tube packed with phosphoric anhydride. The oxygen was from chlorate of potash, or from mixed chlorates of potash and soda.

In a subsequent paper on the “Composition of Water,” I attacked the problem by a direct synthesis of water from weighed quantities of the two component gases. The ratio of atomic weights thus obtained was 15·89.

At the time when these researches were commenced, the latest work bearing upon the subject dated from 1845, and the number then accepted was 15·96. There was, however, nothing to show that the true ratio really deviated from the 16 : 1 of Prout's law, and the main object of my work was to ascertain whether or not such deviation existed. About the year 1888, however, a revival of interest in this question manifested itself, especially in the United States, and several results of importance have been published.