air. To perceive this it suffices to pour on the smoked surface a drop of alcohol, benzine, sulphide of carbon-in a word, of a liquid which moistens the lampblack; but in this case the polarization-phenomena are impaired*. It is better to operate by immersing the smoked surface in a glass trough containing the liquid. This causes, it is true, a little perturbation owing to the circumstance that the liquids (such as alcohol and benzine) dissolve a substance deposited at the same time as the carbon, and become somewhat fluorescent; but this does not prevent the diminution of the intensity of the diffused light (without alteration of the polarization-phenomena) from being distinctly observed. Is it not probable that, if the index of refraction of the liquid were identically the same as that of the lampblack, there would be no light diffused?

It seems to me useless to insist further on this difference of interpretation, to which I attach only secondary importance. The question of knowing if the molecules can be regarded as by themselves effective centres of vibrations, or if the action of these molecules is transferred to the æther which surrounds them so as to modify its general density in the interior of a particle, is perhaps subtile and premature. To arrive at its solution, a very interesting part of the labours of M. Lallemand must certainly be taken into consideration; I mean his photometric researches. He has, in fact, shown that the intensity of the diffused light can be calculated by admitting that the vibration of the diffused ray is the projection of the incident vibration, and supposing that the vibratory motion is propagated with the same energy in all directions.

On the proper Colours of Bodies.

We have seen that, at the time of the diffusion by a smoked surface, beside the polarized light there is always a residue of neutral light. To recognize it, we have only to view with an analyzer, under a visual angle of 90°, the surface illuminated by a pencil of light, or to examine it under any angle when the incident pencil is previously polarized.

I have indicated, in my previous Note, the reasons which prevent me from believing that this residue is due to fluorescencet. I think that it may be explained in part because the lampblack is not composed of pure carbon, partly because this

*The conditions are then almost the same as when lampblack deposited on the hinder surface of a plate of glass is viewed through the glass, which is traversed by the incident pencil—a case of which we have to speak further.

+ Nevertheless this case may present itself: M. Ed. Becquerel has in fact observed a phosphorescence in the lampblack deposited by certain flames; but a surface smoked at the flame of benzine is not phosphorescent.

substance does not realize absolutely the necessary conditions for complete polarization, but above all because multiple reflections must be produced. It is evident, on any theory, that a certain portion of the light diffused by a roughness of the surface must reach the neighbouring roughnesses, and there undergo diffusion a second time; and as the plane of polarization of the light after its first diffusion is generally different from that of the incident radiation, the twice diffused rays will be polarized in a different plane from that of the rays diffused once only.

In the case of the illumination of transparent bodies where particles are scantily disseminated in the medium, one can understand that the effect of these multiple reflections may be insensible; but on a smoked surface, where all the particles are contiguous, there is nothing surprising that the effect should become very appreciable.

Here again I regret being in discord with M. Lallemand, who explains this residue by a phenomenon of isochromatic fluorescence. I do not contest that certain bodies, as sulphide of carbon, may possess this faculty-that is to say, may emit by fluorescence rays of the same refrangibility as the incident light; I see no theoretic objection to admitting the existence of this property, which would be analogous to that of membranes vibrating in unison with all the sonorous undulations which strike them; but M. Lallemand gives it a generality the necessity of which does not appear to me to be proved. Indeed he attributes to it not merely the residue of neutral light observed in the diffusion produced by a smoked surface or other dull black bodies, but also the much more considerable proportion of neutral light diffused by white or coloured bodies. Isochromatic fluorescence is for him the cause of the proper colours of bodies.

The theory of the colours proper to substances appears to me well established, although many treatises on physics present large gaps in this respect: several do not mention it; others give it in an incomplete or erroneous manner*. It will, perhaps, not be needless to explain it briefly, as I conceive it, taking into consideration the laws of polarization by diffusion, the study of which has recently made great progress.

Let us lay aside the phenomena of coloration which proceed from ordinary fluorescence (with change of refrangibility), of coloration by superficial reflection (metallic lustre), and of inter

Verdet's Cours de Physique à l'Ecole Polytechnique explains it, in my opinion, very accurately but with sufficient brevity: vol. ii. p. 268. Dove gives it with many more details (Darstellung der Farbenlehre, Berlin, 1853). I have not made extensive bibliographic researches on the subject; but I remember that the theory in question is found in a great number of publications.

ference; these phenomena are most frequently only superposed to those which are realized in a more general manner.

A black body is completely opaque. It is seen only by superficial reflection: if the surface is polished, the reflection is specular; if the surface is dull, there is diffusion according to the laws we have ascertained concerning polarization. Between absolute polish and perfect absence of lustre we may have all the intermediate degrees.

A white body is transparent for every sort of luminous rays. It is visible, first, in consequence of superficial reflection, exactly as the black body; but, in addition, there arrive at the eye rays which have undergone one or more interior reflections. If the body is polished and homogeneous, we have the well-known appearance of glass or colourless crystals. If the body is dull and homogeneous (ground glass), we have phenomena of surface diffusion as for black bodies, but with a twofold complication: the light which has penetrated the interior emerges again either directly or after interior reflection, undergoing diffusion by refraction; moreover the light diffused exteriorly falls in part on the roughnesses of the surface, and may pass through them. If the body is polished but not homogeneous (porcelain), the surface reflection is specular; but the rays which penetrate the substance are reflected or diffused in the interior, and a great portion of them emerge from the body. Finally, if the body is dull and not homogeneous, we have the combination of the two preceding cases.

It is easy to understand that the phenomena of polarization are completely disturbed as soon as the diffusion is no longer merely superficial. A very simple experiment makes this immediately intelligible. We have seen that, when a horizontal pencil polarized in a vertical plane falls on a plate of glass covered with lampblack, the visual plane being horizontal, and the visual angle 90°, we have only a residue of neutral light, whatever may be the position of the diffusing surface in relation to the incident pencil. If we turn the glass plate so that the pencil must pass through the glass in order to arrive at the lampblack, then the phenomenon is completely changed: the eye remaining in the same position, receives, instead of a neutral residue, light strongly polarized. The reason is easy to comprehend: the pencil of light, penetrating the plate (which is necessarily inclined upon its direction), is refracted and deviates; the lampblack therefore does not receive a pencil making a right angle with the visual ray; and therefore the light diffused in the direction of the latter must be polarized. To this cause of perturbation is joined the change of plane of polarization which the incident ray generally undergoes by its refraction,

and the polarization by refraction experienced by the diffused light in passing through the glass to arrive at the eye*. This fact involves as a consequence that, if we operate exactly in the same manner, employing only a neutral incident pencil instead of a polarized pencil, the diffused rays will be much less polarized in the plane of vision than they are when the light arrives at the lampblack without passing through the glass. Phenomena of the same kind are generally produced when the light has penetrated into the body; and when the latter has no homogeneity and is not polished (chalk), very sensitive apparatus is requisite to discover a trace of polarization.

In coloured bodies the course of things is the same as in white bodies, except that, the body not being transparent to every kind of ray, it is only by superficial reflection or diffusion that the white light is sent back all the light which penetrates into the interior to emerge again is coloured; and the colour is that of the rays which it permits to pass. It is natural, then, that the white light, diffused superficially, should be alone polarized, according to the laws of diffusion by a black body, while the coloured light, which has undergone internal reflection, is not polarized, or only partially so. From this results the fact, observed by several physicists, that if one views through an analyzer, under a visual angle of 90°, a coloured diffusing substance illumined by a pencil of natural light, the colour of the body appears very pure and saturated when the analyzer is turned so as to intercept the rays polarized in the plane of vision, while it is washed with white when the analyzer is in the reverse position or when it is viewed without an analyzert. The experiment can also be made by illuminating the unpolished coloured surface by a horizontal pencil previously polarized in a vertical plane; in a horizontal visual plane, and under a visual angle of 90°, the colour then appears richer than in any other position . M.

When the incident pencil falls perpendicularly on the anterior surface of a plate of glass slightly smoked on its posterior surface, we may assure ourselves that there is no perturbation in the phenomena of polarization of the light diffused after its passage through the glass. In fact, in this case refraction modifies neither the direction nor the plane of polarization of the incident pencil, and, on the other hand, the diffused rays come direct to the eye.

↑ MM. de la Prevostaye and Desains interpret this fact by saying (with some reservation, it is true):-"It may hence be concluded that rays of different tints are not diffused in the same proportions and according to the same laws." Other authors content themselves with accounting for the colour of bodies by saying that they diffuse certain rays more than others: this is the expression of a fact, not an explanation.

This experiment becomes very beautiful when it is effected in the following manner. A large pencil of solar or electric light is caused to enter a dark room, being concentrated by a lens of long focus; near the

Lallemand operated also by throwing a pure and polarized spectrum on the coloured diffusing surface: according to the position of the eye, the different diffused colours are perceived to be more or less polarized; and those which are the least polarized correspond to the proper colour of the body. But M. Lallemand attributes this to fluorescence, while, according to the theory which has just been explained, it is the result of absorption and depolarization by interior reflections.

In support of this theory must be mentioned first the fact that the colour of a body by diffusion is always the same as by transparence. I will here report some experiments which show it in a striking manner:—

A horizontal pencil of sunlight, polarized in a vertical plane, falls on the coloured diffusing surface. The observer views it under a visual angle of 90°, the plane of vision being horizontal: the colour, as we have said, appears very rich. But as the asperities of the surface are rarely minute enough for the diffusion to be perfect, and in certain cases the substance may be contained in a glass vessel, producing specular reflection, it is better to pass the diffused rays through a Nicol or a Foucault, stopping the rest of the polarized rays. The colour of the body then appears with the maximum of saturation and can be analyzed with the spectroscope.

It is convenient to choose for the operation of diffusion a substance the absorption-spectrum of which is discontinuous and characterized by bands.

Let us take smalt, for example. Although in powder its colour is much washed with white, because the thickness to be traversed by the light in the interior of the particles is too little to give rise to strong absorption, it is easy to distinguish in the diffusion-spectrum the characters attenuated of the absorptionspectrum of cobalt.

Let us now take some blood (the spectrum of which is so characteristic) and put it in a glass test-tube, or, still better, moisten with the blood the outside of the tube. Thanks to the Nicol prism placed in front of the spectroscope, the light reflected

point where the image of the sun is formed, where the pencil is narrowest, a large polarizer is placed. Then, at a distance of one or two metres, in the luminous divergent cone a bouquet of deep-coloured velvety flowers is placed, such as pansies or certain varieties of geraniums. The observer views the bouquet at a right angle with the incident pencil, while an assistant turns the polarizer. The tint of the bouquet then appears to pass through alternations of saturated colours and colours washed with white, which are very striking. The observer may also place himself in any position whatever, if he look through an analyzer which he keeps immovable while the polarizer is rotated, or vice versa.