pure glass,-deriving their colour from the individual films of which they are composed. This is obvious from the fact of their becoming colourless by a sufficient inclination of the plates, and also by the introduction of a drop of water or alcohol. When the fluid has evaporated, the films recover their original colour; and though a film of fluid has separated each of the almost infinitesimal layers of the glass, yet they adhere as firmly as ever after the fluid has evaporated. If an oil or balsam is introduced, it passes slowly and unequally between the layers, so that the retreating colour is bounded by a spectrum of the various tints which the film combines. But though the films themselves are glass, yet I have often found between them beautiful circular crystals of silex, which are finely seen in polarized light, and exhibit many of the regular and irregular forms which I have represented in a paper on Circular Crystals lately published in the 'Transactions of the Royal Society of Edinburgh.' They are sometimes dendritic, and assume, round the black cross, foliated shapes like the leaves of plants. At other times, but very rarely, they occur in circular groups,-related to a crystal of silex in their centre. One of these groups is so remarkable as to merit particular notice. Around a minute speck of silex there is formed, at a considerable distance from it, a circular band of equally minute crystalline specks, and at a greater distance a second circular band concentric with the first, and consisting of still smaller siliceous particles, hardly visible in the microscope. By what atomic force, or by what other cause, the central crystal has placed its attendant crystals in regular circles around it, remains to be discovered. I have already described a similar phenomenon, as produced during the formation of circular crystals under constraint, and when crystallizing freely; but I am not aware that any other person has either seen the phenomenon or attempted to explain it. The films of decomposed glass, as I have long ago shown, absorb definite rays of the spectrum like coloured media. They change, in the most distinct manner, the colours of different parts of the spectrum, and frequently insulate bands of purely white light, in or near its most luminous division. [The drawings referred to in this commnnication were laid before the Section, and some of the specimens of decomposed glass were exhibited in the Museum in the course of the evening.] On his own Perception of Colours. By J. H. GLADSTONE, Ph.D., F.R.S. The author described himself as in an intermediate position between those who have a normal vision of colours, and those who are termed "colour-blind." These latter are usually unacquainted with the sensations of either red or green, and it becomes a desideratum to have good observations on those who are capable of acting somewhat as interpreters between them, and those who perceive every colour. By means of Chevreul's chromatic circles and scales, Maxwell's colour-top, coloured beads, &c., the author was able to determine the following points in respect to his own vision. He sees red, in all probability, like other people, but it requires a larger quantity of the colour to give the sensation than is usually the case; hence a purple appears to him more blue, and an orange more yellow, than to the generality of observers. He is perfectly sensible of green, or rather of two distinct greens, the one yellowish, the other bluish; but between them there lies a particular shade of green, to which his eyes are insensible as a colour. This modifies his perception of many greens that approximate to what is to him invisible. The shade occurs in nature on the back of the leaf of the variegated holly, and it may be produced in Maxwell's top by certain combinations of the coloured disc; the simplest being 94.5 Brunswick Green (Blue Shade) + 5.5 Ultramarine =94 Black+6 White. He finds that this shade, though invisible to him as green, is yet capable of neutralizing red when viewed simultaneously, but it does not neutralize so much red with him as with observers of ordinary vision. While able perfectly to distinguish between red and green, the contrast does not readily catch his eye, especially at a distance; in fact, he is somewhat short-sighted in respect to these colours. He has reason to believe that, in his case, there has been a gradual improvement in his actual perception of colours, independently of his greater knowledge of them, though this is in opposition to the general experience of those whose vision is in any way abnormal, and no other instance was known to the late Prof. George Wilson, whose book is the standard one on the subject of colourblindness. On the Chromatic Properties of the Electric Light of Mercury. While examining the brilliant electric light produced in an interrupted current of mercury in the apparatus contrived by Professor Way, the author was struck by the strange manner in which it modified the apparent colours of surrounding objects, and especially with the ghastly purple and green hues which it imparted to the faces and hands of the spectators. This led him to an investigation of the subject, and a prismatic analysis of the light itself. Chevreul's "cercles chromatiques" showed yellow, green, and blue distinctly, but very little red, while the violet became remarkably luminous. The modifications of colour in many bodies of known composition were then related, as for instance the green sulphate of iron which appeared colourless, and the scarlet iodide of mercury which assumed a brownish metallic appearance. Substances capable of fluorescing exhibited that phenomenon with remarkable beauty. On analysing this light by means of a refractive goniometer, the author found it to consist of a great number of separate rays, and not to present in any part a continuous band of light. This was exhibited by means of a diagram in coloured chalks on black paper, by the side of a solar prismatic spectrum. The position of the different rays had been measured, and their relative intensity determined. There are red and orange rays, but they are of the most feeble intensity; some yellow rays of great brilliancy; two bright green rays; one blue ray of great luminosity; and a number of violet rays. One of these latter is situated far beyond the limits of the visible solar spectrum, in fact at about Becquerel's line N, and was bright to the eye, although it had passed through several pieces of glass-a medium that does not easily transmit the extra-violet rays. Its colour appeared to differ considerably according to its intensity, but might be described generally as a redviolet. The prismatic analysis explained fully the changes that red substances undergo when exposed to it-sometimes to brown, and at other times to purple, green, or whatever other colour in addition to red is principally reflected by them: it also explained all the other chromatic phenomena. Professor Wheatstone in 1835 described the spectrum of the electric light of mercury as containing seven definite rays; and Angström has recently given a drawing of the lines that coincides closely with the observations of the author on the more luminous rays, and shows that the Swedish physicist had not seen the extra violet lines. From his figures also it appears that the air is excluded from the luminous cone of mercurial vapour in Way's apparatus. On a New Instrument for determining the Plane of Polarization. Professor Jellett described to the Section a new analysing prism, by which the plane of polarization of polarized light may be determined with great precision. This instrument consists of a long prism of calc-spar, which is reduced to the form of a right prism by grinding off its ends, and sliced lengthwise by a plane nearly but not quite perpendicular to its principal plane. The parts into which the prism is thus divided are joined in reversed positions, and a diaphragm with a circular opening is placed at each end. The light which passes through both diaphragms produces a circular field divided by a diametral slit into two parts, in which the planes of polarization are slightly inclined to one another. If then light which has been previously plane polarized be transmitted, it will be extinguished in the two parts of the field of view in positions which lie close together, and the light will become uniform in a position midway between these. This position determines the plane in which the incident light was polarized, with a precision much greater than has been otherwise attained. Professor Jellett stated that the different observations did not differ from one another by an angle greater than a minute, and that the instrument was equally applicable to the case of homogeneous light. Note on the Caustics produced by Reflexion. By L. L. LINDELÖF, Professor at Helsingfors. There are, no doubt, few branches of mathematical physics that have been more often discussed than the reflexion and refraction of light, and the theory of these phenomena has consequently been gradually reduced to the greatest simplicity. The whole doctrine of catoptrics and dioptrics may indeed be said to be implicitly contained in the elegant principle successively developed by Dupin, Quetelet, and Gorgonne, namely, that a system of rays that can be cut orthogonally by a particular surface, preserves this property after any number of reflexions and refractions. Nevertheless, it appears to me that the theory of caustics has been somewhat neglected. Not but what there are many interesting researches on this subject that have been conducted with abundance of care, but because these, for the most part, refer to certain very restricted cases, as for example, to reflecting surfaces of a particular kind. In examining from a somewhat more general point of view the theory of caustics produced by reflexion, I have arrived at certain results, which appear to me to be sufficiently curious to deserve a short notice. I suppose the reflecting surface to be of any kind whatever, and that it is illuminated by a bundle of parallel rays. Suppose, now, that two of these rays impinge on the surface at two points A and A' infinitely near each other. Unless certain particular conditions are fulfilled, the corresponding reflected rays will not be in the same plane. In order, therefore, that the two rays may meet after reflexion so as to form a point in a caustic, the points A and A' must be related in a certain manner. Now it will be found that, starting from any point A, there will always be two different directions in which the consecutive reflected rays intersect, and by following these directions from point to point, certain curves will be traced on the surface, which play an important part in the theory of caustics, and which may be called catoptrical lines. These lines bear some analogy to the lines of greatest and least curvature, with which they sometimes coincide. Their form and situation depend not only on the nature of the surface, but also on the direction of the incident rays. Each point of the surface is the intersection of two catoptrical lines, which possess the remarkable property that their projections on the plane perpendicular to the incident rays, cut each other at right angles. To each catoptrical line there is a corresponding caustic formed by the rays reflected from the catoptric, and these caustic lines themselves form a caustic surface, which in general consists of two sheets, corresponding to the two systems of catoptrical lines. Let x, y, and z be the coordinates of any point in the reflecting surface, and let the axis of ≈ be parallel to the incident rays. Calling, as usual, the partial differential coefficients of ≈ with respect to x and y of the first order p and q, those of the second r, s, and t, we have for the catoptrical lines the simple equation since dp rdx+sdy, dq=sdx+tdy. The quantities p, q, r, s, and t being all expressible in terms of x and y by means of the equation to the reflecting surface, the two values of dy derived from the above dx equation can also be expressed in terms of x and y. If this differential equation can be integrated, the resulting relation between x and y, together with the equation to the surface, determine the catoptrical lines. The point, 7, and of the caustic corresponding to x, y, z of the reflecting surface, is determined by the following equations: Eliminating x, y, z by means of these three equations and that of the given surfaces, we obviously get the equation to the caustic surface; and eliminating the same quan tities between the same three equations, and the two equations of any catoptrical line, we get the equations to the corresponding caustic line. As to the application of this theory it offers no difficulty. On directing my attention more particularly to surfaces of the second order, I obtained the following results: (1) In the case of a sphere illuminated by parallel rays, the first system of catoptrical lines consists of great circles passing through the same point, the second of small circles cutting the former at right angles. The equation to the caustic surface that corresponds to the first system is [4 (§2+n2+52)—a2]3=27a1 (§2+n3), a being the radius of the sphere, while the second system has for its caustic a straight line passing through the centre of the sphere. (2) If the reflecting surface be an ellipsoid or a hyperboloid, either of one or of two sheets, and the incident rays are parallel to one of the axes, the projections of the catoptrical lines on the plane of the other axes are either ellipses or hyperbolas, whose foci coincide with those of the section of the surface by the same plane. (3) In the case of an elliptic paraboloid illuminated by rays parallel to its axis, the catoptrical lines form parabolas whose planes are parallel to one or the other of the principal sections of the surface. The caustic surface is reduced to two parabolas lying in the planes of the principal sections, and having the axis of the paraboloid for their common axis, but situated in opposite directions. That which lies in the plane of the greatest of the principal sections is turned in the same way as the paraboloid, that lying in the perpendicular plane is turned in the opposite direction. Each of these parabolas has the same focus as the principal section to which it is perpendicular, and a parameter equal to the difference of the parameters of the principal sections. Lastly, each of these caustic lines is perpendicular to the corresponding system of catoptrical lines. (4) In the case of a hyperbolic paraboloid illuminated by rays parallel to its axis, the catoptrical lines also form two systems of parabolas in planes parallel to the planes of the principal sections, and the caustic is again reduced to two parabolas situated in the same two planes, and turned in opposite directions, each having a parameter equal to the sum of the parameters of the two principal sections. There would be no difficulty in applying the above formula to surfaces of revolution, to cylindrical conical developable surfaces, &c., but the preceding will suffice to give an idea of the results that may be deduced in certain cases. On the Results of Bernoulli's Theory of Gases as applied to their Internal Friction, their Diffusion, and their Conductivity for Heat. By Professor MAXWELL, F.R.S.E. The substance of this paper is to be found in the Philosophical Magazine' for January and July 1860. Assuming that the elasticity of gases can be accounted for by the impact of their particles against the sides of the containing vessel, the laws of motion of an immense number of very small elastic particles impinging on each other, are deduced from mathematical principles; and it is shown,-1st, that the velocities of the particles vary from 0 to ∞, but that the number at any instant having velocities between given limits follows a law similar in its expression to that of the distribution of errors according to the theory of the "Method of least squares." 2nd. That the relative velocities of particles of two different systems are distributed according to a similar law, and that the mean relative velocity is the square root of the sum of the squares of the two mean velocities. 3rd. That the pressure is one-third of the density multiplied by the mean square of the velocity. 4th. That the mean vis viva of a particle is the same in each of two systems in contact, and that temperature may be represented by the vis viva of a particle, so that at equal temperatures and pressures, equal volumes of different gases must contain equal numbers of particles. 5th. That when layers of gas have a motion of sliding over each other, particles will be projected from one layer into another, and thus tend to resist the sliding motion. The amount of this will depend on the average distance described by a particle between successive collisions. From the coefficient of friction in air, as given by Professor Stokes, it would appear that 1 1 400000 1 389000 this distance is 7000 inch; the mean velocity being 1505 feet per second, so that each particle makes 8,077,200,000 collisions per second. 6th. That diffusion of gases is due partly to the agitation of the particles tending to mix them, and partly to the existence of opposing currents of the two gases through each other. From experiments of Graham on the diffusion of olefiant gas into air, the value of the distance described by a particle between successive collisions is found to be of an inch, agreeing with the value derived from friction as closely as rough experiments of this kind will permit. 7th. That conduction of heat consists in the propagation of the motion of agitation from one part of the system to another, and may be calculated when we know the nature of the motion. Taking of an inch as a probable value of the distance that a particle moves between successive collisions, it appears that the quantity of heat transmitted through a stratum of air by conduction would be of that transinitted by a stratum of copper of equal thick10,000,000 ness, the difference of the temperatures of the two sides being the same in both cases. This shows that the observed low conductivity of air is no objection to the theory, but a result of it. 8th. That if the collisions produce rotation of the parti. cles at all, the vis viva of rotation will be equal to that of translation. This relation would make the ratio of specific heat at constant pressure to that at constant volume to be 1.33, whereas we know that for air it is 1-408. This result of the dynamical theory, being at variance with experiment, overturns the whole hypothesis, however satisfactory the other results may be. 1 On an Instrument for Exhibiting any Mixture of the Colours of the This instrument consists of a box about 40 inches long by 11 broad and 4 deep. Light is admitted at one end through a system of three slits, of which the position and breadth can be altered and accurately measured. This light, near the other end of the box, falls on two prisms in succession, and then on a concave mirror, which reflects it back through the prisms, so as to increase the dispersion of colours. The light then falls on a plane mirror inclined 45° to the axis of the instrument, and is reflected on a screen in which is a narrow slit. On this screen are formed three pure spectra, the position and intensity of each depending on the position and breadth of the slit through which the light was admitted. The portions of these spectra which fall on the slit in the screen pass through, and are viewed by the eye placed close behind it. A colour compounded of these three portions of three different spectra is seen illuminating the prisms, and can be compared with white reflected light seen past the edge of the prisms. The advantage of the instrument over that described to the Association in 1859 is, that by the principle of reflexion the rays return in the same tube, so as not to require two limbs forming an awkward angle; while at the same time, by doubling the dispersion, the necessary length of the instrument is diminished. By means of this instrument many observations of colours have been taken. Some of these by a colour-blind person are published in the 'Philosophical Transactions' for 1860. Further Researches regarding the Laws of Chromatic Dispersion. In this paper the author has revised, and improved in its details, his method of expressing the refractive index of a medium as a function of the wave-length. He employs to denote the ratio of any particular wave-length referred to that of the fixed line B as unity. The numerical values of the wave-lengths of the lines C, D, E, F, G, H are given, as calculated from Fraunhofer's measures. The author's formula for expressing the refractive index (μ) as a function of λ is |