on the propagation of sound or light are very instructive, because they show clearly the various circumstances that may affect the problem. It seems clear that any investigation based on the effect of the influence of the presence of the molecules on the potential and kinetic energies must make μ2-1 and not μ-1 a function of the density. The investigations treated of in this Chapter belong to this group because our explanation of dispersion has introduced terms affecting the kinetic energy of the medium. The investigations which

lead to such expressions as (1)/D neglect the vibrations of the

molecules but consider their linear dimensions. The molecules are supposed to be regularly spaced, occupying a volume not negligible compared with the total space, and to be made up of some material having a dielectric constant different from that of the surrounding space. I think the experimental facts of selective refraction are sufficient to show that in the region of the spectrum which contains the free vibrations of the molecules, these constitute the paramount factor, but it is quite possible that when we wish to include the changes of molecular distance, which are brought about by changes of pressure or temperature, the linear dimensions must be taken into

account.

There is another method of treating the subject which consists in considering the effect of a number of irregularly spaced molecules. This has been adopted by Lord Rayleigh in his investigations on the scattering of light by small particles. The effect on the primary wave of each particle, whether due to sympathetic vibration or to a change in the optical properties, is as a first approximation a change of phase which when the molecular distance is small compared with a wave-length is equivalent to a change in wave velocity. By this reasoning we are led to the conclusion that μ-1 is proportional to the density. When the total effect is small, μ-1 is proportional to μ-1, so that as a first approximation, there is no difference between the two results, but there is a fundamental difference between the assumptions made in the two cases. If the distribution is regular, we need only consider the average kinetic and potential energies and may from them proceed to calculate the velocity of wave propagation, assuming that the progressive wave contains all the energy. But with an irregular distribution there is a scattering of light in all directions, and consequent loss of energy. The occurrence of μ2 – 1 in one case, and of μ-1 in the other, seems to be due to this distinction in the adjustment of energy, but when the molecules are as close as they are in solids and liquids, there must be considerable approach to regularity, and the scattering must be comparatively small. Hence theoretical considerations are in favour of μ3.

On the other hand Gladstone and Dale's empirical formula depending on μ – 1 has had very substantial successes in the investigation of the effects of molecular composition on refractive power. The effect of the molecules being proportional to their number per unit volume, which is proportional to d/P if d is the density and P the molecular weight, the quantity (u-1) P/d was introduced by Landolt and called the molecular equivalent of refraction. It was found that if in any compound there are n, atoms of one kind, n, of another, n, of a third, the molecular equivalent of refraction could approximately be calculated from the equation

where v1, v2, 3 are quantities which belong to the element.

159. Historical. Augustin Louis Cauchy, whose work has already been referred to at the end of Chapter x., published some important researches in wave propagation and first obtained formulae giving the constants of elliptic polarization of light on reflexion from metallic surfaces. These he published however without proof.

Jules Céléstin Jamin (born May 30, 1818, in the Department of the Ardennes, died February 12, 1886, at Paris) was the pioneer in the experimental investigation of metallic reflexion, and showed that Cauchy's equations represented the facts with sufficient accuracy. Eisenlohr supplied the analytical proof of Cauchy's formulae and showed that the proper interpretation of Jamin's measurements leads to the conclusion that for silver, the refractive index is smaller than one. This result, which did not seem at that time to be reconcilable with the stability of the medium inside the metal, received support from Quincke's experiments which proved an acceleration of phase when light passed through thin metallic films. The matter was finally settled by A. Kundt* (born Nov. 18, 1839 at Schwerin, died May 21, 1894 near Lübeck, Professor of Physics in the University of Berlin) who succeeded in making thin prisms of metals and thus could demonstrate directly that in metals light was propagated more quickly than in vacuo. The apparent anomaly of this result received its explanation when the refraction of absorbing media generally was more carefully studied.

In 1862 Le Roux having filled a hollow prism with the vapour of iodine, noticed that while it absorbed the central parts of the spectrum, it transmitted the red and violet ends, refracting however the red end more than the violet. This phenomenon he called anomalous dispersion. Eight years later, Christiansen noticed the same phenomenon in the

* Wied. Ann. xXXIV. p. 469. (1888.)

case of a solution of fuchsin. The matter then attracted considerable attention, and A. Kundt especially improved the experimental methods. Including a great many colouring matters in his investigations he was able to formulate the general laws which regulate the influence of absorption on refraction. In the meantime, Sellmeyer had published his theoretical investigation, which is now generally recognized to be correct in principle. It only remains to allude to the work of Ketteler, who more than any one else has shown, both by experiment and by mathematical calculation, that all refraction is of one kind, and that even in the case of apparently transparent media like water, it is necessary to take account of the effects of the free vibrations of the molecules both in the infra-red and ultra-violet.

The recent development of the subject has already been sufficiently treated.

CHAPTER XII.

ROTATORY EFFECTS.

160. Photo-gyration. In all cases hitherto considered the transmission of a luminous disturbance has been such that a plane polarized wave was propagated with its plane of polarization remaining parallel to itself. But there are media in which the wave, though remaining plane polarized, shows a continuous rotation of the plane of polarization as it proceeds. If plane polarized light be made to traverse, for instance, a tube filled with a sugar solution, and the emergent light be examined, it is observed that the plane of polarization has been turned through an angle which is proportional to the length of the tube and also depends on the concentration of the solution.

The direction of rotation is different in different substances. It is said to be right-handed when it is in the direction of the rotation of the hands of a watch, looked at from the side towards which the light travels.

Substances which possess this property are often called "optically active," an expression which is not very descriptive and possibly misleading, as the word "activity" has been applied to several different properties. We shall find that the distinctive feature of the rotational property is the different velocity of propagation of circularly polarized light according as it is right-handed or left-handed. We may therefore appropriately call substances "dextrogyric" or "laevogyric" according as they turn the plane of polarization to the right or to the left (yupos, a circle). A substance is simply called "photogyric" if it acts in its isotropic state, but "crystallogyric" if, like quartz, the property is connected with its crystalline nature. Finally all substances turn the plane of polarization when they are traversed by light in the direction of a magnetic field. They become therefore "magneto-gyric." If a special word be required to express the general property not applied to any particular case, we shall use the expression "allogyric" (aλλos, different), while substances which are inactive are "isogyric."

The allogyric property implies some asymmetrical structure, and in the case of solutions, the want of symmetry must be in the structure of the molecule itself. Van 't Hoff and le Bel have indeed drawn important conclusions as to the arrangement of the atoms in the molecule of allogyric substances.

Quartz is the most conspicuous example of a crystallogyric body. If a plate a few millimetres thick be cut out of a crystal of quartz perpendicularly to the axis, and this plate be examined between crossed Nicols, the luminosity of the field is seen to be restored. If the original light was white, the transmitted light is coloured. The explanation of the effect presents no difficulty on the assumption of a rotation of a plane of polarization which is different for different wave-lengths. There is no rotation of the plane of polarization if the wave-front is parallel to the axis. Some specimens of quartz show a right-handed rotatory effect while others are left-handed. It is found that generally the direction of the rotation may be detected by a close examination of the crystal, there being certain small asymmetrical planes at the corners between the hexagonal prism and pyramid, the position of which is different for the two types of crystals. In all substances hitherto discovered, which are allogyric, the angle of rotation per unit length of substance traversed increases with the refrangibility and is approximately proportional to the inverse square of the wave-length.

There is a marked distinction between the magnetogyric and other allogyric effects. In the case of substances which possess the rotatory property in their natural state, the rotation for rays travelling opposite ways is in the same direction when looked at from the same position relative to the direction in which the light travels. Thus if A and B are two ends of a tube containing a solution of sugar and light is sent through the tube from A to B, an observer looking at B towards the light will observe a right-handed rotation. If now the light be sent from B to A and the observer looks at A, the rotation observed by him is still right-handed. If there were a mirror at B, and the ray after traversing the tube from A to B were reflected back towards A, the plane of polarization at emergence would be parallel to the direction it had on first entering the tube at A. This we should indeed expect by the principle of reversibility (Art. 25). In the case of magnetogyration on the contrary the direction of rotation is different as seen by the observer according as the light travels with or against a line of force, but it is the same when looked at from the same position relative to the direction of the magnetic field. Consequently if light travels from A to B, and is reflected back at B, the angle through which the plane of polarization is rotated is increased and finally doubled during the