book: the sum total of the mathematics employed is contained in the text of the two propositions of the third book of Euclid which assert that if any line drawn through a point O meet a circle in P and Q, the rectangle OP. OQ is constant, and that the sum of a pair of opposite angles in a quadrilateral inscribable in a circle is two right angles.

Mr. Heaviside concludes his third chapter with a discussion of a linear operator in general (p. 283), and the means of inverting it, together with a deduction of Hamilton's cubic. The linear operator is treated all through by Mr. Heaviside exactly as it appears in the general theory of strain and stress-namely, as consisting of coefficients expressing the relations between the three components of one vector and those of another, these coefficients being, in general, nine, as when the components of strain in a solid are expressed in terms of direction; but sometimes reducing to six, as when components of stress are expressed in terms of direction.

Mr. Heaviside's mode of treatment will be found to be a valuable side-light to the discussion of the linear vector function in Tait's treatise. Of course, the rather high-sounding phrase "inversion of a linear operator' denotes nothing more than the solution of three homely simple equations; nevertheless, there are some neat relations involved.

This review has already gone much beyond the usual limits, and, in confining itself chiefly to controversial matters, has omitted to notice the most valuable portion of Mr. Heaviside's work, the greater part of which appears in the last chapter. This part of the work has recently been treated, with great commendation, by Professor Fitzgerald in 'The Electrician.' All readers of this volume will agree in regarding it as an able work, and, indeed, one which is of immense assistance to advanced students in Physics.

One final instance of Mr. Heaviside's regard for accuracy and desire for scientific completeness must be mentioned. It is found in Art. 192, in which he justly objects to the equation by which Maxwell expresses the relation between magnetic induction, magnetic force, and magnetization at any point of a medium, viz., B=H+4′′I. To this Mr. Heaviside objects that it makes induction and magnetization identical in kind with magnetic force, which, as he says, "is more than mischievous in theory." His own form of the equation, B=μ(1+k)F, where F is the magnetic force, is in all respects much better.

G. M. MINCHIN.

XVI. Proceedings of Learned Societies.

GEOLOGICAL SOCIETY.

[Continued from vol. xxxvii. p. 419.]

January 10th, 1894.-W. H. Hudleston, Esq., M.A., F.R.S.,
President, in the Chair.

THE following communications were read:

1. 'On the Rhætic and some Liassic Ostracoda of Britain.' By Prof. T. Rupert Jones, F.R.S., F.G.S.

2. Leigh Creek Jurassic Coal-Measures of South Australia: their Origin, Composition, Physical and Chemical Characters; and Recent Subaerial Metamorphism of Local Superficial Drift.' Parkinson, Esq., F.G.S., F.C.S.

By James

This paper contains an account of the lignitic coal of Leigh Creek and associated rocks. Analyses are given, as illustrating comparisons between the Leigh Creek coal and Jurassic and other coal-bearing rocks found elsewhere. The Author discusses the origin of the Leigh Creek deposits, and describes certain peculiarities noticeable in the superficial materials, which he discusses in another paper.

3. 'Physical and Chemical Geology of the Interior of Australia: Recent Subaerial Metamorphism of Eolian Sand at ordinary atmospheric temperature into Quartz, Quartzite, and other Stones.' By James Parkinson, Esq., F.G.S., F.C.S.

South of the Flinders Range fragments of stone of all sizes are found on the ground, the origin of which the Author discusses. He maintains that they were formed by subaerial metamorphism of Eolian deposits.

January 24th.-W. H. Hudleston, Esq., M.A., F.R.S.,

President, in the Chair.

The following communications were read :—

1. The Ossiferous Fissures in the Valley of the Shode, near Ightham, Kent.' By W. J. Lewis Abbott, Esq., F.G.S.

2. The Vertebrate Fauna collected by Mr. Lewis Abbott from the Fissure near Ightham, Kent.' By E. T. Newton, Esq., F.R.S., F.G.S.

XVII. Intelligence and Miscellaneous Articles.

ON THE DEPENDENCE OF THE PHOTOELECTRIC CURRENT ON THE POSITION OF THE PLANE OF POLARIZATION OF THE EXCITING LIGHT IN REFERENCE TO THE SURFACE OF THE KATHODE. BY DR. J. ELSTER AND H. GEITEL.

1T T is possible in many cases to lower the potential required for the spontaneous discharge of an electric current in a gas by exposing the kathode to the action of light. For the same difference of potential the strength of the current depends on the nature of the kathode, the gas, and the light. While kathodes of platinum, mercury, copper, and several other metals require irradiation with ultra-violet light of high intensity, kathodes of sodium, potassium, rubidium, in an atmosphere of hydrogen of about 03 millim. pressure, give currents which can be measured galvanometrically, even with feeble light within the region of the visible rays.

The question may be asked whether this action of light on the electrical discharge depends on the orientation of the vibrations with respect to the surface of the electrode struck.

Experiments with polarized ultra-violet light of sufficient intensity are difficult to make because it is absorbed by the ordinary polarizing arrangements, such as Nicol's prism, tourmaline plates, glass disks, &c., so that only polarization by reflexion remains; even with this method, however, great losses of light are unavoidable. Thus in an analogous phenomenon, the development of electrical sparks by ultra-violet light discovered by Hertz, M. Wanka did not succeed in establishing the influence of the direction of vibration of the light, which he had supposed to exist. This difficulty disappears with kathodes of the alkaline metals, since we can here work with ordinary polarized light; but another difficulty presents itself, that a polished and, if possible, a plane surface of these substances must be produced in a vacuum. requirement is, however, satisfied by using as kathode the alloy of potassium and sodium, which is liquid at ordinary temperatures. When placed in a roomy receiver a sufficient quantity sets plane and horizontal in the central part of the surface.

This

We have investigated the photoelectric action of polarized light as follows.

In the circuit of a voltaic battery of about 250 volts are a sensitive galvanometer, a commutator, and a sensitive cell of the liquid potassium and sodium alloy of the form shown in Wiedemann's Annalen, vol. xlii. p. 564, so inserted that the negative-pole wire leads to the surface of the alkali metal. In order that the active luminous pencil should have a constant section, the cell was coated with opaque varnish, with the exception of a small circle of 15 millim. diameter turned towards the source of light. The cell is so arranged that the rays entering this aperture centrally and parallel strike the centre of the metal surface under an angle of about 65°. Between the source of light and the cell a lens was introduced for the production of parallel light as well as a polarizing arrangement (a Nicol's prism or a set of glass plates).

If the polarizing apparatus is turned while at the same time the strength of the current is measured at the galvanometer, two maxima and two minima are observed in the course of a single rotation. The minima occur when the plane of polarization of the light is parallel to the plane of incidence of the rays on the kathode; the maxima are in positions at an angle of 90° with them. The ratio of maxima to minima is about 10: 1. If while the plane of polarization is parallel to the plane of incidence, a quartz plate about 2 millim. thick, cut at right angles to the optical axis, is placed in the path of the polarized light, the current increases about sevenfold, corresponding with the rotation of the plane of polarization due to the quartz. When the plane of polarization is at right angles to the plane of incidence, a quartz plate has the opposite effect; the strength of the current diminishes, as was to be expected, in a corresponding ratio. Apart from a slight enfeeblement of the current due to the loss of light caused by its interposition, a clear glass plate has no effect in either position.

According to the investigations of MM. Trouton (Nature," vol. xxxix. p. 393), Klemenčič (Wiedemann's Annalen, vol. xlv, p. 77), and Righi (Rend. della R. Ac. dei Lincei, vol. xi. p. 161) it must be taken for granted that, in Hertz's rays of electrical force, the plane of polarization is at right angles to the direction of the electrical displacement. If the motion in the light rays is regarded as analogous, the result of the experiments described would be thus expressed.

The luminous electrical current attains its maximum when the electrical displacements in the luminous ray take place in the plane of incidence, its minimum when they are at right angles thereto. In the former case the electrical vibrations contain a component normal to the kathode, but not in the second. We might be tempted to seek in these changes of potential normal to the kathode, and induced by the electrical rays, the force which impels the negative electricity to leave the kathode. Whether this suggestion is correct, can perhaps be ascertained by further experiments on the dependence of the luminous electrical action on the angle of incidence of the polarized light, and their connexion with the quantities of light reflected from and retained by the kathode.— Berliner Berichte, February 8, 1894. (Communicated by the Authors.)

ON VORTEX MOTIONS IN AIR. BY G. QUINCKE.

At the meeting of the Natural History and Medical Society of Feb. 7, 1890, I discussed the motion of falling spheroids of oil in water, the specific gravity of which was increased somewhat by the addition of chloroform. Such a spheroid falls vertically in water at rest. But if two spheroids of oil fall simultaneously close to each other, they approach and recede from each other in falling. The path and the time of fall depend on the diɛtance apart and the velocity of the falling spheroids. This peculiar motion is caused by the vortices which are produced by the falling spheroids of oil in the water about them, which had hitherto

been at rest. The particles of water in the plane of symmetry between the falling spheroids remain at rest.

Instead of two spheres, one may be allowed to fall near a plane vertical wall, which then acts as plane of symmetry. The spheroid falls as it were with its image in the plane vertical wall, and approaches and recedes from this.

These experiments with heavy oil spheroids in water are tedious, and can only be shown to a small audience.

Analogous phenomena may be produced before a larger circle of hearers by allowing two soap bubbles filled with coal-gas to ascend near each other, or a single bubble near a vertical wall.

In ascending, the distance of the two soap bubbles from each other, or of a single one from its image in the vertical wall, is first smaller and then greater, and the cause again is the vortex movements in the air due to the ascending soap bubbles.

In order to fill two soap bubbles simultaneously with coal-gas they are produced at the ends of a T-piece of glass, blown out in the form of horizontal cups, to which the gas passes from the centre tube through a T-shaped perforated glass stopper.

Similar phenomena occur when small dust particles fall in air or liquid at rest, or if a current of air or liquid strikes against particles of dust at rest. The motion of the small particles is influenced by the presence and form of the solid wall in the vicinity.-Wiedemann's Annalen, July 1894.

ON A NEW APPARATUS FOR THE PRODUCTION OF HIGH PRESSURE. BY PROF. S. W. STRATTON*.

Not long since, while designing a piece of apparatus for the production of high pressure, it occurred to me that many of the difficulties encountered in the measurement of such pressures might be avoided by the employment of several short mercurycolumns connected in series by means of a less dense liquid, as shown in the accompanying sketch.

Such a gauge would possess all the advan

tages of the ordinary mercury-column, and be within the limits of space to be had in the laboratory. For many purposes the last tube only need be made of glass, and the scale reduced accordingly.

Thinking that this principle may be new, and of value to some who are employing high pressures in the laboratory, it is submitted for publication.

The Ryerson Physical Laboratory,
University of Chicago,

May 21, 1894.

*Communicated by Prof. A. A. Michelson.