104 SUMMARY OF CURRENT RESEARCHES RELATING TO 



very clear and vivid manner and seems a very complete presentation of 

 the subject. Tlie book is divided into nine chapters, the first three of 

 which deal with the ultramicroscope and the others with nltramicro- 

 scopic objects. The first chapter discusses the limits of microscopic 

 visibility, and the second explains how ultraviolet light bears upon the 

 matter. The third chapter describes the ultramicroscope itself. The 

 contents of the other chapters include the ultraniicroscopic study of 

 solids, liquids, Brownian movements, colloids, electric transport, and 

 biological applications. 



Study of the Rotation Impressed upon the Plane of Polarisation, 

 by the Lenses of the Microscope under Convergent Light.*— (1. Cesaro 

 points out that Fresnel's formula for the passage of a polarised ray 

 through a series of isotropic media .readily lends itself to a very simple 

 geometrical interpretation which renders it easy to construct the various 

 paths of the ray. For this purpose it suffices to construct two planes : — 

 (1) The plane containing the point of incidence and normal to the 

 refracted ray ; (2) the plane passing through the incident ray and its 

 vibration. The intersection of these two planes gives the desired 

 vibration. The same construction is continued from medium to 

 medium. The author describes a number of experiments which illus- 

 trate his method. 



Numerical Examination of the Optical Properties of Thin 

 Metallic Plates.f — One of the first workers in this field was MacCullagh^ 

 who predicted from theory, and verified by experiment, that if light 

 incident on a gold leaf were plane polarised, the transmitted beam would 

 be elliptically polarised. With the improvement in experimental methods 

 since MacCullagh's day, and the gradual removal of obscurities from 

 the theory of metallic reflection and transmission, an almost exact 

 numerical coincidence may now be looked for between theory and 

 experiment. R. C. Maclaurin, in discussing the subject, points out that 

 the condition of the reflected or transmitted beam is precisely described 

 by means of two quantities — the ellipticity and the difference of phase 

 between the components of the light polarised perpendicular to and parallel 

 to the plane of incidence. The object of his paper is to obtain con- 

 venient formulse for these quantities and to compare them with the 

 results of experiments, selecting the most careful and the most recent 

 that are available. 



Colourless Lines produced by Convergent Light in Crystalline 

 Laminae. |—Gr. Cesaro investigates the mathematical theory of tlie 

 above, when the nicols are crossed at right angles. He starts from the 

 usual equation for the intensity of a ray oblique to the crystalHne 

 laminae and after passage through the analyser, viz. : — 



"D 



l = a^ sin 2a sin 2y8 sin^ tt — - 



A 



when a and fS represent the angles, which one of the planes of vibration 

 of the ray considered makes with the sections of the polariser and the 



* Bull. del'Aoad. roy. de Belgique (Classe des Sciences) 1906, pp. 459-92. 



t Proc. Roy. Soc, Series A, Ixxviii. (1906) pp. 296-41 (24 figs.). 



I Bull, de I'Acad rov. de Belgique (Classe des Sciences) 1906, pp. 368-99 (9 figs.). 



