182 SUMMARY OF CURRENT RESEARCHES RELATING TO 



iii 1900, gave the correct explanation of the phenomenon, and ascribed 

 it to the rotation of the vibration plane of the transmitted plane- 

 polarized waves at the steeply inclined lens surfaces. It will be readily 

 understood that a spherical surface may be considered to consist of a 

 series of minute planes inclined at all angles with the vertical and in all 

 azimuths. The rotatory effect of such a surface on transmitted plane- 

 polarized light waves is, therefore, different in different directions, the 

 result being a distinct uniaxial cross, with quadrants whose intensity 

 of illumination increases with the distance from the centre. This is, 

 in brief, the explanation of the faint uniaxial cross which appears in 

 all high-power objectives between cross nicols. The plane-polarized 

 light waves whose normals are parallel to the principal planes of the 

 nicols suffer no rotation, while all others are rotated to an increasing 

 extent as their azimuth increases, until the maximum rotation at 45° is 

 reached. The reasons why these phenomena are so much more distinct 

 in high-power than in low-power objectives are (1) the larger numerical 

 aperture of high-power objectives, and (2) the fact that in such objec- 

 tives the front lens of the system is a small uncorrected glass hemi- 

 sphere, at whose steeply inclined sides the transmitted light waves are 

 rotated through relatively large angles. The author gives a full account 

 of experiments and observations which confirm his explanation. 



New Half-shade Apparatus with Variable Sensibility.* — F. E. 

 Wright describes the following apparatus, which he has used for work- 

 ing with Fresnel's equation, cot B = cos 2 (i-r) cot A. He mounts a 

 plane-parallel glass plate so that it can be rotated about a horizontal 

 axis in the first (N.E.) quadrant midway between the principal nicol 

 planes. The azimuth angle A for incident waves from the polarizer 

 becomes, therefore, 45° for all angles of incidence i, and the angle of 

 rotation of the transmitted waves can be calculated from the simplified 

 Fresnel equation, cot B = cos 2 («— r). If, now, a second glass plate be 

 taken and rotated about an axis in the second (N.W.) quadrant, the 

 azimuth angle of the incident light waves from the polarizer is - 45°, 

 and the Fresnel equation reduces to cot B = - cos 2 (i—r). For a given 

 angle of incidence the angle of rotation produced by the glass plate in 

 the second quadrant is accordingly equal in value to that in the first 

 quadrant, but opposite in sign. If, now, two glass plates be so mounted 

 that they meet in a fine line, they form a half-shade apparatus of a 

 definite angle of rotation. The author describes his method of mount- 

 ing these plates, and gives a table of his results. 



Determination of the Relative Refringence of Mineral Grains 

 under the Petrographic Microscope, f — F. E. Wright points out that 

 in many instances, especially in the measurement of the refractive indices 

 of fine grains immersed in refractive liquids, it is extremely difficult to 

 detect the faint differences in light intensity which appear at the margins 

 of the grains, and by means of which the differences in refractivity are 

 recognized. Under such conditions the eye of the observer is subjected 



* Joum. Washington Acad. Sci., iv. No. 12 (June 19, 1914) 5 pp. (2 figs.), 

 t Journ. Washington Acad. Sci., iv. No. 14 (Aug. 19, 1914) 4 pp. (1 fig.). 



