476 Prof. Silvanus P. Thompson's Notes 



diate point P. Then the squares of the apparent distances of 

 P from the object and image are as the solid angles of the 

 cones. Again, consider a pencil of rays passing through P, 

 which must mark out corresponding portions of object and 

 image, and it is evident that these areas are also in the ratio 

 of the squares of the same apparent distances. Hence the 

 proposition, which is thus seen to be intimately connected 

 with the notion of apparent distance. 



Terling Place, Witham, 

 May 7. 



LXV. Notes on some New Polarizing Prisms. 

 By Professor Silvanus P. Thompson*. 



[Plate VI] 

 I. On a New Polarizer devised by Mr. Ahrens. 



THE new Polarizer constructed by Mr. Ahrens is a rectan- 

 gular parallelopipedon of calc spar having square end- 

 faces, and having its long sides in the proportion of about 

 1*6 : 1 relatively to the short sides. The actual dimensions 

 of the prism which, at the request of Mr. Ahrens, I exhibited 

 to Section A of the British Association, are : — 



Side of nearly square end-face . 17*5 millim. (nearly) ; 

 Long side of prism 27 millim. 



The square end -faces are principal planes of section of the 

 crystal. 



Two oblique sections are cut in the prism, and run from the 

 highest and lowest edges, a b and c d of fig. 1 (PI. VI.), to the 

 middle of the other face, where they meet in the line S S'. 

 The dihedral angle between these planes of section is nearly 

 32°; the angle between either of them and the principal axis 

 of vision through the prism being therefore nearly 16°. Mr. 

 Ahrens also uses a dihedral angle as small as 30° in some of 

 his prisms. The faces of these sections are polished and 

 united with balsam in the usual manner. 



It will thus be seen that the new prism consists of three 

 wedge-shaped pieces of spar, and that one face of the prism 

 is traversed by a line of junction. 



On looking through the prism, the polarized field formed 

 by extraordinary rays is observed to be bounded perfectly 

 symmetrically by two regions into which the ordinary ray 

 intrudes, the edges of both these regions being marked by 



* Communicated bv the Author. 



