Transparent Inactive Crystal Plates. 159 



of certain factors which underlie the methods for the measure- 

 ment of the optic axial angles, especially the method of Pro- 

 fessor Becke 1 and the writer's modification 2 of the same. 3 



These methods are based on the degree of curvature of the 

 dark hyperbolas or zero isogyres of the interference figure and 

 depend, therefore, on the polarization directions of waves 

 transmitted along different paths. In microscopic work, the 

 influence of the boundary surfaces, not only of the crystal 

 plate, but also of the intervening glass plates, on these waves 

 enters the problem and tends to render it more complicated. 

 In the following pages the general mathematical treatment of 

 the problem of light transmission through transparent inactive 

 crystal plates is given in . Part 1 and several important and 

 apparently new relations are deduced which simplify the 

 presentation materially. In Part 2 results of calculation are 

 checked by series of observations with apparatus specially 

 designed for the purpose. 



The results of the investigation show that the methods pro- 

 posed by Professor Becke and by the writer are approximate 

 methods only ; both furnish results of about the same order of 

 accuracy, the one advantage of the writer's method being that 

 of slightly greater simplicity. They show, furthermore, that 

 a theoretically correct method is not attainable because of 

 many factors, each of only slight influence, which enter the 

 problem and complicate the relations seriously. 



Part l. 4 — Theoretical. 



The Boundary Conditions? 



Light waves, in passing through a crystal plate, encounter 

 peculiar conditions, both on entering the plate and emerging 

 from it. At the limiting surfaces of the plate, the crystalline 

 material ends abruptly and the system of forces which result 

 from the crystal structure are suddenly cut off from further 

 action. On emerging from the plate the light waves pass from 

 the influence of these forces to that of an entirely different 



1 Tschermak's Mitteil. , xxiv, 35, 1905 ; xxviii, 290, 1909. 



2 This Journal (4), xxiv, 332-338, 1907; Tschermak's Mitteil., xxvii, 

 293. 1908. 



3 In the course of this investigation the writer has corresponded frequently 

 with Professor Becke and is indebted to him for several suggestions and for 

 his open consideration of the points in question. 



4 In the preparation of this section the following books and papers have 

 been consulted especially : Drude, Lehrbuch d. Optik ; also Drude in Win- 

 kelmann's Handbuch d. Physik ; Liebisch, Lehrbuch d. Kristalloptik ; 

 Pockels's Lehrbuch d. Kristalloptik ; and P. Kaemmerer, Uber die Reflexion 

 u. Brechung des Lichtes an inaktiver, durchsichtigen Kristallplatten, Neues 

 Jahrb., Beil. Bd. xx, 159, 1905. 



5 The subject of boundary conditions is thoroughly treated by P. Drude in 

 Winkelmann's Handbuch der Physik, vi, 1169, 1906 ; also in Drude's Physik 

 d. Aethers, 511, 1894. 



