Angular Measurement of Optic Axial Emergences. 9 



In the figure, OA is an optic axial direction in the crystal, OB "is 

 the direction of optic axial emergence into air, and OC is the direc- 

 tion of emergence into a liquid of refractive index ^u; ON is the 

 normal to the crystal plate. Then , the angle of emergence into air, 

 is NOB, whilst 0, the angle of emergence into the liquid is NOG 

 and sin*/sin0 = ft-, it is required to calculate the angle , from 

 the observed value of a 6. 



Then, since sin a/sin 9 = ^ 



- = sin {g~ Q 0)} 



/* sin a 



__ sin ac cos (y. 0) cos a sin (a 0) 

 sin a 



= cos (a 0) cot a sin (a 0) 



cota = cotfa 0) -- 



J 



0) 

 Or again, since sin a/sin = a, 



sin a 4- sin 



;t 1 sin a sin 



_ sin ^0 + 0) cos |(a 0) 



, a 

 whence tan - = - -- tan - ........... . (2) 



2 yu 1 2 



a form more convenient than (1) for logarithmic calculation. 



To test the accuracy of the method, measurements have been made 

 011 biaxial plates of different optical properties, liquids of various re- 

 fractive indices being used. The index of refraction of the liquid 

 employed is conveniently determined with the Ptilfrich refractometer ; 

 the refraction is so affected by differences of temperature and of 

 purity that it is necessary to determine it for the liquid as actually 

 used ; the liquid does not need to be specially purified. The measure- 

 ments given in the two appended tables were made on plates of 

 topaz, each of them cut perpendicularly to the acute bisectrix. By 

 measurement of the optic axial angles, the apparent emergences into 

 air for sodium light were found to be 53 24' and 54 42', respec- 

 tively. 



These two sets of measurements suffice to show that the method 

 possesses very considerable accuracy, although the values of a 

 measured are not very large ; the numbers also seem to indicate 



