of the double refraction in strained glass. m 



483 



beams, shown in cross-section, whose thicknesses are r 1} r 2 . Let 

 a be the distance from the scale to the diaphragm, b the horizontal 

 distance between the two beams and e the vertical height of the 

 central axis of the second beam above that of the first. 



Then if P be any point of the scale, the pencil of rays which 

 ultimately form an image of P in the focal plane of the telescope 

 is the broken cone bounded by the rays APA^^A^ BPB r B 2 B z in 



Now in investigating the relative retardations, all that we are 

 concerned with is the path in the strained glass. 



Now the paths in the glass may be found by the following 

 construction. 



Imagine the beam EF removed a distance (/j, — 1)6 to the 

 left, as E'F' (Fig. 4), and similarly the diaphragm AB removed 

 (fji— l)a to the right as A'B'. Then the paths of the actual rays 

 in the glass will now lie inside a straight cone A'PB', the paths in 

 the two glass beams of any ray which emerges as PQ in the real 

 case being given by the intercepts PQ U Q2Q3 of the corresponding 

 ray PQ' in Fig. 4. Consider the relative retardation of the two 

 oppositely polarized parts of the ray PQ. 



Fig. 4. 



This can easily be shown to be 



CI 7 ! cos 2 6 sec yfrd^ + I 2 CT 2 cos 2 6 sec ^rdr^ 



J Qi J Q 3 ' 



7T . 



— } — Q being the angle which the ray PQ makes with the direction 



of the axes of the beams and i|r the angle PQ' makes with the 

 horizontal perpendicular to the sides of the beams. 

 This gives for the retardation 



(7cos 2 0secv/r 





y v y 2 being measured vertically from the neutral axes CD, E'F' in 

 the two beams. 



VOL. XI. PT. VI. 



34 



