of the double refraction in strained glass. 485 



length of the spectrum examined was about 4^ cms., so that tan 

 never exceeded 



\ i| = -04 about. 



Accordingly cos a at most differed from unity by a quantity of 

 the order 0016 which was quite negligible, seeing the accuracy of 

 the final measurements could certainly not be greater than \ per 

 cent. 



yjr was a quantity of the same order as 6 and the effect of the 

 term in y\r will have been to reduce the preceding error by nearly 

 one-half, so that the total error introduced by putting the factor 

 cos 2 #sec yjr = 1 will be only about 1 in 1000. This we may cer- 

 tainly neglect. 



If we do so 



r=C(py -qy'). 



Now the intensity due to a very thin pencil, whose cross-section 

 at Q is dx'dy', will be 



Idx dy' si n 2 2y si n 2 irr / \, 



I being a constant and y being the angle between the axes of the 

 polarizer and analyser and the axes in the glass. 



Hence the intensity due to the whole of the light from P 

 which passes through the diaphragm 



= /sin 2 2<yfdx'dy' sin 2 irr/X, 



the integral being taken over the area of the diaphragm. 

 This gives : Intensity 



T . ,. [dx'dy't. 2irC . „ ZirCq . , ,. 



= /sm 2 27j-^-^(l -cos— ^- ( py - q V ) cos — ^- (y - v ) 



. 2irC . 2wCq. , A 



- sin ^-r (pij - q v ) sin —^ (y ' - v J , 



7) being the height of the centre of the diaphragm above KL. 



The diaphragm being circular, the sine-integral vanishes and 

 the others give 



7sin 2 2 7 (?£- - cos -^- (py - qn') ^t J x (a) J , 



, 2irCqp 



where a = — ~- , 



\ 



p is the radius of the diaphragm and J x is the Bessel's function of 

 order unity. 



Now if a < 7T x 1-22, J, (a) > 0. 



34—2 



