74 Mr Spurge, On the curves of constant intensity of [Jan. 28, 



and the equation of motion is 



q r 2 



op (1 — /a) a 



Hence the periodic time is 



W / 6p (1 - ft) 



r ' * q 



which is the result already obtained. 



(4) On the curves of constant intensity of homogeneous polarized 

 light seen in a uniaxal crystal cut at right angles to the optic axis. 

 By C. Spurge, B.A. 



Introduction. 



Sir George Airy has shown in his Tract on the Undulatory 

 Theory that if a plate of Iceland spar bounded by planes perpen- 

 dicular to the axis of the crystal be placed between a polarizing 

 and analyzing plate the brightness of any point of the image formed 

 after passing the analyzer is given by the formula 



a 2 \ cos 2 a — sin (2yjr — 2a) sin 2i|r sin 2 — > 



where I is proportional to the square of the radius vector from 

 the centre of the image to the point considered and i/r is the other 

 polar co-ordinate of the point considered, viz. the angle the radius 

 vector makes with a fixed line, a is the angle between the plane 

 of polarization at the analyzing plate and the plane of first polariza- 



IT 



tion. If a = or -we have for the intensity 



f nrl] 



a 2 jl-sin 2 2i|r sin 2 - 



irl 



and a 2 sin 2 2-\Jr sin 2 -—- respectively. 



Thus in either case the curves of equal intensity are given by 

 an equation of the form 



irl 



Constant = sin 2 2yjr sin 2 — - , 



A. 



or k 2 = sin 2 2o/r sin 2 r 2 



where k 2 is put for the constant 



and r 2 = — , 



A 



