of Faint Interference-bands. 485 



worth while to test the matter with bands that are well under 

 control. 



In the first experiments light polarized by a Nicol fell upon 

 a slit, against which was held a somewhat stout selenite. 

 Direct examination of the slit through an analysing Nicol 

 revealed no colour on account of the thickness of the selenite ; 

 but when a dispersing-prism was added, the resulting spectrum 

 was marked out into bands, whose brightness and contrast 

 depended upon the relative orientations of the Nicols and of 

 the selenite. The theory of these bands is well known ■^. If 

 the Nicols be parallel, and if the principal sections of the 

 Nicols and the selenite be inclined at the angle «, the expres- 

 sion for the brightness is 



1— sin^ 2«sin^^/9, 



where p denotes the difference of retardations of the two rays 

 to whose interference the bands are due. At the brightest 

 place p = 0, and at the darkest sin^^p = l, so that 



/i = l-sin2 2a. 



The bands are thus invisible when a = 0, and increase gra- 

 dually in distinctness with «. When « = 45°, the darkest 

 place is absolutely black f- 



The selenite was mounted upon a divided circle, and the 

 observation consisted in finding the two positions, on either 

 side of «=0, at which the bands manifested themselves with 

 the desired degree of distinctness. The anoular interval 

 between the two positions was then taken as representing the 

 value of 2a. In order that the bands should be recognizable 

 with certainty it was found that 2« must be at least 14°. For 

 a distinct and continuous impression 2a = 17°. Corresponding 

 to these, we have for l—h, 



sinn4°=-0585, sinH7°=-0855. 



In these observations the earliest recognition of the bands 

 was somewhat interfered with by a want of smoothness in the 

 spectrum due to irregularities in the selenite. Any irregu- 

 larity, whether of this kind or caused by dust upon the edges 

 of the slit, gives rise to horizontal markings in the spectrum 

 which distract the eye. In a second set of experiments this 



* See, for example, JEnc. Brit. "Wave Theory," § 22. _ 

 + This presupposes an infinitely narrow slit. In practice the width 

 must he reduced until, in this position, the hands are sensibly black. 



