218 Mr. W. B. (yurtmel on the Anomalous 



piece of mica in two and attaching one of the pieces to a 

 device by means of which it could be rotated through an 

 angle and the angle read off. These two pieces of mica were 

 placed in the same path as the fuchsin, the fixed piece and 

 the fuchsin in the lower half of the path, and the movable 

 piece in the upper half, the line of separation of the mica 

 precisely on a level with the edge of the fuchsin ; in both 

 upper and lower halves of the other path was a very thin film 

 of fuchsin that served as an absorbing screen. When both 

 pieces of mica were at right angles to the beam of light their 

 effect was null, because they affected both sets of bands alike, 

 being of equal thickness. It could be ensured that they 

 were equally thick by removing the fuchsin and observing 

 whether the upper and lower spectral bands coincided when 

 both pieces of mica were in the same plane. 



It is usual to calibrate a compensator by turning it through 

 different angles and noticing the angles corresponding to 

 different numbers of bands displacement. However, for this 

 w^ork, as the displacement that had to be measured was 

 always less than a single band, it did not help to know the 

 angle corresponding to one band displacement or two bands 

 displacement, because the greatest change of curvature of the 

 calibration-curve comes between zero and one. 



A formula w^as therefore used which may be deduced as 



follows: — If a piece of mica of thickness t is traversed by a 



ray which meets it at an angle of incidence i, as shown in 



fig. 2, PL IX., the length of the path of the ray will be increased 



by fjil—d, if the index of refraction of the mica is represented 



by /^. 



Also , , t 



I = t sec r = 



d = l cos (z — r) 



fj,l^d = I[fjL — cos (i — r)], 

 which reduces to 



t^Vfjb'^ — sin'^i — cos i) . 



The introduction of the mica at right angles to the ray will 

 shorten its path by (//, — 1) f. The number of wave-lengths 

 retardation produced by a piece of mica in the path of the 

 ray, when the mica is moved from a position at right angles 

 to the ray through an angle i, is the difference of these two 

 quantities, and we have at once 



n\ = t(^'y fjL^ — sin^z — cos i) — (/jL — l)t. 

 In using a compensator with this type of interferometer 



