DISPERSION IN ARTIFICIAL DOT'KLK RKFRACTION. 275 



The linking of the lx'<l-|>]at<> was measured experimentally and found to be elastic 

 in its nature, the recovery being eomplete. 



Generally the experiments showed no trace of permanent set, the readings being 

 the same when unloading as when loading. 



We may safely assume therefore that 82, 8z 3 +<r (8:, 8/t) is pmjxirtional to W, so 

 that the correction to be applied to W ou account of these errors is of the form 



KW. 



The value of K is uncertain and depends very largely on the circumstances of each 

 experiment. 



Using KVKUKTT'S and AMAOAT'S values of YOUNG'S modulus for glass (i.e., between 

 600,000 and 700,000 kilogs.-weight per square centimetre), the part of K due to relative 

 rise and fall of the two beams was calculated to be about 0'0004. Thus for 

 W = 50 kilogs. the proportional correction is as high as 2 per cent. 



The part of K due to the sinking of the l>ed-plate was found experimentally to be 

 of order 0'00026. Also the experiments could be arranged in such a manner that the 

 two corrections operated in different senses; and this precaution was always taken. 

 Their combined effect will give K of order O'OOOl, and even for the highest loads used 

 the correction will be small. 



In practice this correction KW a was determined from the observations themselves, 

 in a manner explained in 17. For most sets of observations it was found to be 

 insensible. 



7. Itijhn'nn- of Obliquity on, IMntivc- Retardation, 



We may consider the glass .as optically made up of a series of horizontal homogeneous 

 layers. In passing from one of these layers to another, the refraction takes place 

 approximately in a plane perpendicular to the optic axis. 



1 1 will l>e sufficient for our purpose to consider a ray passing through in a cross- 

 section, that is, in a plane throughout perpendicular to the optic axis. If the 

 curvature of such a ray be negligible, we may take it that we can neglect the 

 curvature of all oblique rays. 



Now if n be the index of refraction at a point in the glass distant y from the 

 neutral plane, 



/^,, Ix-iiig tin- index of refraction for the unstrained glass. It may then be proved that 

 the curvature of a ray passing through nearly horizontallv is approximately /<///. 



Now it has been shown by KKRR ('Phil. Mag.,' October, 1888), and by POCKKLS 

 ('Ann. d. Pliysik. P.MIJ. p. 745), that the absolute variation due to stress in the 

 index of irtraetimi for either ray is of the same order as the difference in the two 

 indices due to the same cause. In general, for the highest stress employed, the 



2 N 2 



