THE AID OF THE ACHROMATIC FRINGES. 



45 



angle (reading a), and re-establishing the ellipses again at the micrometer 

 (A/')- To find a, an index was attached to the end of the rail (radius of ro- 

 tation 23.6 cm.) and the motion of this index over a glass millimeter scale 

 was read off with a lens. For really refined work it would have been neces- 

 sary to adjust a micrometer tangent screw to find a; but this did not seem 

 called for here. The results were in case of two series (2 cos i= 1.306) : 



These coefficients (which are here below the computed value) were found 

 graphically. The discrepancy for the correction due to increasing obliquity 

 of the plate Pp is but (e thickness, n index of refraction, r angle of refraction, 

 the incident being i = y) 



e (sin 7 cos 7 tan r)Ao: = o.i4 



per unit of a, if = 0.775 cm -> . u== l -55> an d 7 = 27.1. 



A further discrepancy may be sought for in the fact that if the surface 

 Pp (fig. 23) does not pass through the axis of rotation, this plate is both 

 rotated and displaced. The error so introduced may be either positive or 

 negative. If the displacement of plate is e' = e(i cos a), the equation 



should read 



cos 7 



2 AN COS 



= b (sin /3 + sin 7) 



where e is the distance of the plate from the axis. The following experi- 

 ments were therefore made with some consideration to greater symmetry of 

 apparatus. The constants were: /3 = 7o.5, 7 = 27.1 and therefore i = 

 48.8, or 2 cos 1 = 1.32. The data found were in different adjustments; 



