72 THE INTERFEROMETRY OF 



or to the rear. The data obtained for the range of displacement were now: 

 Images and telescope toward rear, y = 0.124, 0.140 cm.; ^ = 0.150, 0.142 cm.; 

 images and telescope toward front, y = 0.146 cm., ^ = 0.154 cm. 



These differences are again incidental. The following data were subse- 

 quently found: Telescope inclined rearward, ^ = 0.100, o.no cm.; 0.143, 

 0.140 cm.; telescope vertical, ^=0.150, 0.150 cm.; 0.162, 0.151 cm.; tele- 

 scope inclined forward, y= 0.150, 0.133 cm.; 0.145, 0.162 cm. 



In the first experiment the illumination was insufficient, so that the finer 

 fringes escaped detection. Hence, it is here also probable that slight depar- 

 ture from collinearity in the rays b b', normal to the edge of the prism P', is 

 without consequence. Discrepancies are introduced by changes in the in- 

 tensity of light conditions which are often hard to control. 



As the range of displacement is not a quantity which can be accurately 

 ascertained, the effect of the insertion of a glass-plate compensator, 0.434 cm. 

 thick, was determined, with a similar end in view, for different angles of the 

 rays b b' (nearly normal) to the edge of the prism P'. The results were : 

 Telescope inclined toward front, y = 0.122, 0.123 cm.; telescope vertical, 

 2"= 0.122, 0.122, 0.122 cm.; telescope inclined toward the rear, y = 0.120, 

 o.i 2 1 cm. These are the differences of the displacement corresponding to 

 the linear central fringes normal to the sodium lines, obtained in the presence 

 and absence of the plate. The path-difference computed above was 2=0.2428 

 cm. This is as near 2y as the observations warrant. 



It follows, therefore, even if the observations are in their nature not very 

 precise, that if the rays b and b' meet at such small angles as any reasonable 

 adjustment may introduce, the effect may be disregarded. Furthermore, 

 that the difference between x = 2e cos 5/2 (where e is obtained by moving 

 the mirrors M and N parallel to themselves) and 2y (obtained by moving 

 P' at right angles to its edge) is to be ascribed to the sliding along or across the 

 edge. The rotation of fringes which necessarily occurs in displacement inter- 

 ferometry by the shifting of the ellipses is augmented or decreased in the 

 former case (x) by the equivalent of the sliding in question. The reason for 

 this has clearly been suggested in connection with figure 18, Chapter I, 

 and figure 49, Chapter II. 



35. Range of displacement varying with dispersion. The interesting 

 method in Chapter I, 25, where the opaque mirrors are replaced by two 

 identical gratings (halves of the same grating) with the object of obtaining 

 successive orders of dispersion, may be used in connection with figure 43 of 

 the present chapter. It is therefore the object to find the range of displace- 

 ment y of the prism P' when the fringes pass from the initial transverse 

 hair-lines to the final transverse hair-lines (fig. 45), through the longitudinal 

 maximum of size. The same difficulty inheres in this method as in the above, 

 viz, it is not possible to state precisely when the hair-lines have vanished; 

 but the successive orders of range of displacement are so different that inter- 

 pretable results are obtained. The experiments in the large interferometer 



