REVERSED AND NON-REVERSED SPECTRA. 31 



line joining a and b. Since a and b here correspond to c and c' in figure 17, let 

 a be continually displaced to the right, as indicated by the arrows, figure 18. 

 In proportion as the positions ab, a'b', a"b", are taken, the fringes must pass 

 by rotation from /, into /', into /", etc. i.e., over about 90. In the present 

 experiment, c, figure 17, can never pass across c', for they are essentially 

 separated by the edge of the right-angled prism P' . Hence the rotation can 

 not exceed 90, for the vertical through a can not cross the vertical through b. 

 This is not the case when a grating replaces P', as in figure 1 2 ; nor is it 

 the case when, as in Chapter II, inverted spectra are treated, and the patches 

 a and b slide along the edge of the prism. In such cases figure 18 may be 

 continued symmetrically toward the right (mirror images), and the limit of 

 rotation is therefore 180. All these suggestions are borne out by experiment. 



Moreover, if the first prism P, figure 14, is tilted slightly on an axis parallel 

 to LT, a (fig. 1 8) will be lowered and b raised. If a and 6 are on the same 

 level, the fringes are always vertical and pass through a vertical maximum, 

 when ab is a minimum. On the other hand, if a and b are not in the same 

 level, as in the figure, fore-and-aft motion brings the rays c and c' (fig. 17) 

 to or from the edge of the prism P'. Hence the case ab passes into a"b", or 

 the reverse; in other words, the fringes pass through a horizontal maximum 

 when ab is a minimum, etc. This is also shown by experiment. 



Moreover, if a, figure 18, is the angle (in the observer's vertical plane) of 

 ab to the horizontal, the horizontal distance between c and c' will be ab cos a, 

 which is zero when a = 90, and both c and c' are at the edge. Suppose the 

 full breadth of the strips are at the edge, so that the fringes present the 

 strongest, coarsest, but narrowest field of case 2, figure 16. Then if either 

 c or c' retreats until the fringes vanish, the width of the appreciably effi- 

 cient strip cc' will be ab cos a = t=s = o.fe, nearly. This is probably the 

 best method of estimating the width in question. Usually, however, away 

 from the edge, the succession i, 2, 3, figure 16, is obtained. In such a case 

 the breadth of efficient strip is t/2 =0.350. 



The experiment made by moving screens with slits, forward or rearward, 

 successively, by which the appearance and evanescence of fringes may be 

 repeated through several cycles, is next to be explained. Here it is merely 

 necessary to remember that the spectra c and c' are reversed, or that the 

 colors of like origin and wave-length are successively farther apart. When 

 the screens are alternately moved, therefore, the same phenomenon is in turn 

 produced in slightly different colors. But as ab continually increases, whereas 

 the efficient breadth of the strips does not, the fringes soon pass beyond 

 appreciable smallness. 



When, as in the earlier methods, but a single grating is used with two 

 successive diffractions through it, the patches a and b are obviously in the 

 same level when the longitudinal axes of spectra coincide. Hence the fringes 

 are essentially vertical. 



In the experiment with screens, 5, 5', figure 14, it is obvious that path- 

 difference remains constant. The distance from the same wave-front in the 



