122 THE INTERFEROMETRY OF 



io~ 8 /42Xio~ 3 =1.4X10^. Treating the case in terms of the interferences of 

 thin plates and two wave-lengths, X and X-f-dX, 



. AX Aw i . . , 



nK = constant, or = = tor each period 



X n n 



while 



X 2 



n\ = = 2 A7V cos 6 or AN = X 2 /2 AX cos 



AA 



since (0 = 45) approximately, 



X = 6oXio- 6 cm., AX = 6Xio~ 8 cm., cos 6 = 0.71, &N = 0.041 cm. 



agreeing as nearly as may be expected with the experimental datum. The 

 apparatus thus serves incidentally for investigating such properties of spec- 

 trum lines as Michelson in particular has detected. Finally, with the sodium 

 arc the data of figure 81 were found, where black dots denote fringes, open cir- 

 cles a clear yellow field. The mean trend is about AJV = 0.043 cm - P er period 

 or wave-length gained. White fringes coincided with n = z. 



With white light the interference grid does not usually reappear rhythmi- 

 cally, nor does it correspond to the zero period of figure 80 i.e., to the ovals 

 for sodium light. It was exactly of the size of the fourth period, in yellow 

 light ; it always coincides with the central ellipses of the spectroscope as stated, 

 but does not require sharp horizontal and virtual coincidence of the super- 

 posed images. The reappearance of the achromatic fringes obviously depends 

 on conditions different from the case of sodium light. 



In a flash of the arc, showing many sharp spectrum lines in all colors, each 

 of the lines gives evidence of the phenomenon i.e., if the residual fringes 

 are oblique, each such line is strongly helical in appearance. 



If a single compensator (i.e., a glass plate in one interfering beam) is used 

 and the path-difference annulled, the fringes are visible again, but very rapidly 

 grow smaller with the increase of glass-path. If compensators of nearly like 

 thickness and glass are used in both beams, they nearly neutralize each other 

 if at the proper angle one to the other. But there is almost always an out- 

 standing micrometeric difference in thickness (if ordinary glass plate is used) 

 of great importance in modifying the residual phenomenon. The following 

 experiments, for instance, were made with a compensator 0.944 cm. thick 

 in the rear and 0.958 cm. thick in the front beam, both of the same glass. The 

 half -silver mirrors were 0.7 cm. thick. The wide-slit experiments are supposed 

 to start after the spectrum ellipses first to be found (fine slit) have been cen- 

 tered. The fringes are always clear and very sharp when the white slit images 

 accurately coincide. 



With the compensators A, B at the proper angle and rotating in the same 

 direction (fig. 82), fringes of very slight enlargement were seen with the lines 

 nearly vertical. If the compensators A, B were rotated at a proper pace 

 in the opposite direction to each other, A, B, figure 83, the fringes /' and j" 

 grew rapidly smaller and turned toward the horizontal. Since the fringes 

 are large circles and the beams here rise and fall, respectively, while a greater 



