92 THE INTERFEROMETRY OF 



With the use of an ordinary glass mercury lamp (27 storage cells, 5 amperes) 

 the fringes are found with difficulty when the beam at the first grating is 

 wide. On using a vertical blade of light the definition was improved. The 

 fringes are faint, very susceptible to motion, and at times even absent. They 

 occur, however, as a single set, as was anticipated, showing that the above 

 duplicated fringes are actually due to the two sodium lines. The mercury 

 fringes are easily rotated and pass through a horizontal maximum with fore- 

 and-aft motion. Rotating G about a normal axis may further increase this 

 maximum size to a limit at which the fringes appear irregular or sinuous. A 

 displacement of the mirror M over 0.7 cm. was easily permissible, without 

 destroying the fringes. They occur, as above stated, within a certain adjusted 

 spot area of the field of view. An attempt was again made to detect a Zeeman 

 effect by placing the poles of an electromagnet on the two sides of the lamp ; 

 but here again no difference was discernible on opening and closing the electric 

 circuit. The field, however, for incidental reasons, could not be made strong 

 enough for a critical experiment. 



43. Inferences. After these experiments (made with the apparatus figure 

 57, free from glass plates and depending on reflections only) the cause of the 

 phenomenon is no longer obscure. Obviously one of the paired grids in figure 

 66 or 67 belongs to each sodium line. The retardation of one phenomenon, 

 rotationally, as compared with the other, is due to the difference in wave- 

 length between D\ and D%- The phase-difference between numbers 4 and 6 

 (fig. 67) is thus equivalent to 6 Angstrom units. If the displacement of G' 

 is about 0.3 cm., there should be about 0.5 mm. displacement, fore and aft, 

 for i Angstrom unit. If the grating, G', is on a micrometer, this should be a 

 fairly sensitive method of detecting small differences of wave-length, or give 

 evidence of doublets lying close together. The sensitiveness clearly increases 

 with the length of path of the component rays and may thus be increased. 



With this definite understanding of the phenomenon, it is desirable to deduce 

 the equations, which in the occurrence of parallel rays would not differ essen- 

 tially from those of Chapter II or III. It is useful, however, to treat the new 

 case of crossed rays. In figure 69 the angles of diffraction are 61 and 62, if the 

 incidence of light, L, is normal at G and at an angle i z at G', G and G' being 

 parallel. The mirrors are set symmetrically at angles a\ and <r 2 to the normal 

 in question, and the diffracted rays are reflected at angles 0:1/2 and 0:2/2, 

 respectively. The reflected rays cross the normal at an angle /3. Then 



sin 6 'i = \/D\ sin 2 = X/Dz sin i z 



where Di and D z are the grating constants. From the figure 



"1/2 = 01+0-1 90 o: 2 /2 = 2 +0"2 90 0i = o:i-f-/3 2 



From these equations, 



D z sin i = D z sin (20 2 +2(r 2 +j8) DI sin () 

 If Di = D 2 , then 6i=6 2 , ffi = ff z , and therefore i z = o. 



