REVERSED AND NON-REVERSED SPECTRA. 123 



glass thickness is introduced, this result is to be expected. It shows the im- 

 portance of the differential glass-path. 



The preceding thick half-silver mirrors (0.7 cm.) were now replaced by 

 thinner half-silvers, the glass plates being each about 0.3 cm. thick. The 

 fringes after being found had not appre- 



ciably changed. Another pair of half- 



silvers of the same thickness was then 



\:T: T ~x^ >?~ 



83 



f 



if; 



L I i 



installed with like results. But now, 



on adding the compensators (0.944 and ' \i/ tn' j^/ q^ 

 0.958 cm.) as above, a marked enlarge- 82 /- -^ -J+ r _,X^* 



ment of fringes resulted. Small differ- / /* /* 



ential thicknesses must here have been 

 accidentally compensated. Opposite rotations, as in figure 83, rapidly pro- 

 duced very fine, nearly horizontal fringes /'/". Rotation as in figure 82 

 left the vertical fringes nearly intact, but on passing from the position AB to 

 A 'B' very marked enlargement occurred, as follows: 



Mean angle of glass plates. 45 o +45 



Mean angle subtended by 

 one fringe in the telescope . 0.0015 rad. 0.008 rad. 0.0005 rad. 



The compensator plates were now exchanged and the fringes found after 

 centering. They proved to be very much smaller, the angle subtended in 

 the same telescope being only about 0.0002 radian. The preceding accidental 

 compensator has therefore been destroyed by exchange. 



On passing through the normal position of one plate in figure 82, the fringes 

 usually incline toward one side or the other. Thus there can be little doubt 

 that the fringes in question are due to slight difference of glass-path or ex- 

 tremely sharp glass-wedge excess in one or the other component beam. In 

 fact, I found eventually that fringes could be enlarged by rotating the proper 

 compensator around a vertical axis. Large fringes (up to 0.002 radian in the 

 given telescope) are usually colored and curved and not so available as smaller 

 fringes highly magnified. It is in this way (double rotation) that it was pos- 

 sible to make the white fringes coincide in order with the ovals of the fringes 

 for homogeneous light (w = o), the orders met with above being the w = 2 and 

 n = 4. The fringes resemble those of Fresnel's biprism; but as they are seen 

 with a wide slit or in the absence of a slit only, as they coincide with the cen- 

 tered spectrum ellipses of a fine slit and as they are a definite order (second, 

 for instance) of the fringes seen with a flame of homogeneous light, they are 

 necessarily referable to the colors of thin plates. 



Hence the equation for these fringes may be assumed to be (as may be 

 seen from figure 84, where A and B are the compensators) 



n\ = (ee'} (n cos (r a) cos i} 



when e and e' are the thicknesses of the two half-silver plates, p. their index of 

 refraction, i the angle of incidence, r the angle of refraction of an incident ray, 

 and where a is the outstanding angle between the faces of the differential 



