138 THE INTERFEROMETRY OF 



fringes completed the phenomenon, after which it paled to whiteness. These 



25 fringes passed within Aa = o.75', or per fringe about 0.03' or 1.8" of arc. 



Of course, this is merely an estimate from the small angles of turn involved. 



The complementary fringes with sodium light are available indefinitely. 



1 counted about 100 fringes for an angle of 2.7' i.e., 1.6" per fringe. 

 Finally, using the spectrum fringes of the spectroscope, about 120 fringes 



were counted within 3' i.e., 1.5" per fringe. All of these values are larger 

 than the computed value \/zR without correction, but in view of the large 

 number of fringes within exceedingly small angles A a, sharp agreement is 

 not to be expected. 



71. Equations. To completely trace out the air- and glass-paths in the 

 present apparatus would lead to complicated equations of no further interest 

 here. I have, therefore, contented myself with the preceding experimental 

 result, which is probably more accurate than it appears. To the first order 

 of small quantities one may assert that the rotation of the mirror m (fig. 88) 

 over an angle a (here to be called Aa) cuts off the path 2.RAa from the b ray 

 and adds the same path to the a ray. Hence the total change of path is 4.RAa. 



Again, though the additional glass-paths at HI and H 2 (being equally 

 incremented for both the a and b rays) compensate each other, this is not 

 true at H\ and Hz for the b and a rays. Since the b ray at Hz receives no 

 increment, the total glass-path increment at HZ is effective. The glass-path 



2 at Hz may be written as heretofore, 



/ i r\ 



? I sin 2 u sin 2 



V 2 2 / 



and hence if Ai= 2Aa, since * is decreased by 20. at Hz, the glass-path incre- 

 mented (dz /di), Az may be found by differentiation to be 



e sin (i r) 



2- - Aa 



cos r 



Finally, the compensation at the micrometer-screw at d is 2AAT cos i. Hence 

 when the center of ellipses is restored to the fiducial line, 



AJV 4R 2e sin (i r)/cos r 



Aa 2 cos i 



Here 2R is the normal distance between the a and b rays, e the thickness of 

 the glass-plate f/j, and i, r the angles of incidence and refraction. 



In the apparatus 2* was not measured, but made nearly 90 by eye 

 adjustment. 2R was measured. Hence, in the first set of experiments, 



= 27.5, 



and 



A./V 42 2X0.70X0.30/0.89 cm. 



r -- = - - =29.5 



. 

 Aa 2X0.707 radian 



This is larger than the corresponding experimental value 27 cm./radian, but 



