REVERSED AND NON-REVERSED SPECTRA. 145 



so that the size A<p is influenced inversely as the effective thickness e (i.e., the 

 difference of thickness) of plates and depends on the position N of the microm- 

 eter. It N=N e = e(p cos R+ 25/X 2 cos R) /cos i 



di X 



dn 26 (n cos R tan i cos i tan R-{- 2B tan */X 2 cos R) 



X cos 7? 



2e tan 



Since t = 4S, # = 27 9', X = 60X10^ cm. 



_ _ 6oXio- 6 _ 

 ^"20(1.55X0.89-0.513X0.71+0.03) 



The parenthesis is 1.05. Hence 



0=-^- nearly 



which would make the effective glass thickness e = o.o6 cm. and 0.02 cm. for 

 A v ? = 5Xio- 4 radian and isXio- 4 radian, as above. Moreover, the rays K, 

 figure 93, entering the telescope from the foreground directly and the rays L 

 reflected into it by the plates of the interferometer, will not be parallel when 

 the fringes are of maximum size unless the plates M and N are equally thick. 

 Finally, the size of fringes in general (apart from wedge-shape of plates) will 

 be inversely as the effective differential thickness e of the plates used. 



If we collect the above equations* we may write roughly (since e = -, 

 nearly), 



uK. t>K. 



so that the measurement of the long distance d depends ultimately on the 

 area of the ray parallelogram 2bR, the differential thickness e of the corre- 

 sponding half-silvers, and the (relatively to Aa) enormous displacement A0 of 

 the achromatic fringes. 



Finally, if optic plate-glass were used for the half-silvered mirrors, the 

 parallelism of rays KL would coincide with the occurrence of centered or 

 circular achromatic fringes; while the whole preliminary adjustment of mirrors 

 for parallelism would consist in bringing the image from LMN'T, figure 93, 

 and from LM'NT, successively into coincidence with the direct image from K, 

 in case of a very distant source of light. 



The remarkable sensitiveness which accrues to the method, if the angular 

 displacement of fringes is measured in the ocular of a long telescope, comes 



* The text unduly accentuates the glass-paths, whereas the air-paths are more impor- 

 tant. I shall give a rigorous deduction of all the path-differences in my next Report to 

 the Institution, where they will be sustained in detail by experiments. 



