REVERSED AND NON-REVERSED SPECTRA. 133 



It is obvious that 2AN cos i will increase with 2R, the distance apart of 

 the parallel rays ae and bf, figure 88, as well as with the rotation a. But the 

 relations are not obvious, and experiments were therefore made for the rela- 

 tion of AN and a in case of different distances apart (2R= 10, 21, 25, 28 cm.) 

 of the rays in question. The results are given in figure 91, where the abbre- 

 viation r = AN/Aa. In figure 92 and table 35, furthermore, this value, as 

 obtained from figure 91 graphically, is compared with 2R. The results are 

 not quite smooth; but as zR is the distance apart of two spots of light, it can 

 not be specified sharply. Moreover, a variety of other discrepancies of ad- 

 justment enter which need not be detailed here. From figure 92 it appears 

 that on the average r/2R = o.o24 in terms of degrees or =1.35 in terms of 

 radian. Hence we may consider an equation of the form 



= A/V cos i 



So computed cosi would be 0.73 instead of 0.71, but the difference is refer- 

 able to the outstanding glass-path and outstanding air-paths which have not 

 been included. 



68. Groups of achromatic fringes. With the good adjustment stated, a 

 number of further experimental measurements of the mean position (AN) of 

 the fringe patterns on the micrometer at H 3 were made, with results as fol- 

 lows: The size of the individual fringes was about 0.0225/35 = 0.00064 radian 

 in the telescope at T i.e., about 0.034 of arc. The fringe patterns will be 

 designated primary, secondary, etc. The data are io 3 AN cm. 



Tertiary +2.6 2.7 ... ... 2.7 cm. Xicr 3 



Secondary +1-3 1-2 1.3 1.4 1.4 



Primary 0.0 o.o o.o o.o o.o 



Secondary ~i-3 i-i 1.2 1.2 



One group was visible on one side and two on the other and one or more 

 frequently escaped capture by the micrometer. The wave-length difference 

 of these positions is exceedingly small. Using the above expression, AX = 

 X 2 /2AN cos 8, 



36Xio- 10 



AX = - - =1.9X10 cm. nearly 



2X1.3 X io~ 3 Xo.7i 



But there is no suggestion in this datum. The displacement AN is 

 equivalent to a glass thickness e, where AN = e(/j, i), roughly. Hence e = 

 i.3Xio~ 3 /53 0.0025 cm. This precludes the possibility of reflections from 

 the two sides of the half -silver film, since this is about 1,000 times thinner, 

 apart from its index of refraction. 



Some experiments were also made with the primary achromatic fringes 

 (treated as a single group and not individually, as the angle of measurement 

 of a was not correspondingly delicate) to determine AN/ A a. Two series 

 with different adjustments showed results as given in table 35 (2^ = 21 cm.). 



