12 



THE INTERFEROMETRY OF 



displacement. The arrow-shaped forms are also often satisfactory, and may 

 be obtained by adjusting the two bright patches on the reflecting grating 

 into coincidence, by the eye, in the absence of the telescope. The grating G' 

 is moved fore and aft for this purpose on the slide s, figure 2, until the two 

 bright strips become one. 



In making the first adjustment, I incidentally combined the first-order 

 spectrum from N with the second-order spectrum from M, as shown in figure 5, 

 under the impression that the wider D groups from the latter were due to 

 slight curvatures of mirrors. The fringes were nevertheless easily found and 

 showed no anomalies, except that observation had to be made near M or N. 



It appears from figure 5 that the equations for this case imply 



sin i + sin 0" 2 = 2\/D 2 

 sint sin 0' 2 = \/D 2 



where the angles i and 6 are equal (0' 2 = #"2). Thus sin i = ^\/2D 2 and sin 



= X/2Z) 2 , A being the grating constant (Z? 2 = 2ooXicr 6 cm.). 



Hence 



sin i = o. 4420 sin 02 = 0.1423 

 * = 26i4' 2 = 8n' 



while from the first grating, D 1 = 352Xio" 6 cm., 0i = 938'; whence 



The trial readings given in table i of the micrometer for a passage of 

 20 fringes each were found without special precautions, which is equivalent 



TABLE i. 



to an average of icr 6 X3o.i cm. per fringe. As the line of symmetry lay 

 very near the two D\D^ doublets, this is obviously an approach to half a wave- 

 length. For accurate work AA and D\D' Z should be superposed, in which 

 case the fringes would lie between and actually correspond to their mean 

 wave-length. 



A number of measurements like the above were now made with different 

 types of fringes. The mean values successively taken from 3 or 4 batches 

 of 20 fringes each were 



io 6 5<? = 29.4, 30.0, 31.2, 30.6, 29.7, 30.1, 30.0, 30.0, 30.8 cm. 



The results were less decided when long fringes were used. The mean 

 value of the io sets is thus deX io 6 = 3o.i9 cm. per fringe. Actual or approx- 

 mate coincidence of the D lines made no appreciable difference. 



