132 Prof. Nagaoka and Mr. T. Takamine on Crossed Spectra 

 which is known by observation, 

 /-p. m — V 



-^- = 2*. 



1-1 



If we make observations on lines of wave-lengths A/, \" , . . „. 

 we shall have similarly 



8*=. 



o 



Thus the difference between wave-lengths X and A/ is 

 S\=A/— A,= 



/p, _ ?»' — 1 -^ wi — 1 



i-- £ , 



e e 

 The expression simplifies for — = — 7 ; when this condition 



is satisfied for m=m', the rings due to A, and X' must 

 coincide. 



e e' 



The most favourable case is evidently P— =P'— 7, but w p 



cannot always make the optical thickness of the air-plate 

 fulfil this condition, so that there is usually a small residual. 



€ / e 

 Putting — - _ — =£, and remembering that P' — P is usually 

 m m 



small compared with P or P', 



a={(F-P)(l + l) + P'f}f. 



When SA is approximately known, we may arrive at a 

 more exact value by using crossed spectra, in which the 

 above formula for &\ is practically utilized. For this pur- 

 pose, it is in the first place necessary to have a line of 

 standard wave-length, and to determine the zero-correction 

 of the micrometer attached to the interferometer. As the 

 screw is not generally free from periodic errors, the scale 

 cannot be always relied upon, and one must have some 

 means of checking the readings. This is easily done by 

 using two neighbouring lines of mercury 5790 and 5769.. 



