350 Prof. D. B. Brace on Achromatic Polarization 

 From these equations we obtain 



8\ d 



oW = ;? = "' ( 12) 



s\ 



where n represents the ratio of the number of bands in the 

 interval BX in the two cases. 

 Hence 



S(N-N') 



-s—^-^ ™ 



6X 

 Since when d diminishes the bands move in the negative 

 direction, i. e. towards the violet, as shown by equation (10), 

 the total number passing any point, say the sodium line, for 

 a change of path from d to d' will be 



Hence 



Hence 



=N'-N=«*'-rf)(^ + !-£ 



-S\Y (14) 



N-N' d-d 1 m n-l 

 N d N n ' ' 



. . (15) 



N- mn 





n — 1 



which gives the order. For example, if n = 2, N = 2wj, i.e., 

 if every alternate band of the first coincides with each one 

 in succession of the second, the number of passages necessary 

 to obtain this coincidence from the original complete order 

 of coincidence is one-half the original order of the plate 

 whose thickness is varied. In the substances examined the 

 order for sodium light was approximately double the number 

 of bands easily seen between the red and the blue in the 

 primitive spectrum. For example, in starting with about 

 eight bands visible in the field, fifteen passages for the sodium 

 line were counted in doubling the order, thus making the 

 original order fifteen. Although increase in thickness in- 

 creased the number of visible bands, the order could be 

 determined to a certainty. 



If we call N the order of the sodium band, and assume it 



