and Differential Double Refraction. 351 



to be the central band in the normal spectrum, then, as the 

 sodium band was double the number of visible bands, we 



have approximately -j- and -j- as the orders of the red and 



the violet respectively. If now we make the^ order for 

 sodium nN+1 where n may be a whole or fractional quan- 

 titv, the corresponding order fo other parts of the spectrum 



will be increased in the ratio of — . Thus for the red 

 it becomes 



3 XT /nN±l\ 3 3 



and for the violet 



4 ( N )~ 4 ± 4 



This shows that when the order for the sodium band is 

 increased n times by increasing the thickness of the plate n 

 times, a single passage in the positive or negative direction, 

 changing the order to rzN+ 1, gives a difference of coincidence 

 between the original band of the one spectrum and the 

 nearest band of the other of one-fourth the distance between 



the new bands, or r -. As - 01 band can under the most 

 4« 



favourable conditions be distinguished, « = 25 will represent 



the limit of the ratio of the thicknesses which may be used 



by this method. The same method and reasoning apply in 



determining the order and the limit of error for any other 



part of the spectrum. 



The following arrangement (fig. 1) was used for making 

 direct comparisons between two crystalline plates. 



Two slits S and S ; were used for producing two prismatic 

 spectra at B and B' above each other. The adjustment of 

 the total reflecting prism allowed the spectral lines to be 

 brought into corresponding positions above each other in 

 both spectra. The two crystalline specimens — usually single 

 wedges — were each mounted in an ordinary Babinet's com- 

 pensator. The wedges were adjusted so that the incident light 

 was normal. The slits were placed immediately after the 

 wedges, and were made as narrow as possible consistently with 

 the bands remaining visible. The cross-hair of the observing 

 telescope was made to coincide with one of the sodium lines 

 in each spectrum. Since the opening of the slits S and S' 

 and also the angle of the wedges were small, the thickness d x 

 and (h in each wedge may be considered constant. The 



