64 PROCEEDINGS OF THE AMERICAN ACADEMY. 



large value of m — 1 points to one or more other bands in the ultra- 

 violet. As I have already shown, a strong absorption-band exists a little 

 below A = 20 and a weak one at A = 25. Though the formula as it 

 stands represents the dispersion in the red, yellow, and green fairly 

 well, it breaks down if we try to apply it to the values found in the ultra- 

 violet by the photographic application of the method of crossed prisms. 

 This is due to the fact that we are getting into the region in which 



A 2 

 — ^ — is no longer approximately equal to one. 



This quantity increases in magnitude as A decreases, and the values of 

 n will, consequently, be higher than those calculated on the assumption 

 that the quantity is equal to unity. To meet this contingency we must 

 use the formula (neglecting the weak band at A = 25), 



m'\ 2 m"X 2 



n°- = 1 + -i + 



A 2 - A' 2 ' A 2 - A" 2 



Since m = 2.13 = m" + 1> we can take in" = 1.13. 



The value of the refractive index n, for A = 34 calculated from the 

 original formula, is n = 1.1, the value observed is 1.3; in other words 

 the value is raised by the influence of the remote ultra-violet band. 

 Using this observed value of n, it is possible to calculate the wave-length 

 A" of the ultra-violet band, assuming as above that m" = 1.13. 



This was found to be A" = 18, which looks reasonable. Of course it 

 is impossible to determine the centre of the band experimental!}', since 

 the nitroso cuts off everything below 20. Whether or not a return of 

 transparency would be found further along by employiug fluorite plates 

 and a vacuum spectrograph, it is impossible to say. The calculated 

 value of \" is about what we should expect it to be, judging by an 

 inspection of the photographs of the absorption in this region. 



We are now in a position to calculate other values of n in the ultra- 

 violet and compare them with the observed. For A = 36 (the wave- 

 length for which the lowest value of n was found experimentally), n 

 calculated by first formula was n = .92, by second formula n = 1.08, 

 observed n = 1.05. For A = 31, by second formula n = 1.42, observed 

 n = 1.43. Obviously we cannot apply the formula to that portion of 

 the curve between wave-lengths 23 and 29 until we know the value of 

 the extinction coefficient within this region. I feel certain that there 

 are absorption bands in the infra-red. not only on account of the indica- 

 tions which the dispersion formula gives, but because when working 

 with prisms of large angle I found that a fairly strong absorption oc- 



