O. 0. Lester — Oxygen Absorption Bands. 155 



The second differences of the new formula are constant as 

 they are in that of Deslandres, and it is evident from the near 

 approach to constancy observed in the second differences of 

 both N" and X, that some law based on this property is the 

 true one. That the lines follow some very definite arrange- 

 ment is seen from the smoothness of the on-curves and from 

 the smallness of the differences between the observed and cal- 

 culated values. It is quite probable that the proposed formula 

 will be found to represent the line series of other band spectra 

 more closely than the old. This I have not as yet investigated. 

 Assuming the proposed law to be exact we have on the other 

 hand a criterion of the accuracy of the measurements of the 

 wave lengths. It is quite likely that if the series were longer 

 the formula would need an additional term, possibly one 

 depending on the wave length. This is a matter for further 

 investigation. The formula may have some theoretical 

 importance also, as the formulae so far deduced theoreti- 

 cally have not contained the first power of n. 



Deslandres' second and third laws are only approximate for 

 this spectrum but a correction for them could not be obtained 

 with certainty, owing, in the case of the third law, to the 

 shortness of the band series. 



The points of chief importance in the foregoing discussion 

 may be summarized as follows : 



1. The general accuracy of the determination of the wave 

 lengths in the groups A, B, and a has been greatly increased 

 and the series which compose them considerably extended. 



2. The band a' has been measured and its relation to the 

 other groups studied for the first time, and in addition a new 

 band a" has been observed and studied at X = 5377'2. 



3. The oxygen absorption spectrum has been shown to con- 

 sist of two distinct series of bands instead of one, the series of 

 bands occuring in pairs just as do the series of lines in a band. 



4. Deslandres' first law has been shown to be entirely 

 inadequate to represent the line series of the several bands and 

 a modification is proposed which gives results agreeing with the 

 observed values to about the limit of error of the measure- 

 ments. 



In conclusion I wish to express my thanks to Prof. A. "W". 

 Wright, whose kindly interest and criticism have been of great 

 benefit throughout this investigation, and through whose aid 

 the excellent photographs of the spectrum were obtained. 



Sloane Physical Laboratory, Yale University. 

 May 1, 1904. 



