148 0. C. Lester — Oxygen Absorption Bands. 



where a and b are constants and n takes on all integral values 

 from to n. 



2. When several series arise from the edge of a band they 

 are similar in all respects, and all bands belonging to the same 

 substance have the same number of series. 



3. In a series of bands the vibration numbers of the edges 

 form a series similar to that of the lines in a single band. 



These laws are the most general in their application that 

 have yet been announced. Deslandres tested them on many 

 spectra, although he never published details showing the exact- 

 ness of agreement. Kayser and Range* have obtained a gen- 

 eral confirmation upon bands of many substances, including 

 those of N, C, CO, CN, and I, but the laws do not apply 

 equally well to all cases and occasionally appear to degenerate 

 into mere interpolation formulae. The difficulties in the way 

 of obtaining more exact expressions for the laws are in measur- 

 ing the wave lengths of bands accurately enough to warrant 

 taking into account small variations of the reciprocals, and, in 

 the case of the third law, in finding a long enough series of 

 bands capable of precise measurement. Most of the bands 

 hitherto investigated are in the upper part of the spectrum, 

 where a small error in the wave length causes a large error in 

 the reciprocal. 



Measurement of Wave Lengths. 



In the measurements of Rowland and Higgs to which ref- 

 erence is made above, both use the same unit, viz. 10" 7 mm., 

 and their results appear to be equally accurate. For those 

 lines in B and a which both have measured and for which the 

 agreement is *01 of a unit or closer, the value adopted in the 

 present work is the mean of the two. In case the disagree- 

 ment is greater than one would attribute to errors of obser- 

 vation, the value adopted is the mean of my own final result 

 and the one which it confirms, provided such agreement is 

 decidedly stronger with one than with the other. In some 

 cases the mean of all three measurements was taken. For the 

 large majority of the lines in A and a the values given are the 

 means of my own and Higgs' results alone. Those of a' and 

 a" have not been given before. Since *01 of a unit is about 

 the limit of accuracy in general, it has been thought best to 

 retain only two decimal places in the wave lengths except in 

 the case of B, where many of the lines are taken as Higgs and 

 Rowland give them. It may be added further that the third 

 decimal place rarely affects even the seventh place of the 

 reciprocal, 



* Ueber die Spektren der Elemente : Abhandl. der Berl. Akad., 1888-92. 



