Absorption System of Sulphur Dioxide. 517 



The general formula, therefore, expressing the whole 

 system of lines in the whole ultra-violet band group is 

 33751-6 +/>x 223-225 + ?2x2-73, where p=-7, -6, .... 

 .... +12, +13, andn=-44. -43, .... .... +36, +37. 



The whole band group, therefore, consists of 21 sub- 

 groups, each containing S2 absorption lines. It is obvious 

 from this arrangement that there must exist in the band 

 group 82 series, each containing 21 lines with a constant 

 difference of 223*225 between their wave-numbers, and we 

 thus arrive at the true physical explanation of Miss Lowater's 

 discovery that the lines can be arranged in series of constant 

 wave-number differences. Miss Lowater, however, arranged 

 her observed lines in 44 such series, but it must be remem- 

 bered that there were 42 lines which she was unable to 

 include in her series. Moreover, also the values of the 

 mean wave-number differences she found seem to vary far 

 more than her experimental error would permit. For 

 example, in her 42nd series the first and nineteenth members 

 have wave-numbers 32202*1 and 36231*6 respectively, and 

 these give a mean wave-number difference of 223*8. The 

 mean wave-number difference calculated from all 44 series 

 is about 223*3, which would point to an experimental error 

 of about 4*5 in the wave-numbers of each of the above two 

 lines, an error which is very much greater than is possible 

 from the accuracy of her work. In general it would appear 

 that, although Miss Lowater's discovery of series of lines 

 with constant wave-number differences is perfectly sound,, 

 yet her arrangement of the lines in these series is not the 

 best possible. 



We have calculated the wave-numbers of all the lines 

 which the above formula establishes to be present in the 

 whole group, and they amount to 1722. These we have 

 arranged in the 82 series of constant difference, and com- 

 pared them with Miss Lowater's observed values after 

 reducing- the latter to vacuum. The agreement between 

 the observed and calculated values is exceedingly good, but 

 it cannot be claimed that this agreement by itself is an 

 absolute proof of the validity of the formula. The difference 

 in the wave-numbers of any two consecutive lines in the 

 spectrum is 2*73, and this is not much more than twice 

 Miss Lowater's maximum experimental error, and therefore 

 the difference between any observed line and the nearest- 

 calculated line cannot be much greater than the maximum 

 experimental error. On the other hand, the agreement 

 between the observed and calculated values is on the 



