568 Prof. E. C. C. Baly on Light 



out of the three atomic frequencies active in the water 

 molecule. We therefore have to find a solution satisfying 

 the following conditions if the analogy with sulphur dioxide 

 is complete. Three atomic frequencies must exist of which 

 one is 2*4531 X 10 n , the least common multiples of two pairs 

 of these three must be 7*5 X 10 n and l*7301x 10 12 , and the 

 least common multiple of all three atomic frequencies must 

 be a number of which exact multiples give the central 

 frequencies of the great absorption-bands at 6 //, and 3 fju. 

 The three atomic frequencies tire at once found to be 

 1-0635 xlO' 1 , 2-1159 x 10 n , and 2-4531 x 10 11 . The least 

 common multiple of the first two is 75 x 10 11 , the least 

 common multiple of the last two is 1*7301 XlO 12 , whilst 

 the least common multiple of all three is 6'1326 X 10 12 . 

 The first two conditions are therefore satisfied. As regards 

 the last condition, 6*1326 X 8 x 10 12 is the frequency corre- 

 sponding to the wave-length 6*115 /x, the value observed 

 by Coblentz being 6*1 /*, whilst 6*1326 x 16 x 10 12 corre- 

 sponds to the wave-length 3*057 //,, the values observed 

 by Coblentz and by Paschen being 3 05 //, and 3*07 jjl 

 respectively. All three conditions therefore are exactly 

 satisfied, and the fact that the atomic frequency of oxygen 

 in the water and sulphur dioxide molecules is the same 

 would seem to be of great importance. 



It now becomes possible to put this solution to a very 

 severe test by calculating from the above frequencies the 

 wave-lengths of the component absorption-lines in the two 

 great absorption-bands, and comparing them with Sleator's 

 observed values. His measurements were made over the 

 following regions : 1*35 fi to 1*45 /i, 1 81 /i- to 1*92 /x, 

 2 52 ijl to 2*87 fi, and 5*02 fi to 6*83 fi. The last two 

 sets deal with portions of the two bands w T ith centres at 

 3'057 fi and 6*115 //, respectively, and since the third set 

 contains the greater number of individual measurements 

 it will afford the best opportunity of testing whether the 

 atomic frequencies given above are correct. As stated, 

 there are present in the band two series of sub-groups, 

 the central lines of each of which form a series with 

 constant frequency difference, the two constant frequency 

 differences being 7*5 XlO 11 and 1*7301 X 10 12 respectively. 

 Now the central frequency of the band at 3 /jl is 6*1326 

 x 16 x 10 12 or 9*81216 x 10 13 , and obviously the frequencies 

 of the complete set of the central lines of the sub-groups 

 will be given by 9*81216 x 10 13 + m x 1*7301 x 10 12 and 

 9*81216 x 10 13 + n X 7*5 x 10 11 , where m and n equal 1, 2, 



