Light Absorption and Fluorescence. 11 



water molecule is the convergence frequency of these 

 three, 6*1326' X I0 13 , we also have to take into account 

 the intra-molecular frequency of the OH group. Now, 

 in the molecule H-O-H there are two frequencies active 

 for oxygen and one for hydrogen, and thus there are two 

 possible intra-molecular frequencies for the OH group, 

 depending on which oxygen frequency is concerned. In 

 addition, therefore, to the three atomic frequency series 

 the molecule will also show two intra-molecular or OH 

 frequency series. Each of these intra-molecular frequencies 

 is the convergence frequency of two atomic frequency 

 series, and will be associated with subsidiary frequencies 

 to form a band group. If I be the central intra-molecular 

 frequency, the only subsidiary frequencies associated with I 

 will be given by l±nA l and 1±A 2 , where A x and A 2 are 

 the two atomic frequency series converging at I, and 

 n=l, 2, 3, etc., with an upper limit defined by the critical 

 value. There will also exist two series of frequencies, 

 I], 21], 3I l5 etc., and I 2 , 2l 2 , 3I 2 , etc., each associated 

 with its subsidiary frequencies ; and these intra-molecular 

 frequency series will coiwerge at the true molecular 

 frequency. 



In the case of the water molecule there are two intra- 

 molecular frequency series — namely 7*5 X 10 n , which is 

 the convergence frequency of the atomic frequencies 

 1-0635 xlO 11 and 2*1159 x 10 11 , and 1*7301 x 10 12 , which 

 is the convergence frequency of the atomic frequencies 

 2*1159 xlO 11 and 2-1531 xlO 11 . Since it is known that 

 2'1531 x 10 u is one of the atomic frequencies of oxygen, 

 and since the two intra-molecular frequencies are the 

 two possible combinations to form the OH group, it would 

 follow that 1*0635 X 10 11 is the second oxygen frequency 

 and that 2-1159 X 10 11 is the hydrogen frequency. 



When the. subsidiary frequencies associated with a given 

 true molecular frequency are considered, instead of only 

 the subsidiary frequencies M±?iA, there will exist as sub- 

 sidiary frequencies M + >iI + ?»A, where n and m = 0, 1, 2, 

 etc., each having its own critical limit : I is one or other 

 of the intra-molecular frequencies, and A stands for the 

 two atomic frequencies which have I as their convergence 

 frequency. This will obviously result in the whole group 

 of subsidiary frequencies associated with a given molecular 

 frequency being divided into sub-groups. The central sub- 

 group will be given by ?i = 0, and the central lines of the 

 snb-groups will be given by m = 0. This is exactly the 

 structure that has been observed in the case of water and 



