ON ABSORPTION SPECTRA OF ORGANIC COMPOUNDS. 235 



quantum. In other words, the molecule will be endowed with the frequencies 

 M-TiA. 



Emphasis may be laid on the fact that, under normal conditions, when the 

 molecule is in radiant equilibrium with its surroundings the subsidiary frequencies 

 M + »A are actually observed ; and further, that in these series of subsidiary 

 frequencies tho maximum observed vahie of v is one less than the critical value ; 

 that is to say, the subsidiary frequencies associated with two consecutive values 

 of the molecular frequency do not overlap. Obviously, if the molecule is screened 

 from all external radiation with frequency equal to its atomic frequencies — that 

 is to say, it is cooled to low temperatures — the whole of the above deductions 

 as to subsidiary frequencies fail, and the subsidiary frequencies must therefore 

 vanish. This has been observed, since at very low temperatures only the central 

 molecular frequencies remain. 



In the foregoing the simplest case only was dealt with of a binary molecule 

 formed by the combination of atoms of two different elements. Exactly the 

 eame conditions will, of course, obtain in more complex molecules, but added 

 to these will be new conditions resulting from the existence of groups of atoms 

 within the molecule. For instance, even in the apparently simple case of the 

 water molecule the conditions will be more complex, owing to the undoubted 

 fact that in this molecule the hydroxyl group exists as an integral portion of 

 the molecule. Whilst, of course, the true molecular frequency will be the 

 convergence frequency of all the atomic frequencies, it is the subsidiary fre- 

 quenciee that will exhibit a greater complexity. This complexity, however, is 

 only one of degree, and its explanation follows exactly the same principles as 

 were laid down for the simplest possible binary molecules. The specific case 

 of the water molecule may be discussed in which there are three atomic fre- 

 quencies, 1-0635 X lO'i, 21159 x IQH, and 2-4531 X 10". Whilst the true mole- 

 cular frequency of the water molecule is the convergence frequency of these 

 three, 6'1.326 X 10^^, -we have also to take into account the intra-molecular fre- 

 quency of the OH group. Now in the molecule H — — 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 intra-molecular or OH series. 

 Each of these intra-molecular frequencies is the convergence frequency of two 

 atomic series, and will be associated with subsidiary frequencies to form a 

 band group. If I be the intra-molecular frequency, the only subsidiary fre- 

 quencies associated with I will be given by I + wAj and 1+ 71A2, where Ai and 

 A= are the two atomic frequency series converging at I, and n = 1, 2, 3, &c., 

 with an upper limit defined by the critical value. There will also exist two 

 series of frequencies, Ii 2It 3Ii, &c., and I2, 2I2, 31=, &c., each associated 

 with its subsidiary frequencies. These intra-molecular frequencies will converge 

 at the true molecular frequency. 



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

 series, namely 7-5 X 10", which is the convergence frequency of the atomic 

 frequencies, 1-0635 x lO^' and 2-1159 x lO", and 1-7301 X 10l^ -which is the 

 convergence frequency of the atomic frequencies 2-1159 X 10'' and 2-4531 X lO^. 

 When the subsidiary frequencies associated with the given true molecular 

 frequency are considered, instead of only the subsidiary frequencies M + nA, 

 there will exist as subsidiary frequencies M+wI+toA, where n and m = 0, 1, 2, 

 &c. , 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 sub- 

 sidiai-y frequencies associated with the given molecular frequency being divided 

 into sub-groups. The central sub-group will be given by n = 0, and the central 

 lines of the sub-groups will be given by m = 0. This is exactly the structure 

 that has been observed in the case of water and sulphur dioxide, both of which 

 molecules have three atomic frequencies. Perhaps the most striking experi- 

 mental confirmation is to be found in the fact that in any one sub-group the 

 subsidiary frequencies are formed from only those atomic frequencies which 

 have the intra-molecular frequency as their convergence frequency. None of 

 the previous theories are able to account for tliis selective association of the 

 atomic frequencies. 



