516 Prof. Baly and Mr. Garrett on the Ultra-violet 



The general structure of the whole ultra-violet band group 

 will be as follows : — From the general theory as laid down 

 in the previous papers the wave-numbers of the principal 

 lines in the band — that is to say, the heads of the sub- 

 groups — will be given by 33*751*6 ±nK, where K is one of 



the fundamental bands of the infra-red, and ra = 0, 1, 2, 3 



It has already been found, as shown above, that K is the 

 least common multiple of two of the basis constants, 273 

 and 8*177, and has the value 223*225. The wave-numbers 

 of the heads of the sub-groups, therefore, will be given by 

 33751*6 + hx 223*225. Again, the fundamental infra-red 

 band with the wave-number of 223 225 according to Bjerrnm 

 is itself complex and consists of a group of lines the 

 wave-numbers of which are given by 223*225 ±v r , where v r 

 stands for the two basis constants 2*73 and 8*177. Since, 

 however, 8*177 = 3 X 2*73 almost exactly, the structure of 

 this fundamental band will be given by 223*225±nx 2*73, 



where n=0, 1, 2, 3 The upper limit of n is defined by 



the overlapping of the band with the next infra-red band, 

 and it is not possible to state with any exactness how far 

 the two consecutive bands overlap. From what follows it 

 will be seen that on the long-wave side the upper limit of n 

 is about 44, while on the short-wave side the limit is about 37. 

 In the fundamental infra-red band, therefore, there must be 

 -82 lines, namely, the central line together with 44 lines on 

 one side and 37 on the other. 



The lines in the ultra-violet band are due to the com- 

 bination of the central wave-number with the infra-red 

 vibrations, and therefore the component lines of the central 

 ultra-violet sub-group will be expressed by 33751' 6 ±n x 2*73. 

 The other sub-groups are due to the combination of the 

 wave-numbers of the lines in the fundamental infra-red band 

 and their integral multiples with the central wave-number 

 33751*6. Thus the first sub-group on each side of the central 

 sub-group will be given by 33751*6 ± 223*225 ±n x 2*73, and 

 the second sub-group by 33751*6 + 2 x 223*225 + ?i x 2*73, 

 and so on. 



There appear to be seven sub-groups on the less refran- 

 gible side of the central sub-group and thirteen on the 

 more refrangible side. When each individual sub-group is 

 considered and the wave-numbers of its component lines 

 calculated, it appears, on comparison with Miss Lowater's 

 list of lines, that the group is slightly asymmetric, for there 

 are 44 lines on the less refrangible side of the centre and 

 37 on the more refrangible side. 



