512 Prof. E. C C. Baly on 



multiples of the constants give rise to absorption bands 

 which are far more intense than the neighbouring multiples 

 on each side. On the other hand, if there are two constants 

 or bases, then there must exist a convergence-frequency of 

 the two as it were, which is the least common multiple of 

 the two bases. It is to be expected that such a frequency 

 would necessarily be especially active since it is keyed with 

 both series. I suggest, therefore^ that this is the reason why 

 an infra-red absorption band is especially pronounced in 

 intensity, namely, that its frequency is either an even multiple 

 of the two bases which are active, or that it is the least 

 common multiple of the two bases. If this principle be 

 accepted, it seems entirely to solve the difficulty connected 

 with the intensity of the absorption bands, and makes the 

 calculation of the values of the bases a simple matter. 



Whatever may be the relative intensities of the longer- 

 wave infra-red absorption bands of water vapour, the most 

 intense bands in the short-wave region are those at 6*25, 

 6-0, 3-0, 2'0, and 1-5/*. The reciprocals of these are 160, 

 166-6, 333*3, 500*0, and 666'6 respectively. Eucken has 

 already pointed out that 2*5 is one of the basis constants of 

 water, and the above values at once suggest that there is 

 a second basis constant of 6*6. The first wave number 

 160 = 64 X 2-5 = 24x6-6, while the second one 166-6 is the 

 least common multiple of the two bases. The last three 

 frequencies are the least common multiple multiplied by 2, 

 3, and 4 respectively. 



It would seem probable that the intensities of the absorp- 

 tion bands due to the several multiples of the bases would 

 decrease as the value of n increases in the expression 



Jin 

 2^1' 



and consequently in the short-wave infra-red region where 

 n is large, the bands due to these multiples acting alone will 

 be very faint indeed. When, however, that frequency is 

 reached which is the least common multiple of the series, 

 then a very strong absorption band is evidenced. It follows 

 further from this, that the only possible regions of still shorter 

 wave-length at which absorption bands of water can occur 

 will be frequencies which are multiples of 166*6. Since all 

 such absorption bands are multiples of 166*6, there must 

 naturally exist a constant difference of 166*6 between their 

 frequencies, and thus a physical explanation is found for 



