Light Absorption and Fluorescence. 515 



iirst sight as if they all could be expressed with very fair 

 accuracy as multiples of 4. This, however, gives no expla- 

 nation of the remarkable intensity differences in the bands, 

 and, further, all the consecutive multiples of 4 do not appear 

 as bands, even between 10 //, and 13 fi, where perhaps they 

 might be expected to evidence themselves. The two most 

 -characteristic and outstanding bands are those at 3*26 //, and 

 6'75/u-, and the wave numbers of these are almost exactly 

 308 and 148, and on the least common multiple principle 

 these may be looked upon as the least common multiples of 

 4 and 7*6, and of 4 and 3* 7 respectively. On this view, 

 therefore, we have three basis constants of benzene, namely, 

 3*7, 4*0, and 7*6, which explain the two most characteristic 

 bands of benzene. Other combinations of these basis con- 

 stants can be made as follows: — 



24 x 7*6=46 x 4 = 184, which is the wave-number corre- 

 sponding to \ = 5*43/x, a value exceedingly close to 5*5 at 

 which Coblentz found a strong band. Again we have 

 60x7*6 = 115x4 = 460, which is the wave-number of 

 \ = 2*174 fi and clearly corresponds to Coblentz's measure- 

 ment of 2*18 p. Further, 2x148 (the wave-number of 

 \ = 6-75)=296 corresponding to 3*37 ^t, which in all pro- 

 bability is hidden in the great band at 3*26 //,; 3 x 148 = 444 

 corresponds to 2*25 /a, which is hidden in the great band at 

 2*18 fi, but 4 x 148 = 592, which corresponds to A, = l*68/z, 

 the value obtained by Coblentz. These three basis constants 

 therefore explain all the important infra-red bands of benzene 

 except those at \ = 9*78 and A,= 2*48 //., the remainder being 

 exhibited either at the lowest common multiple of two 

 of the basis constants, or some multiple of it, or at some 

 frequency which is n multiple of two of the constants. As 

 regards the hand at \ = 2*48/x, it is somewhat remarkable 

 that the narrow absorption lines composing the ultra-violet 

 band group of benzene can all be arranged symmetrically 

 round the wave-number 4050 as centre. This number is 

 10 v 405, which latter is very near the reciprocal of 2*48 /x. 

 Now no combination of the above three basis constants gives 

 a number near this value: and since this value appears to be 

 a fundamental one for benzene, it is in all probability due 

 to there being a fourth basis constant, 10*125. The lowest 

 common multiple of 4 and 10*125 which is 405 gives a wave- 

 length of 2*47 fi, which is exceedingly near to Coblentz's 

 value of 2*48 fi. We are therefore left with the band at 

 \ = 9*78/x, which, however, does not seem to be a specially 

 characteristic band of benzene in spite of its intensity, since 



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