( (>()() ) 



soon as I is of the same onler of niagiiitiule as ?j' or surpasses 

 Ihis quantity, (lie fraction i)econies so small that it may be neglected, 

 and it will remain so, if we omit the term — 4| in the numerator. 

 We may therefore write in all cases 

 ex 1J 



so tliat the index of absorption becomes 



k = — . ^-^- (26) 



This formula shows that for 5 = the index has its maximum 

 value 



n 



^■a = .— (27) 



and tiiat for | =i ± r»i, it is r' -(- J times smaller. 



The frequency corresponding to this \alue of g can easily be cal- 

 culated. If « may be neglected, a question to which we shall return 

 in § IS, (11) may be put in the form 



5 = '«'("»'-«') (28) 



Hence, foi' $ ^ q= n; 



7n {ii'' — w„') =r d= rij ^ ± r « </'. 

 or, on account of (10) and (18), 



2 m V n 



in {n^ — ;;„") = ± r « r/ ^ ± , 



T 



2v7i 



T 



If n — iio is much smaller than n^, we may also write 



71 = M„ ± - (29) 



T 



The preceding considerations lead to the well known conclusion, 

 somewhat paradoxal at first sight, that the intensity of the maximum 

 absorption increases by a diminution of the resistance, or by a lengthen- 

 ing of the time during which the vibrations go on undisturbed. In- 

 deed, if // is diminished or t increased, it appears by (10) and (12) 

 that ij becomes smaller and by (27) ko will become larger. This result 

 may l)e understood, if we keep in mind that, in the case ?j = iio, 

 the one most favourable to "optical resonance", in molecules that 

 are left to themselves for a long time a large amount of vibratory 

 energy will have accumulated before a blow takes place. Though 

 the blows are rare, the amount of vibratory energy which is converted 

 into heal may therefore very well be large. 



