100 Dr. C. V. Burton on the Scattering and 



was caused to pass through mercury vapour at a pressure of 

 •001 mm. The radiation laterally scattered was most intense 

 where the primary beam entered, and gradually fell off 

 as the beam penetrated further into the vapour ; the 

 intensity being reduced to one-half after a depth of 5 mm., 

 had been traversed. The proportional reduction of amplitude 

 in traversing a layer comparable in thickness with \J2tt is 

 evidently quite small, and the approximations of § 34 can be 

 used. For the present let attention be confined to the 

 primary (or incident) and secondary radiations ; also let 

 the possible influence of the Doppler effect and of collisions 

 between molecules be disregarded. 



53. The coefficient of extinction, for light of any assigned! 

 frequency, is proportional to sin 2 7, where y is the amount 

 by which the secondary radiation from a molecule lags 

 in phase behind the resultant incident radiation : a result 

 derived from the sole assumption that no absorption of 

 energy takes place. But when we want to express y as 

 a function of the particular frequency (p) in question, some 

 further assumption must be made, and one that readily 

 presents itself is that y is related to p as it would be in a 

 purely dynamical system To express such a relation, new 

 quantities have to be introduced, though these do not appear 

 in the final result. If the free vibrations of a singly-free 

 system with co-ordinate u are conditioned by * 



u + ku + ™ 2 w = 0, 



so that the natural (undamped) frequency is n/2ir, then the- 

 prolonged action of a force proportional to cospt will give 

 rise to a vibration which lags in phase behind the force by 7, 

 where 



tan 7 = pKJ{n 2 —p 2 ) f . 



Since the effective range of frequency with which we are 

 concerned is extremely narrow, no appreciable error is. 

 involved in replacing this last equation by 



tan 7 = nic/(n 2 —p 2 ) , 



whence 



2^2 



n k 



S111 7=7-5 2X2 ,22 * « « ' 0>1> 



' (n 2 — p 2 ) 2 -\-n 2 /c i x ; 



54. Let the energy-flux in the incident beam between the 

 limits p 2 —p l and p 2 =p 2 + d(p 2 ) be f{p)d(p 2 ). Then since 



* In the present optical application, the presence of the term <ii must 

 be attributed wholly to radiation from the molecule, 

 f liayleigh, < Theory of Sound,' vol. i. §46. 



