524 The Rev. Professor O'Brien o?i the 



other words, that the light is circularly polarized, then we 

 have 



= w cos (fit — k z), Yj = u sin [nt — k %\ 

 V = nu, p = u. 

 Therefore the formulas just obtained give us 

 T N 



or 



V 



(4.) 



which was to be proved. 



N T 



20. We may here remark that these values of — and — 



are independent of the amplitude of vibration {u). This shows 

 that the integration of the equations in article 10 is not merely 

 approximate, but exact. See also the remarks made in article 

 13. 



21. By the results thus obtained the formulae (2.) become 



T N ■ 



Now, since — must be very small compared with w + — (see 



article 11),— must be very small compared with (l+<7); 

 hence we have, approximately. 



Hence, the length of the luminous wave being A, the time 



of vibration being r, and therefore 



2 7r 2 7r , Z" T 



\ — -y-, ' T = — J and .*. — = — , 



we find that 



which formula shows the dependence of the length of the wave 

 upon the time of vibration, i. e. upon the colour. 



Again, if a^ be the intensity of the vibration at any parti- 



