282 Mr. W. Gordon Brown on 



Hence the total deflexion of the primary focus is given by 



4)-^(^>»4^-'>(H)- 



Similarly for the secondary focus the deflexion S( ^ ) is 

 and since A fi — 1 A 1 a — 1 



yLtr x ' d F yLtr! 



we have s/l\ tan 2 <£/yu,+ r 



<t)- i ffP5 J > 



These formulae were given by Coddington, but of late have 

 been somewhat ignored by textbook writers, though used 

 with success in the design of some modern photographic 

 objectives. 



XXV. Note on Reflexion from a Moving Mirror. 

 By W. Gordon Brown *. 



WITH regard to the question of alteration of amplitude 

 by the Doppler effect, which was raised by Mr. Edser 

 in Octoberf, I should like to point out that the relation between 

 the kinematics and electromagnetics of the problem is very 

 clearly brought out by the Faraday tube theory of radiation. 

 In this theory a tube of force lying along the direction of 

 the ray is supposed to transmit transverse vibrations like an 

 elastic string. The displacement of the tube from its equi- 

 librium position alters the direction of electric intensity. 

 If it is assumed that the magnitude of the component parallel 

 to the ray is unaltered, then the transverse component of 

 electric force will be equal to this unaltered intensity mul- 

 tiplied by the tangent of the angle between the tube and the 

 ray. Thus if r measures distance along the ray, z is the 

 transverse displacement, and R, E are the r-, *- components 

 of electric intensity, 



e=r|? (1) 



Or 



The magnetic force is the product of the velocity of the 



* Communicated by the Author, 

 f Phil. Mag. vol, xxyiii. p. 508. 



