126 Lord Rayleigh on the Passage of 



regarded as perfect it is so much simpler in its conditions as 

 to justify a separate treatment. Some particular cases of it 

 have already been considered by Prof. J. J. Thomson*. The 

 cylinder is supposed to be infinitely long and of arbitrary 

 section ; and the vibrations to be investigated are assumed 

 to be periodic with regard both to the time (t) and to the 

 coordinate (z) measured parallel to the axis of the cylinder, 

 t. e., to be proportional to , ^" w+ ***. 



By Maxwell's Theory, the components of* electromotive 

 intensity in the dielectric (P, Q, R) and those of magnetic 

 induction (a, b, c) all satisfy equations such as 



~dx 2 + dy' 2 + dz 2 ~~Y 2 alt*' ' ' ' ' U 

 V being the velocity of light ; or since by supposition 



dz* - ' de ~ p ltj 



i + £y+«*-°. ( 2 ) 



am <PR 



d.v 2 dy 



where k 2 =p 2 /Y 2 — m 2 (3)f 



The relations between P, Q, R and a, b, c are expressed as 

 usual by 



da __ dQ dR . 



dt~ds~~lfy' W 



and two similar equations ; while 



da db dc n , K * 



dx dy dz. 



S+2+2- ■ ;-» 



The conditions to be satisfied at the boundary are that the 

 components of electromotive intensity parallel to the surface 

 shall vanish. Accordingly 



R=0, (7) 



p S +( 4= o > <«> 



* ' Recent Researches in Electricity and Magnetism/ 1893, § 300. 

 t The k 2 of Prof. J. J. Thomson (loc. cit. § 262) is the negative of that 

 here chosen for convenience. 



