T H E 

 LONDON, EDINBURGH, and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



[SIXTH SERIES.] 



JANUAR Y 1913. 



I. J he Correction to the Length of Terminated Rods in 

 Electrical Problems. By Lord Rayleigh, O.M., F.R.S.* 



IN a short paper " On the Electrical Vibrations associated 

 with thin terminated Conducting Rods " f I endeavoured 

 to show that the difference between the half wave-length of 

 the gravest vibration and the length (/) of the rod (of uniform 

 section) tends to vanish relatively when the section is re- 

 duced without limit, in opposition to the theory of Macdonald 

 which makes X = 2*53 I. Understanding that the argument 

 there put forward is not considered conclusive, I have tried 

 to treat the question more rigorously, but the difficulties in 

 the way are rather formidable. And this is not surprising 

 in view of the discontinuities presented at the edges where 

 the flat ends meet the cylindrical surface. 



The problem assumes a shape simpler in some respects if 

 we suppose that the rod of length I and radius a is surrounded 

 by a cylindrical coaxial conducting case of radius b extending 

 to infinitv in both directions. One advantage is that the 

 vibrations are now permanently maintained, for no waves can 

 escape to infinity along the tunnel, seeing that I is supposed 

 great compared with b J. The greatness of I secures also 

 the independence of the two ends, so that the whole cor- 

 rection to the length, whatever it is, may be regarded as 



* Communicated by the Author. 



+ Phil. Mag. vol. viii. p. 105 (1904) ; Scientific Papers, vol. v. p. 198. 

 X Phil. Mag. vol. xliii. p. 125 (1897) ; Scientific Papers, vol. iv. p. 276. 

 The conductors are supposed to be perfect. 



Phil Mag. S. 6. Vol. 25. No. 145. Jan. 1913. B 



