Ps kOS: 
X. On the Electrical Vibrations associated with thin terminated 
Conducting Rods. By Lord Rayieicu, O.M., F.R.S.* 
N his discussion of this subjest Prof. Pollockt rejects the 
simple theoretical result of Abraham and others, ac- 
cording to which the wave-length (X) of the gravest vibration 
is equal to twice the length (/) of the rod, in favour of the 
calculation of Macdonald which makes X=2°53/. On this I 
would make a few remarks, entirely from the theoretical 
point of view. 
The investigation of Abraham? is a straightforward one ; 
and though I do not profess to have followed it in detail, | 
see no reason for distrusting it. It relates to the vibration 
about a perfect conductor in the form of an elongated 
ellipsoid of revolution ; and the above-mentioned conclusion 
follows when the minor axis (2)) of the ellipse vanishes in 
comparison with the major axis /. As a second approxima- 
tion Abraham finds 
Ret Ore Lee Gry a ys ie CL) 
Pre lO ee( ilo te ies oe a) 
But a question arises as to whether a result obtained for 
an infinitely thin ellipsoid can be applied to an infinitely 
thin rod of uniform section. So far as I see, it is not 
discussed by Abraham, though he refers to his conductor as 
rod-shaped. The character of the distinction may be illus- 
trated by considering the somewhat analogous case of aerial 
vibrations within a cavity having the shape of the conductor. 
If the section be uniform, the wave-length of the longitudinal 
aerial vibration is exactly twice the length; but if an ellip- 
soidal cavity of the same length be substituted, then, however 
narrow it may be, the wave-length will be diminished in a 
finite ratio on account of the expansion of the section towards 
the central parts§. This example may suffice to show-that 
no general extension can be made from the. ellipsoidal to the 
cylindrical shape, however attenuated the section may be. - 
.. When we ask whether the extension is justifiable in the 
present case, we shall find, I think, that the answer is in the 
affirmative so far as the first approximation is concerned, but 
in the negative for the second approximation. 
Let us commence with the consideration of the known 
solution for an infinite conducting cylinder of radius 7 
* Communicated by the Author. 
+ Phil. Mag. vii. p. 635 (1904). 
Tt Wied. Ann. Ixvi. p. 485 (1898). - - 
§ See ‘ Theory of Sound,’ § 265. 
where - 
