350 
LORD RAYLEIGH OR THE CONSTANT OE MAGNETIC 
consider the small anomalous differential effect upon the external magnet to be 
sufficiently explained by the observed difference of resistances. 
Correction for finite length. 
15. If the tube were infinitely long the difference of potentials at its ends due to 
the unit current in one winding would be 4 n. But on account of the finiteness of 
the length a correction is required, whose approximate amount is given in Gordon’s 
paper. 
Fig. 2. 
& 
L 
A 
B 
M 
Considering, in the first place, one layer of windings of radius A a, we know that the 
external effect is the same as would be produced by a uniform distribution of 
imaginary magnetic matter over the ends, positive (say) over A a and negative over 
Jib, the superficial density being equal to the number fin) of windings per unit length. 
The potential at L of the matter on A a is 
or approximately 
27 mi (La—LA), 
/A c? . Afd\ 
m \LA 5 LA 3 / 
TTin 
Similarly the potential at L for the matter on B b is 
7 Tin AB 
/Ac? 
j A« 4 \ 
—irm 
\LB 
Alb 3 /’ 
at L for 
this . 
layer of winding 
/ Aa? 
A« 4 LB 2 + LA.LB + LA 2 ' 
\LA.LB 
4 
LA 3 .LB 3 
in which ?nAB denotes the whole number of windings in the layer. This result has 
now to be integrated so as to represent the effect of the helix, whose inner and outer 
radii we may call Acq and Aa 2 . The mean value of Aa 2 is 
Ad, 3 - A«j 3 
3(Aa 2 —Atq)’ 
A a 2 5 — Aafi 
5(Aa 2 —Acq)' 
and that of A a 4, is 
