322 Prof. J. J. Thomson, On the Transmission of — [Jan. 28, 
2 
k? = m* — = : 
Arr wr 
=m? pee ; 
o 
where o is the specific resistance of the wire, « its magnetic 
permeability, then 
Re cp pn 1 J,(ina)* 
=o : Ae aglow cee Segoe i); 
V* m* —n? a” JS, (ina) ©) 
where c is the electrostatic measure of the capacity of unit length 
of the wire, V the velocity of propagation of electro dynamic action, 
and J,(x) denotes the Bessel’s function of zero order which is 
not infinite when 2 = 0. 
In deducing the above equation Maxwell’s theory of electric 
action has been assumed. We must consider different cases of 
equation (1) corresponding to different values of na and c. 
Case I. na exceedingly small. Here 
J,(ina)=1, J, (ina) =— dina, 
so that equation (1) becomes 
yee — Pee 
: 27a‘ pv’ 
ei (aoe 
or Mm" = 5s : reer eae ee (2). 
From the following table we see that this formula will be 
approximately true whenever 47upa*/o is less than 5, as it only 
involves the assumption that inaJ,(ina)/J, (ina) is approximately 
equal to 2. Unless p is of the order 10” we may put 
nt 4qr wap 
Oo 
Value of 4urpa*/a | Value of anaJ,(ina)/J,(ina) 
1 2(1-5), 
bo 
bo 
Cn 
= 
| 
Ep! > 
a 
Swen One 
OW =e es 
‘ 2(z 3%). 
* The factor « is omitted in the paper quoted. 
