ON ELECTRIC CONDUCTIVITY. 415 
as components along these lines, when the twist is applied, which being now 
different in amount give a component =ce in a direction perpendicular to the 
axis and bisecting the angle between them, e denoting a coefficient depending 
eur the stram, “Thos the eftect is that‘of a set of %*@ 2 * , 9% 
stream lines parallel to the axis, and a true solenoid e 
superimposed upon them (see Trans. Roy. Soc., 1879, ae 
Part I. p. 74). 
Let us now define the constant connecting the con- : 
ductivity with the strain. Consider a cube of the ° Fi, 2. 
conducting material, whose conductivity, uniform in all directions, is %, and 
let it be distorted to the amount indicated by the dotted lines (fig. 2), then 
we shall have 
k(1+ac) and k(1—ac) 
as expressions for the conductivity in the strained material in the directions 
ad and cb’, o denoting a constant and a the amount of distortion, represented 
by the angle aca’. In the case of a tube, twisted at the rate per length L, 
the distortion in a cylindrical layer, radius p, is re , and therefore the quantity 
denoted above by ¢ is equal to ce : 
Now, the magnetic force exerted by a solenoid of length L and radius p, 
carrying a current =co ie dp per unit length, on a point in the middle of its 
AXIS 1S 
_ 2ncagpdp 
ad p+(s) 
Denoting by dp the thickness of the layer, we find for the action of the tube 
F=2nc0¢ { Jri+($) -Je+($) } 
R, and R, being its inner and outer radius ; or introducing the strength of the 
current 7=c7(R;— Ri), 
1 2 1G, 2 
ive) VE) t 
= oe opt. 
Denote by D, the distance from the magnet at which the circle C must be 
placed in order to compensate the magnetic force Mz, exerted by the circle § 
(and possibly also by other unmovable parts of the apparatus) before twisting ; 
by D, the corresponding distance, when the weights are put on; and by 
