Lonization Curves of Radium. 737 
idea of the moving wire. The point P moves about an 
Instantaneous centre at the intersection of the normals at B 
and A: approximately, therefore, about the centre of cur- 
vature of the wire at the point C. ‘Thus the curvature of the 
locus PQR at the point P is therefore the curvature of the 
path of the ray at the point OC, not at P. Hence if the locus 
is given, it is possible to calculate the curvature at different 
distances from the end of the path of a ray, which, it must 
be remembered, is the same for all a rays. Becquerel cal- 
culates the radii of the circles through PBA, QBA, RBA, 
and so on; but this is not exactly what we now require. 
He gives, however, a table of most 
careful measurements of the various 
points on the trace: and it is there- 
fore possible to make an approximate 
calculation of the curvature at various 
points of the path. 
Let PAB, P/AB be two different 
paths. let p be the radius of cur- 
vature at C, a point midway between 
Aand B. Let s be the distance of 
C from P, and w the angle made 
with the tangent at any fixed point 
on the moving wire with the ver- 
ical AB. Let PM=y, AM=z. 
Then approximately P’N=CP’. dy, 
and See Ns tO 
OF ae py LP =3e 
Becquerel states the following results * :— 
Values of y. Corresponding Values of 2z. 
oa "00719 
2 ‘01489 
oh "02293 
“4. ‘03160. 
“o "04028 
'b "04973 
Hs "05928 
OF. id: PES ue aT ebe 
if ‘ Urere ol Oo So4 
And AB=2 cms. 
Hence when s=1'1, d2=:0036.cm., and 6y="1 cm. 
Thus p=1°1 x °1+°0036=30 cms. approximately. 
* Comptes Rendus, cxxxvi. p. 1519 (1908). 
