720 Prof. A. S. Eve on Changes in Velocity in an 
The conditions being as in cases L, II., and V., 
Wl W A /ET, ,l A /T ,o n 
^=IP _ 2PV T tanh lVET • • ( } 
and the central bendino- moment 
and exr. 
>anding this 
M- Wl 
{'-SO- 
where I 
, _ 7T 2 EI 
or 
48EI 1 - 1 
y-ssKar+-^>.<w 
120V P, 
7T" 
10 
(f>sj(f.y-*}- • <»> 
Here as in case V. for calculation o£ bending- stresses 
P 
method (b) is evidently a good approximation only when p- is 
small, i. e. when the bar is short or the lateral load great : 
P 1 
for p- = - the error is 3 per cent. 
Other cases with the same simple loadings as the above 
naturally suggest themselves, such for instance as those in 
which clamps fixing the ends at any assigned inclination to 
the axis of ^increase or decrease the flexure due to the lateral 
and axial loads, and those in which the longitudinal loads not 
passing through the centres of area of the ends of the strut 
or tie-rod may increase or decrease by their eccentricity the 
deflexion and bending moment resulting from the lateral 
loads. 
LXV. 7 he Changes in Velocity, in an Electric Field, of the 
a, /3 and Secondary JRays from Radioactive Substances. By 
A. S. Eve, M.A., Assistant Professor of Mathematics, and 
Lecturer in Radioactivity, McGill University, Montreal*. 
IN a paper on Secondary Radiation communicated to this 
Magazine in December 1904, it was stated by me that 
the secondary rays from substances, due to the /3 and 7 rays 
of radium, were homogeneous in character, and on that 
* Communicated bv the Author. 
