28 
MB. G. T. WALKER. ON BOOMERANGS. 
mxv — nv, mi — hv, Iv — w,u, 
each divided by a quantity differing from q by squares of small quantities. Hence, 
if jx = S, V = 2, the normal force at any point will be 
{lu mv -{- w), 
and the component couples 
— Ki'ylu -|- mv + ?e), ku{Iu -j- mv + w), 0, 
where squares of small quantities are omitted. 
Now if, due to the “ rounding,” a transverse line Rid' (fig. 4) through any point P 
be a circular arc of radius p, and if its middle point Q have co-ordinates x, y, then, 
denoting QP as measured along the inward normal QN by s, the direction cosines of 
the normal at 
X + s cos <^, y — s sin (j) 
will be 
S cos (p 
■ > 
p 
s sin (j) 
5 
P 
1 . 
In addition to this the line RR' will, owing to the twisting, be turned about the 
y 
tangent at Q through an angle which may be taken as —, where t is a constant 
length. The superposition of this small distortion on the former will add to the 
direction cosines terms 
y cos 0 y sin 0 
- j — - ? 0, 
r T 
Let the linear and anguhtr velocities of the body referred to the axes 1, 2, 3 be 
U, V, W, Wj, Wg, Wg, 
where w is small compared with and Wj, w.j compared with cjg. The com¬ 
ponent velocities iq, iq, of P will then be 
u — [y — s sin Wg, 
v + { a: -p s cos if)) ojg, 
iv — (a: -f- 5 cos wg -j- (y — s sin (f>) o)^. 
The resultant force due to the pressures will have negligible components parallel 
to the axes 1, 2, and the force Z along the third axis is the integral over the 
surface of 
