MR. G. T. WALKER ON BOOMERANGS. 
39 
small negative twist; examination of the equations will show that these distortions 
will combine to produce the required results. An estimate of the efficiency of the 
shape may be made from the fact that as far as my experience goes, a boomerang of 
this type may be thrown more than twice as far as a spherical object of the same 
weight. 
In figs. 6 , 7 are given the plan and elevation of the path obtained with a boomerang 
Fig. 6. 
I'jievation upon a vertical 
plane tlirougli AC. 
designed to continue in its circular route as long as possible. The arms of the imple¬ 
ment are at right angles, and the twist and rounding exaggerated a little ; the initial 
plane of rotation is vertical, and as much energy as possible is imparted in the act of 
throwing, while the aim is slightly uphill. 
The numerical value of is somewhat increased and that of diminished, so that 
when the w'eapon in its return journey is over the thrower’s head, its axis of rotation, 
instead of being vertical, is inclined a little towards the inner side of the curve that 
it has described; the forward velocity, though reduced, being still unexpended, tbe 
original curve is continued, and the existence of fi., implies that the plane of rotation 
will tilt slightly upwards and the tendency to fall be overcome. 
After the end H of this second loop has been reached, the forward velocity has still 
further diminished, and gravity brings the boomerang, still spinning fast in a nearly 
horizontal plane, to the ground near the starting-point. I have obtained second loops, 
which were thirty yards in length when measured horizontally, while, if the point H 
be high enough in the air, a third loop will be described before tlie boomerang alights. 
In figs. 8, 9 is represented the flight of a boomerang, of which the arms form an 
angle which is larger by about thirty degrees than that of the previous case. The axis 
