MR. G. T. WALKER ON BOOMERANGS. 
25 
two components of angular velocity (denoted subsequently by Oj, fl^), whose axes lie 
in the plane of the boomerang, are determined. 
The flight may be regarded as a case of steady motion of which the circumstances 
gradually vary. It is only with very badly made instruments that small oscillations 
are at times perceptible; with ordinary boomerangs, the accident of grazing the 
ground or meeting a sudden puff of wind will not cause visible vibrations. 
Fig. 2. Plan. 
The scale of this and the following diagrams is 1 : 1000, or 28 yards to 1 inch, approximately. 
Fig. 3. 
Elevation upon a vertical plane through AC. 
Let the plane containing the arms of the boomerang (in future called the primary 
plane) be taken as that of XY, with the centre of gravity as the origin, and the pro¬ 
jection upon this plane of the resultant velocity as OX ; OZ is drawn on the more 
convex side. If then the rectangular components of linear and angular velocity of 
the body be U, 0, W, and n^, Hj, Og, it may be observed that W is always small 
compared with U, and Hg compared with fig. Throughout the motion is 
positive, Ilg negative, and fig positive. The time of flight is about nine seconds, and 
the greatest distance fifty yards ; the mean values of and may be estimated at 
one-sixth and minus one-third respectively, while in C.G.S. units U is two thousand 
and fig is thirty. 
The angular velocity 6^ of the axes is small and positive throughout the motion, 
except near the conclusion, when it sometimes vanishes and becomes negative. 
For theoretical purposes I have regarded the body as replaced by one of extremely 
thin material with the same general shape and twist; the transverse section will be 
a circular arc with its convex surface on the same side as the more rounded surface of 
the wooden weapon. 
Experiment shows that if a thin rectangular plate be advancing with velocity v in 
a direction that is inclined at a small angle a to its plane, the air-pressure produces a 
VOL. CXC.-A. 
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