:\rf^ G. T. WALKER ON BOOMERANGS. 
^58 
in wliicli, owing to the experimental difficulties, the numerical values of the coeffi¬ 
cients ma}' be regarded as lacking in accuracy ; they may lioweAmr he relied upon as, 
at any rate, of the correct order of magnitude. Of iv I have observed nothing except 
that it does not exceed 500, and is probably smaller and negative. 
A comparison of the theoretical results (3) and (4), or (6) and (7), obtained with 
different data for kU will show that the forrnulce, as calculated, must be looked upon 
as giving only a rough estimate of the motion regarded quantitatively ; but, in spite 
of the calculated value of w being excessive (between 600 and 1200 when cos 6 = |), 
it will be seen that the discrepancies are of the kind that might be anticipated, and 
that the theoretical equations are qualitatively consistent with the experimental 
results given in (8). 
Another piece of evidence is that furnished by non returning boomerangs. If it 
be desired to make an efficient missile that shall travel in as straight a path as 
possible, it is natural to manufacture a boomerang without twist and with the 
curvature of the two faces the same. It is this form that many of the cruder 
Australian weapons possess. 
Experiment and theory alike show, however, that if initially 9 have a positive 
value less than a right angle {t.e., the natural method of throwing be adopted), then 
will be positive and Og will be negative as long as 6 is less than a rio-ht angle: 
when the jdane of rotation has reached and passed through the horizontal joosition 
Dj remains negative. The shape of the path is indicated in fig. 5 , and it will be seen 
that it is far from straio-ht. 
o 
Fig. 5. 
A path in one vertical plane could be secured by throwing an undistorted weapon 
^vifh its plane of rotation accurately vertical; the least inclination, however, would 
grow, and the plane of initial motion be departed from ; in any case, except for the 
reduction in the resistance of the air, the path in a vertical plane would yield no 
greater range than would be afforded by a spherical missile of the same w’eight. 
We might attain the same end by designing the shape so as to make H,, Ho small 
when 9 0 , and throwing the boomerang with its plane approximately horizontal. 
In that case the plane would remain horizontal, and the axis OX in it would soon be 
pointing in a direction slightly above the tangent to the path ; a much longer flight 
would then be maintained, as the effect of gravity would be balanced by the upward 
pressure of the air on the lower surface of the projectile. 
It is interesting to notice that this is the method that experience has taught the 
blacks to adopt. Iheir best non-returning weapons always have strongly developed 
positive rounding (the more curved surface is uppermost when thrown) and often a 
