BOOMERANGS. 



517 



given. The direction of the axis of rotation is indicated by <>;i\ itig the 

 projections of a line of constant length measured along it. The scale 

 of these diagrams is about 1 :1000.) 

 The angular velocity (1) is in- 

 creased by an increase of twist and by 

 an increase of rounding; it also in- 

 creases when cos 8 increases, where 8 

 is the inclination of the plane of rota- 

 tion to the horizontal. The curling to the left (2) is increased by an 

 increase of twist, or of cos 0, and, in general, by an increase of rounding. 



Fig. 5. — Elevation through C A. 



Fig. 6.— Plan. 



Fig. 7.— Elevation through (' E. 



Fig. 8.— Plan. 



If it be desired that the boomerang should describe a second circle 

 in front of the thrower (figs. 6, 7), it must be thrown much harder, so 



that when one circle has been described 

 it may still have sufficient forward 

 velocity. When the projectile has 

 described the first circle and is over 

 the thrower's head, the axis of rotation 

 must point in an upward direction in 

 front of him; if it pointed behind him 

 the subsequent path would be behind 

 his back, and a figure of S (figs. 8, '.') 

 would become possible. For a path 

 with a second loop in front of the 

 throw T er he should accordingly choose a boomerang with much twist 

 and much rounding, and throw it with his ho&y leaning over to the 

 left, so that the angle 8 

 between the axis of rota- 

 tion and the vertical may 

 be slightly in excess of a 

 right angle. The increased 

 twist will mean that the 

 first circle has a smaller 

 circumference and that 

 there will be more pace 

 left after it has been described, and the increased rounding will keep 

 the plane of rotation from becoming horizontal too soon. 



Fig. 9. — Elevation through C A G. 



