62 Mr. J. W. Sharpe : 



downward flight the C.G. will again recover much of its former 

 speed. When it is approaching the summit of its path, at 

 its greatest elongation from the point of projection, its speed 

 is attaining a minimum ; and therefore, in this portion of 

 the path, the orientation of the principal plane has its maximum 

 rate of change per unit of distance traversed by the CG: 

 consequently at this period the steering effect is much more 

 marked than at any other. From this description of the 

 circumstances of the boomerang's flight, it is clear that the 

 reaction of the air sets up a precessional motion of the axis, 

 like that imparted to the Earth's polar axis by the attractions 

 of the Sun and Moon upon the equatorial protuberance, the 

 orientation of the axis being altered by a very small angle, 

 always in the same sense, in each revolution of the body. 



If a thin piece of slate be thrown into still water, its motion 

 underneath the surface will give a good illustration of the 

 boomerang's motion in air, the slate steering itself through 

 the water in the same way as the boomerang steers itself 

 through the air. 



To explain more particularly the action of the air : — 

 Consider the boomerang just after it has started. It is 

 whirling with great rapidity in a nearly vertical plane, the 

 axis of the whirl being coincident with the maximum 

 principal axis of inertia at the C.G., i. e. with the axis of the 

 instrument ; and this axis points leftward, and is very nearly 

 horizontal. Take the motion at an instant when the line 

 joining the horns is vertical, and the convex edge is facing 

 forwards. The upper horn, owing to the twist, has its 

 forward surface slightly turned against the air ; this surface 

 is slightly convex, and the other surface, the hinder one, is 

 still more convex. The result of this is to cause the com- 

 ponents, in the principal plane, of the air pressures upon the 

 forward face of the upper horn to be a maximum towards 

 the convex edge, as indeed would be the case even if both 

 surfaces were flat, according to the law of the reaction of a 

 fluid upon a plane moving through it, whereby the plane 

 tends to set itself at right angles to its course, i. e. to the 

 path of its centre of inertia. Now resolving the air pressures 

 in three directions, parallel respectively to the principal axes 

 at the C.G-., it will be seen that those components which are 

 at right angles to the line joining the horns tend to twist the 

 upper horn backwards, that is they impart a very small 

 angular momentum about that principal axis which is parallel 

 to the line of the horns, and the axis of this angular momentum 

 is directed upwards and outwards from the centre of the 

 boomerang ; and that the action upon the lower horn opposes 



