On the Boomerang . 65 



of which is always greater than that of the other one, o wing- 

 to its velocity being the sum of the velocity of the C.G. and 

 of that due to the rotation. 



The motion of a cardboard model follows exactly the same 

 principles ; but, on account of the flatness of the surfaces 

 and the absence of twist, the precessional motion has to be 

 brought about in a different manner. The shape is not con- 

 fined to any particular pattern. In fact the following is a 

 most convenient form, yielding curious and complicated 

 flights. It can be cut out from a visiting-card. The head, 



which ought to be comparatively large, consists merely of a 

 narrow rim about a large hole ; and a long arm is attached 

 to it. This arrangement secures a considerable moment of 

 inertia about the axis without making the weight too great. 

 If supported with its plane sloping upwards, and struck 

 sharply and fairly at the end of the arm so that its edge cuts 

 the air truly, it will rise in front of the thrower without 

 turning either right or left, come to rest, sail whirling, at 

 the summit of its path, and return to the point of projection. 

 But if the line of the projecting blow be very slightly in- 

 clined towards the plane of the model, the precessional motion 

 will be obtained. 



To explain the precessional motion, take a model of the 

 ordinary boomerang form. This is projected with its plane 

 nearly horizontal, and inclined slightly upwards ; and it is 

 so struck that the initial axis of angular momentum is not 

 exactly coincident with the axis of the model, i. e. with the 

 normal to its plane through the C.G. The consequence 

 is that throughout the motion these two axes, as well as 

 the instantaneous axis of rotation, are never quite coincident, 

 but always very nearly so. In each revolution the axis of 

 angular momentum receives only a very small displacement, 

 whilst the other two circle once round it, the plane of the 

 model alwajs touching the surface of a right circular cone of 

 very flat angle, whose axis is coincident with the axis of 

 angular momentum, and is directed upwards. There is now 

 no screwing effect, like that of the propeller of a screw- 

 steamer ; nor is there any assistance to the precessional 



Phil. Mag. S. 6. Vol. 10." No. 55. July 1905. F 



