On the Boomerang. 63 



the action upon the upper one, and this too in all phases of 

 the rotation. But the components which are parallel to the 

 line of the horns tend to twist the upper horn over, so that 

 its convex edge, which is in the present position the forward 

 one, tends to turn slightly inwards towards the left ; and the 

 lower horn experiences a similar and similarly directed action. 

 This effect occurs chiefly just before and just after the line of 

 the horns is at right angles to the path of the C.G. The 

 bend in the boomerang is the chief factor in this effect ; but 

 the rounding, i. e. convexity, especially that of the " upper " 

 surface, materially assists it. Thus this action upon the two 

 horns imparts to the missile, in each revolution, a very small 

 angular momentum about that principal axis at the C.Gr. 

 which is at right angles to the line joining the horns, and the 

 axis of this momentum is directed backwards. 



Again, the components which are in the direction of the 

 boomerang's axis, and which, on account of the slightness of 

 the twist, are much larger than the others, set up, by their 

 action upon the upper horn, an angular momentum about the 

 same axis as the last set of components, i. e. directed back- 

 wards in the principal plane ; and therefore their effect con- 

 spires with that of the last set. In this case, however, the 

 lower horn opposes the upper one. Now the actual speed of 

 the upper horn is the speed of the C.G. plus that due to the 

 rotation about the C.G. ; whilst that of the lower one is the 

 difference of these two speeds, the speed due to the rotation 

 being far greater than that of the C.G. Consequently in 

 each revolution the angular momentum imparted by the 1st 

 and 3rd sets of components of the air reactions are not the 

 sum, but the difference, of the momenta imparted to the two 

 horns, the upper horn, i. e. the one with the greater velocity, 

 prevailing in this respect over the lower one ; and the most 

 important phase of each rotation is that in which the line of 

 the horns is passing through the position in which it is at 

 right angles to the path of the C.G. When this line is 

 nearly parallel to the path, these differential effects hardly 

 exist at all. 



Combining all the above described results, it will be seen 

 that the axis of angular momentum (and with this the in- 

 stantaneous axis of rotation and the axis of the boomerang 

 itself are always either very closely, or exactly, coincident) 

 is in each revolution displaced through a very small angle 

 upwards to the right by the first set of components, and by 

 the other two sets is rotated backwards towards the thrower, 

 the latter effect being decidedly the larger of the two by 

 reason of the superiority of those components which are 



