366 A STUDY OF THE BOOMERANG. 



These two planes have to form a small angle between then 1 , and I 

 found that the way of effectively throwing the instrument and the 

 manner of throwing it depend mostly on the size of this angle of 

 inclination, which may vary from zero to three degrees, although the 

 number 3 is not the utmost limit for successful throwing. The greater 

 the angle between these limits, the less inclined toward the horizon the 

 initial plane of rotation must be, all other points being the same. In- 

 stead of a plane, one side of each wing may form a curved surface little 

 deviating from a plane, without the quality of the instrument being 

 impaired. For brevity's sake, the joined planes of the two wings may 

 be termed the plane side or lower side of the boomerang; it is the side 

 facing the ground during the flight. The opposite surface of the 

 boomerang may be termed the rounded or upper side. The surface 

 form of this side seems to be quite arbitrary; however, a good form 

 and perhaps the best one is such that the instrument, placed with this 

 (upper) side on a plane table, tits the table exactly either by a plane 

 surface or by a. plane curve. In practice an approximation to this de- 

 mand is sufficient; also a moderate upward curving of both wings will 

 answer. 



The tapering of the wings from the middle of the instrument toward 

 the ends may be very slight both in regard to thickness and breadth j 

 for example, if the instrument is three-eighths of an inch thick in the 

 middle, it may be two-eighths of an inch at the ends, and if 2i inches 

 broad in the middle, it may have If inches at the ends. 



It may not be out of place here to mention a curious instance trans- 

 mitted from antiquity. The old Grecian geographer, Strabo (book iv, 

 chapter iv, 3), says : 



The Gauls use a piece of wood reseuibliug a pilum, which they hurl not out of a 

 thong, but from their hand, and to a farther distance than an arrow. They princi- 

 pally make use of it in shooting birds. 



APPROXIMATE THEORY OF ITS FLIGHT. 



As to the mechanical theory of the flight of the boomerang I can say 

 but little. Firstly, the rotation of the instrument about its free axis 

 through the center of gravity is the fundamental condition of success. 

 The faster the rotation, the longer the boomerang floats in the air. 



Secondly, the nutation of the axis of rotation has to be considered. 

 This nutation decreases with the angle of inclination of the two wings 

 of the boomerang and increases with the increase of the said angle. 

 In the case of a small angle, the plane of rotation keeps parallel to the 

 initial position of this plane, or very nearly so. If the two wings form 

 one plane with their lower sides (this angle being zero), the instrument 

 has no perceptible nutation, and must be thrown perpendicularly to the 

 vertical plane passing through the hand. The instrument then rises 

 and returns nearly in the same plane that it went up. This throw is 

 rather difficult. In the second case, the angle of inclination of the two 



