Such a remark by one of the ablest mathematiciaus of his time was not forgotten. On the contrary, it was remembered on the next occasion when I had opportunities of studying the flight of bomerengs thrown by the hands of Australian Aborigines, and then I perceived that in its rotary motion through the air, a hollow centre of greater or less diameter, but usually of about one-third of the disc, was described by the whirl of the bomereng, and it occurred to me that the centre of the whirling motion might be found in a line of equilibrium which should divide the surface acting on the air into three portions, in such manner as that the eccentric portions should equal the central one.[1]
The discovery of this centre, insignificant as it may appear, was still something new, for on attaching a centre to a bomereng, it was possible to show that this centre was not only during its rotary motion the centre of that motion, but also the centre of gravity when in a state of rest, while it was apart from and quite clear of every part of it.
The natives when bent on exhibiting the more curious flights, twist the bomereng, by placing it at the fire, evidently for the purpose of giving it the property of spiral movement, thus showing how well they understand the screw-action upon the air. On making a small wooden model with a spiral turn like a screw, and giving it by means of an attached centre, and the fork and cord of a humming-top, rapid rotary motion, the model ascended to the roof of the room with such force as to be broken in pieces against it. . . . .
The inner edge of the bomereng is found to form a cycloid. . . . The outer edge consists of two parabolic curves whose foci appear to overlap, so as to be both in the axis of motion. These curves are presented by a section of the half-bomereng, when at an angle of 45° with the axis."
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When these facts and Sir Thomas Mitchell's theory were promulgated, it was pointed out that the principle had been applied long before by Mr. R. Hodgson, who claimed to be the discoverer of the parabolic-propeller, and whose experiments, it was affirmed at the time, were successful. Mr. Hodgson's blades were each sections of a parabola, and attached to the shaft in positions coincident with the plane of a right cone placed longitudinally with the apex foremost. Mr. Hodgson's theory was that blades of a parabolic form, fixed at the angle chosen, would take a better grasp of the water, and have, therefore, a greater propulsive force than any other; and that, from the property peculiar to the parabola, that all rays of light coming parallel to its axis are reflected into its focus, so also all water thrown off from a blade of parabolic form must diverge from it in the direction of the focal point, and that consequently a propeller with parabolic blades must allow the water to escape from it much more readily than any other.
The discussions which arose in consequence of Sir Thomas Mitchell's application of the principle involved in the flight of the Wonguim is not without interest, and the reader may refer with profit to the Mechanics' Magazine, from which I have extracted the above notes.—See vol. XLI., pp. 238, 256, 268; vol. XLII., p. 234; vol. XLIX., p. 130; and vol. XLIX., p. 547; years 1844-5 and 1848.
from an expedition into the interior of Australia, Sir Thomas Mitchell exhibited some of the native weapons in this country, among others was the boomerang. The flight of this singular weapon through the air, to use the words of Mr. Bailey, then Vice-President of the Royal Society, "was enough to puzzle a mathematician." One curious point about it was its resemblance to a weapon used by the ancient Egyptians for killing wild-ducks, as this pastime is found represented on the walls of a tomb at Thebes. Interest in the weapon thus excited, Sir Thomas tried a number of experiments with it, the ultimate result of which is the invention of the boomerang-propeller. Into the question of relative merits as between the screw, the boomerang, and the paddle-wheel, we shall not enter. The friends of each are, of course, confident of the superior virtues of their power, and intolerant of any other. Sir Thomas Mitchell's discourse is in part controversial, being a reply to certain strictures by Capt. R. Fitzroy.'"
