as when it is, in effect, of screw form, or if the distribution of K is not uniform, the form of the curve is different. In the former case, for example, the curve does not approach the line of zero torque asymptotically as the instantaneous centre runs to infinity, and the form of the curve is otherwise modified.
It is manifest that, from the considerations stated, the problem is far too complex at present for complete mathematical solution, that is for the flight path to be plotted from given data, etc., though it would appear possible to effect some approximation if the conditions are restricted artificially to a sufficient degree. The author believes that under ordinary circumstances the
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Fig. 201. Fig. 202.
portion of the torque curve utilised is that in Fig. 200 in the region about and on the right-hand side of the maximum, so that the falling off of the velocity of translation, with that of rotation fully conserved, results on the whole in a diminution of the torque, and thus a reduction in the rate of precession, so that the flight path, instead of being a converging spiral, as would he the case on the basis of the gyroscopic pendulum, becomes of approximately circular form, so that the boomerang returns to its point of departure. This effect is probably helped by the fact that as the plane of rotation becomes more and more nearly horizontal the total pressure reaction becomes less and less, since the total pressure reaction may be computed by a simple resolution of forces.
412
