The above refers only to slow motions, and the results given, from experiments with very small velocities; and it is to be expected, that with very rapid motions the form of the fore, as well as the hind part, of the projectile, will influence the amount of resistance in a much higher degree.
Form of hind part.
That form for the hind part will be best which has the greatest pressure upon it, when moving with a certain velocity.
Best shape for fore and hind part.
The ogivale form seems, from experiment, to fulfil the former condition. The best form for the hind part, for rapid motions, has not been determined; it may, however, be considered to be of much less importance than the shape of the fore part.
Form determined by extent of range.
Of course the best form can be determined by extent of range, but deductions from this will depend upon such a variety of circumstances, the effects of some of which must be entirely hypothetical, that the correctness of any formulæ obtained in this manner must be very uncertain.
Form suggested by Sir I. Newton.
Sir Isaac Newton, in his “Principia,” has given an indication of that form of body, which, in passing through a fluid, would experience less resistance than a solid body of equal magnitude of any other form. It is elongated.
Axis of elongated bodies must be fixed.