hemisphere in plane and in spherical presentation. This is probably due to the fact that this problem forms the basis of prop, xxxiv., Book II., of the “Principia” as touching the Newtonian Medium. It was evidently the aim of the early workers to ascertain the extent to which Newton's results would prove applicable to a real fluid.
In the case in question it was found by Hutton that—
(1) The pressure on the hemisphere in either presentation varies, according to the Newtonian law, that is as the square of the velocity; and,
(2) The resistance in plane presentation is approximately two-and-a half times as great as in spherical presentation, instead of only twice as great as demonstrated by Newton. This result was subsequently confirmed by Vince, whose relative figures were 1 to 2.46.
These results were considered at the time as a substantial confirmation of prop, xxxiv., or, rather, as showing that the behaviour of a real fluid does not greatly differ from that of the discontinuous medium; probably we have here the reason why many subsequent writers have been misled into assuming the applicability of the Newtonian sine2 law in the case of the inclined aeroplane. In point of fact the coincidence, had it been far more complete, would be of no significance whatever; the system of flow in actuality bears no resemblance to the dynamic system of Newton.
The fallacy of the sine^ law was first clearly demonstrated by Vince in his paper (to which reference has already been made); he gives experimental data showing that the resistance in the line of flight varies, for small angles, as sine1.73 of the angle; this, if we neglect the influence of skin-friction, corresponds to a pressure normal to the plane varying as the sine.73. The fact that the index here is less than unity can be reasonably accounted for on the assumption that part of the resistance is due to skin-friction, which is roughly constant in respect of the inclination.
