In order to get a more precise idea of the character of the alteration introduced into these theoretical conditions by the variation of any of them, let us, still confining ourselves to the use of the whirling-table, suppose that the plane in question while possessing the same weight, shape, and angle of inclination, were to have its area increased, and to fix our ideas, we will suppose that it became 4 square feet instead of 1 as before. Then, from what has already been said, ‹V›, the velocity, must vary inversely as the square root of the area; that is, it must, under the given condition, become one-half of what it had been, for if ‹V› did not alter, the impelling force continuing the same, the plane would rise and its flight no longer be horizontal, unless the weight, now supposed to be constant, were itself increased so as to restore horizontality. I have repeated Table XIII under the condition that the area be quadrupled, while all the other conditions remain constant, except the soaring speed, which must vary. +--------+-----------+-----------------+----------------------+ | | Soaring | Work. | Weight. | | | speed +-----------------+----------------------+ | α |(feet per | Work expended | Weight of like | | | second) | per minute. | planes which | | | ‹V′›. |‹A› = 4 sq. ft. | 1 H.P. will drive | | | |‹W› = 500 gr. | through the air | | | |  = 1.1 lbs. | with velocity ‹V′›. | +--------+-----------+-----------------+----------------------+ | | | ‹Foot-pounds.› | ‹Pounds.› | | 45° | 18.4 | 1,217 | 30 | | 30 | 17.4 | 634 | 57 | | 15 | 18.4 | 312 | 116 | | 10 | 20.4 | 237 | 154 | | 5 | 24.9 | 148 | 244 | | 2 | 32.8 | 87 | 418 | +--------+-----------+-----------------+----------------------+ ‹W› is the weight of the single plane; ‹A› is the area; ‹R› is the horizontal “drift.” ‹Wt› is the weight of like planes which 1 H. P. will drive at velocity ‹V›. Work is ‹RV›. I. If Work is constant, ‹R› varies as ∛‹A›. II. If ‹R› is constant, Work varies as 1/(∛‹A›). III. If ‹W› is constant while ‹A› varies, the weight which 1 H. P. will support varies as √‹A›.