Having ascertained this point, had our tables of angular resistance been complete, the size of the surface necessary for any given weight would easily have been determined. Theory, which gives the resistance of a surface opposed to the same current in different angles, to be as the squares of the sine of the angle of incidence, is of no use in this case; as it appears, from the experiments of the French Academy, that in acute angles, the resistance varies much more nearly to the direct ratio of the sines, than as the squares of the sines of the angles of incidence. The flight of birds will prove to an attentive observer, that, with a concave wing apparently parallel to the horizontal path of the bird, the same support, and of course resistance, is obtained. And hence it appears that, under extremely acute angles with concave surfaces, the resistance is nearly similar in them all. Six degrees was the most acute angle, the resistance of which was determined by the valuable experiments of the French Academy; and it gave 4/10 of the resistance, which the same surface would have received from the same current when perpendicular to itself. Hence then a superficial foot, forming an angle of six degrees with the horizon, would, if carried forward horizontally (as a bird in the act of skimming) with a velocity of 23·6 feet per second, receive a pressure of 4/10 of a pound perpendicular to itself. And if we allow the resistance to increase as the square of the velocity, at 27·3 feet per second it would receive a pressure of one pound. The flight of the _corvus frugilegus_, or rook, during any part of which it can skim at pleasure, is (from an average of many observations) about 34·5 feet per second. The concavity of the wing may account for the greater resistance here received, than the experiments upon plain surfaces would indicate. The angle made use of in the crow's wing is much more acute than six degrees: but in the observations that will be grounded upon these data, it may safely be stated that every foot of such curved surface, as will be used in aërial navigation, will receive a resistance of one pound, perpendicular to itself, when carried through the air in an angle of six degrees with the line of its path, at a velocity of about 34 or 35 feet per second.