That, as precedents for the construction of a successful flying machine, the investigation of some species of birds as a base of the principles of all is correct only in connection with the species and habits of the bird; that the general mechanical principles of flight applicable to the operation of the same unit of wing in all species are alone applicable to the flying machine.

That these principles of operation do not demand the principles of construction of the bird.

That as the wing is in its stroke an arc of a screw propeller’s operation, and in its angle a screw propeller blade, its animal operation compels its reciprocation instead of rotation.

That the swifter the wing beat, the more efficient its effect per unit of surface, the greater the load carried, and the swifter the flight.

That the screw action being, in full flight, that of a screw propeller whose axis of rotation forms a slight angle with the vertical, the distance of flight per virtual “revolution” of “screw” wing far exceeds the pitch distance of said “screw.”

That consequently a bird’s flight answers to an iceboat close hauled; the wing force answering to the wind, the wing angle to the sail, the bird’s weight to the leeway fulcrum of the ice, and the passage across direction of the wing flop to the fresh moving “inertia” of the wind, both yielding a maximum of force to bird or iceboat.

That the speed of reciprocation of a fly’s wing being equivalent to a screw rotation of 9,000 per minute, proves that a screw may be run at this speed without losing efficiency by centrifugal vacuum.

That as the object of wing or screw is to mount upon the inertia of the particles of a mobile fluid, and as the rotation of steamship propellers in water—­a fluid of many times the inertia of air—­is already in excess of the highest speed heretofore tried in the propellers of moderately successful flying machines, it is plain that the speed employed in water must be many times exceeded in air.

That with a sufficient speed of rotation, the supporting power of the inertia of air must equal that of water.

That as mere speed of rotation of propeller shaft, minus blades, must absorb but a small proportion of power of engine, the addition of blades will not cause more resistance than that actually encountered from inertia of air.

That this must be the measure of load lifted.

That without slip of screw, the actual power expended, will be little in excess of that required to support the machine in water, with a slower rotation of screw.

That in case the same power is expended in water or air, the only difference will lie in the sizes and speed of engines or screws.