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. That the _greater_ the speed, the _less_ weight of engine, boiler, and screw must be, and the stronger their construction. That, in consequence, solid metal worked down, instead of bolts and truss work, must be used. That as the bird wing is a screw in action, and acts _directly_ between the inertias of the load and the air, the position and operation of the screw, to the load, must imitate it.