346 Proceedings of the Royal Society 
because the pinion should be free to move in an upward, downward, 
forward, and backward direction. It should also be able to rotate 
around its anterior margin to the extent of nearly a quarter of a 
turn. All the movements referred to are derived in the author’s 
models from a direct piston action , from the reaction of the air, the 
elasticity of the wings and springs, and the weight of the machine 
bearing the wings. They are restrained and directed by the 
gearing apparatus extending between the piston and the wings, but 
more especially by the different lengths, strengths, and directions 
of the elastic springs themselves. The piston is made to descend 
with a very violent hammer-like motion at the beginning of the 
down stroke, the movement being gradually slowed as the wing 
descends to a certain point, at which the movement is re¬ 
versed and the piston ascends more slowly, its ascent being 
occasioned for the most part by the reaction of the air, the elas¬ 
ticity of the wing and of the springs at its root, and by the descent 
of the engine propelling the wings. The driving power, the 
weight of the apparatus, the recoil of the air, and the elasticity of 
the wings and springs are thus made to act in concert, the different 
forces being active and passive at intervals, and no two forces 
acting together at precisely the same instant of time. 
If a longitudinal section of a bamboo cane, 10 feet in length and 
half-an-inch in breadth, be taken by the extremity and made to 
vibrate, it will be found that a wavy serpentine motion is produced 
in it, the waves being greatest when the vibration is slow, and 
least when it is rapid. It will further be found that, at the 
extremity of the section where the impulse is communicated, 
there is a steady reciprocating movement devoid of dead points. 
The continuous movement in question is no doubt due to the fact 
that the different portions of the reed reverse at different periods, 
the undulations induced in the reed being to an interrupted or 
vibratory movement very much what the continued play of a fly¬ 
wheel is to a rotatory motion. 
If a similar reed has added to it at its outer or distal half 
tapering rods of whalebone radiating in an outward and backward 
direction to the extent of a foot or so, and the whalebone and the 
reed be covered with a thin sheet of india-rubber, an artificial wing 
resembling the natural one in all its essential properties is at once 
