piece of thin, stiff card-board and cut a cross out of it; a slight obliquity is then imparted to the arms or planes, and a piece of wood is cemented through the centre to act as a vertical axis; if, then, rotation be imparted to it by the finger and thumb, it readily rises to the ceiling of the room. Varying the experiments as regards shape, etc., it is found advantageous to construct the planes broader towards the circumference; secondly, to bend the broad ends or tips somewhat downwards; and, thirdly, to impart a slight screw-form to the vanes in imitation of that possessed by a feather.

The boomerang, used as a missile by the Australian natives, affords an example how a horizontal force can be transformed into a lifting force. The wheel, here exhibited, has been devised with the idea of securing the planes in their true position, especially towards the tips, and of discarding all dead weight in those parts near the centre of the wheel where the motion of rotation is too slow to assist in elevating it. To effect these, I have constructed a horizontal wheel in which the circumference is, as it were, the basis or skeleton, and the radii act by tension so as to retain a light vertical axis in the centre. In this manner a surprisingly large, strong, and light wheel is obtained, the necessary weight of the circumference being utilized, as will afterwards be explained.

Two systems of radii are attached to the circumference of the wheel, each system containing eight pairs of tension strings; the tension of all these radii can be thus increased simultaneously by simply widening the systems on the axis.

By an inspection of the model, it will be seen that narrow pieces of tracing-cloth are attached between each pair of the tension strings; the anterior edge of each plane is attached to the upper side of the circumference, and the posterior edge to the lower side of it. The thickness of the rim thus gives the degree of obliquity of the planes, namely, 5° at the tips, while the planes are nearly horizontal near the axis. By this arrangement the resistance of the air to the motion of the radii is utilized in buoying up the wheel; and as the axis can be turned directly by a crank, the necessary speed of the circumference can be obtained by simply making the wheel large enough, thus dispensing with the friction which would arise if multiplying wheels were used—size of the wheel forming no theoretical objection in the limitless expanse. The waste of power by resistance and friction can be thus reduced to a minimum.

Though there must be great difficulty in observing the shape and position which the individual feathers and wings of birds assume while in actual flight, yet it is easy to fix them in a current of air and so watch the effect. In this way it will be seen that the posterior and thin edge of the feather yields more than the other parts in flight, especially towards the tips. The

tip end is also raised, so that the feather becomes less curved longitudinally, and assumes the figure of a thin and slightly bent knife, with the concave side downwards, the screw of the feather unwinding as it were.

If the feathers and wings of birds were straight when quiescent, and if every transverse section were inclined to the same angle—if, for instance, they were planes when not in action—then, when they came to be acted on by the air, they would, unless perfectly rigid, lose that proper figure essential to buoyancy, for the tips would twist more than the other parts, and the longitudinal section would become convex downwards. Perfect rigidity of a plane would necessitate too much weight.

We therefore see them formed with a twist or screw in the reverse direction to that in which the air itself twists them when in action. Then, when they come into action, they assume of themselves the proper and best figure, so that every part can act at nearly the same angle upon the air.

The action of the air itself confers the requisite rigidity, and the greater the speed or pressure, so much greater is the rigidity; the wing then assumes a knife-like figure approaching to a plane but slightly concave downwards.

This appears to be the figure of the wings of birds while sailing and wheeling, for when they are viewed when the eye is in the same plane as the wing they appear as shown in fig. 3, in which the wings are represented as mere lines. It will be noticed in the case of this wheel that this is also the figure which the tensile radii assume when in action.

The method here adopted allows of the very important advantage of using extremely thin anterior edges for the planes, whereby the air is cut, so to speak, for the nearer they approach to a mathematical line the better, as the resistance to the horizontal motion of the radii is surprisingly lessened.

When these planes are revolved with the same velocity as the wind, it is clear that even in a gale the wind cannot give any pressure against them except on the under and elevating sides.

Sailing birds first acquire a great initial velocity generally by flapping their wings. Naturalists and observers differ as to the direction of the vibratory motion of the wing in this kind of flight, probably on account of different birds being selected as examples, and omitting in some cases to mention whether the forward motion of the bird itself is included in the asserted direction of the stroke. For instance, a bird fastened by a string, or one which may be rising vertically, or, better still, a hovering bird, which we will assume to strike vertically downwards with its wings, would not really when in transit move them vertically downwards, although the stroke or attempt might be so; for the downward stroke compounds with the horizontal motion of the bird producing a forward and downwards or