THE TROCHOIDED PLANE. 71 
There is a distinction between the vertical lift we see when a 
bird hovers or rises straight up from the ground, as exemplified by 
skylarks, hawks, partridges, and the horizontal flight of ducks, 
pelicans, and albatrosses ; in the first case, the wing which is in 
effect a plane, is rotated in a cone, and kept normal to a trochoid 
during each revolution ; the connecting-rod is moved in a plane at 
right angles to the axis ‘of the cone, and the guides are horizontal ; 
the plane of the wing being in the line of the connecting-rod, and 
ma at right angles to it ; the path cut in the air by this motion is 
zigzag, one of the pieces between two angles being half a tro- 
choi d, the two half trochoids making up each revolution of the 
axis of the wing. 
In horizontal flight the conical movement is the same, but the 
connecting-rod is at right angles to the plane of the wings, and 
flight is the resultant of gravity, and the waves of air being thrust 
downwards and backwards by the wings. The part played by the 
plane of the body and tail in flight is the same as that of the 
second plane in Fig. II. : have not put the second plane in 
all the models of wings, as I think it useless before the power of 
the machine is sufficient to overcome its specific gravity. ig. 
and all subsequent models the second plane.) Peacocks’ 
tails, and the plumes of birds of -parhiline, are a hindrance to flight, 
d the effects of sexual selection. 
e same action takes place in the wing that I mentioned about 
the leech’s head, and is equivalent to sliding the plane along the 
connecting-rod towards the guide-pin, so that the centre of effort 
moves first in a circle, then in an ellipse, and finally in a straight 
line. I have shown the first and last movements in Fig. VII and 
Fig. III. 
These are the motions we often see when the passing breeze sets 
a blade of grass rotating ; it is common with flat leaves having 
thin stalks, and must have a observed by every one present. 
Fig. VII will show the geom 
These remarks refer to an wings, but, in addition, it is observ- 
able that jointed wings can be trochoided by opening and shutting 
the wing, the pep ema Fa working in a vertical plane trans- 
versal to the line 
A little ponsicerntton will show that turning, rising, and descend- 
ing, are merely resultants dependent on the position of the centre 
of gravity, and the direction the waves are thrown in; by depressing 
one side of the tail, and raising the other, a portion of the thrust 
is directed to one side; and in the construction of a flying-machine, 
it is an unnecessary waste of power to try to to lift the enormous 
rudders that are given such prominence to in many of the schemes 
we see depi icted. 
As to the soaring of birds, that branch of flight has been well 
argued lately in “ Vature,” and it is quite clear to me that the 
