IMPROVEMENTS IN PADDLE WHEELS OF STEAM VESSELS
Year: 1854

page_text: the 2106.)
PROVISIONAL SPECIFICATION left by Pierre (Peter) Fougerat at the
Office of the Commissioners of Patents, with his Petition, on the 27th
February 1854.
I, PIERRE (PETER) FOUGERAT, do hereby declare the nature of the said
Invention for "IMPROVEMENTS IN PADDLE WHEELS OF STEAM VESSELS" to be as
follows:-
J
b'
The mathematical principle from which the improvements of my Invention
are derived is founded on the following deduc-
tions-Let o be the circle or outer periphery
of the paddle wheel, and a plus, or added to
ya, equal to the square of the radius R. Then,
in order that the parallelism of a, b, be kept
throughout the revolution of a round the
periphery of the paddle, let a¹ and y" be the
co-ordinates of the point b, in 'relation to
the same axles as the given circles, then will
a, b, equal a, x equal x, added to a and y¹. By substituting the valves of
x and y in these two equations, the result becomes (-a)² xy²=radius ²;

page_text: consequently, the circle o' has a similar radius as that of the first circle, but
its centre is removed further along the positive axis of a at the distance a.
From the above, it follows that the four centres o¹, o, o¹¹, and ov, may be
obtained by placing the right angle parallel to the axle of the a, in the posi-
tions a, b, a, b, and the same for the axle of the y, &c.
In the case of only one of these circles, o' for instance, as regards the given
circle o, and let us suppose, firstly, their centres fixed; secondly, that the
circumferences become rigid, invariable bodies, having no other property than
that of turning around their centre in their plane, of which the positions should
also be supposed invariable; thirdly, that the right angle a, b, is fixed in
cushions by its extremities a and b to the two circles, and in any position what-
ever a, b, but which ought to be in any case the one of those which it occupied
when it described the circle o¹.
Assuming that the two circumferences turn round their respective centres
with the same angular momentum, and in the same direction, the right
angle a, b, will retain, when in motion, its primitive length, and its
parallelism to itself or to the axle of the x, whch it was parallel to at
starting. If then it be supposed the right angle a, b, constantly horizontal,
which would only require that the centres o and o' should be on one and the
same horizontal line, and at a distance o, o'-a, we see that every rigid
surface c, a, d, perpendicularly fixed to a, b, which ought also to become rigid,
will, in motion, have the property of remaining constantly vertical, or at least
constantly perpendicular to o, o', which might be kept horizontal or inclined,
as may be desirable.
The right angle a, b, might also be supposed constantly vertical, which
would only require that the centres o and o¹ should be upon one vertical, or
rather, in one and the same vertical plane. If therefore a, b, becomes a surface
it will have the property of remaining constantly vertical, and we shall thus
have a second arrangement for the same principle.
Such is the principle which I propose to apply to the construction of the
paddle wheels of steamers.