54 
SUGGESTION OF A MECHANICAL INTEGRATOR. 
[719 
D is moving downwards, E is out of gear with D; the continuous rotation of A 
will communicate an intermittent rotation to E, in such manner nevertheless that, to 
each entire revolution of A or rotation through the angle 27r, there will (the throw 
remaining constant) correspond a rotation of E through the angle n. 27r, where the 
coefficient n depends upon the throw*. And evidently if A be driven by a wheel 
A', the angular velocity of which is ^ times that of A, then to a rotation of A’ 
2^ 
through each angle —-, there will correspond an entire revolution of A, and therefore, 
A, 
as before, a rotation of E through the determinate angle n. 27t ; hence, X being 
sufficiently large to each increment of rotation of A', there corresponds in E an 
increment of rotation which is nX times the first-mentioned increment; viz. E moves 
(intermittently and possibly also with some “ loss of time ” on E coming successively 
in gear and out of gear with D, or in beats as explained) with an angular velocity 
which is = nX times the angular velocity of A'. And thus the throw (and therefore n) 
being variable, the velocity-ratio nX is also variable. 
We may imagine the wheel A as carrying upon it a piece L sliding between guides, 
which piece L carries the pivot B of the link BC, and works by a rack on a toothed 
wheel a concentric with A, but capable of rotating independently thereof. Then if a 
rotates along with A, as if forming one piece therewith, it will act as a clamp upon L, 
keeping the distance of B from the centre of A, that is, the half-throw, constant; whereas, 
if a has given to it an angular velocity different from that of A, the effect will be to 
vary the distance in question; that is, to vary the half-throw, and consequently the 
velocity-ratio of A and E. And, in some such manner, substituting for A and E the 
bands A and A' of the foregoing description, it might be possible to establish between 
these bands the required variable velocity-ratio. 
* If instead of the wheel or arc D with a reciprocating circular motion, we have a double rack D with a 
reciprocating rectilinear motion, such that the wheel E is placed between the two racks, and is in gear on the 
one side with one of them when the rack is moving upwards, and on the other side with the other of them 
when the rack is moving downwards; then the continuous circular motion of A will communicate to E a 
continuous circular motion, not of course uniform, but such that to each entire revolution of A or rotation 
through the angle 27t, there will correspond a rotation of E through an angle n.27r as before. This is in 
fact a mechanical arrangement made use of in a mangle, the double rack being there the follower instead of 
the driver.