(the total amount that the wheel turns) equals the sum of all the small (amounts of turning), each equal to: a bit of (disc turning) multiplied by the (distance from the center of the disc to the edge of the wheel) applying to that bit
If we look back at our discussion of integrating ([p. 72]), we see that the capital words here are just the same as those used there. Thus we have a mechanism that expresses integration:
(the total amount that the wheel turns) equals the integral of (the distance from the center of the disc to the wheel) with respect to (the amount that the disc turns)
The scheme of this mechanism is shown in [Fig. 20].
For example, suppose that the screw measures the speed at which a car travels and that the disc measures time. The wheel, consequently, will measure distance traveled by the car. The mechanism integrates speed with respect to time and gives distance.
Fig. 20. Scheme of integrator.
This mechanism is the device that Lord Kelvin talked about in 1879 and that Dr. Bush made practical in 1925. The mechanical difficulty is to make the friction between the disc and the wheel turn the wheel with enough force to do other work. In the second differential analyzer, the angle indicator set on the shaft of the wheel solves the problem very neatly.
Fig. 21. Graph of air resistance coefficient.