| y = |  | 1 | dt |
| x |
Then
| Dₜ y = | 1 | , Dy t = x, |
| x |
| t = | x dy |
The connections therefore are:
| Shaft t | To Integrator, Wheel |
| Shaft x | To Integrator, Screw |
| Shaft y | To Integrator, Disc |
The light wheel then drives the heavy disc. Clearly only the angle-indicator device makes this possible at all. Naturally, the closer the wheel gets to the center of the disc, that is, x approaching zero, the greater the strain on the mechanism, and the more likely the result is to be off. Mathematically, of course, the limit of 1/x as x approaches zero equals infinity, and this gives trouble in the machine.
There is no standard mathematical method for solving any differential equation. But the machine provides a standard direct method for solving all differential equations with only one independent variable. First: assign a shaft for each term that appears in the equation. For example, the highest derivative that appears and the independent variable are both assigned shafts. The integral of the highest derivative is easily obtained, and the integral of that integral, etc. Second: connect the shafts so that all the mathematical relations are expressed. Both explicit and implicit equations may be expressed. Third: for any shaft there must be just one drive, or source of torque. A shaft may, however, drive more than one other shaft. Fourth: choose scale factors so that the limits of the machine are not exceeded yet at the same time are well used. For example, the most that an integrator or a function table can move is 1 or 2 feet. Also, the number of full turns made by a shaft in representing its variable should be large, often between 1000 and 10,000.
Of course, as with all these large machines, anyone would need some months of actual practice before he could put on a problem and get an answer efficiently.