⌠ and _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. AN APPRAISAL OF THE MACHINE The second MIT differential analyzer is probably the best machine ever built for solving most differential equations. It regularly has an accuracy of 1 part in 10,000. This is enough for most engineering problems. If greater accuracy is needed, the second differential analyzer cannot provide it. Once in a while the machine can reach an accuracy of 1 part in 50,000; but, to balance this, it is sometimes less accurate than 1 part in 10,000.