Fig. 15. Example of a doubling
mechanism.
On the MIT differential analyzer No. 2, however, we are better off. A much more convenient device for doubling is used. We make use of: a gearbox in whichthere are two shafts that may be geared so that one turns twice as much as the other, and two angle-indicator transmitters and receivers. Looking at the drawing ([Fig. 16]), we can see that: shaft a drives shaft c to turn in step, shaft c drives shaft d to turn twice as much, and shaft d drives shaft b to turn in step. Here we can accomplish doubling by closing the pairs of switches that connect to the gearbox shafts.
Angle indicators: T, transmitters, and R, receivers
Fig. 16. Another example of a doubling mechanism.
Above, we have talked about a mechanism with gears that would multiply the amount of turning by the constant ratio 2. But, of course, in a calculation, any ratio, say 7.65, 3.142, ···, might be needed, not only 2. In order to handle various constant ratios, gearboxes of two kinds are in differential analyzer No. 2. The first kind is a one-digit gearbox. It can be set to give any of 10 ratios, 0.1, 0.2, 0.3, ···, 1.0. The second kind is a four-digit gearbox. It can be set to give any one of more than 11 thousand ratios, 0.0000, 0.0001, 0.0002, ···, 1.1109, 1.1110. We can thus multiply by constant ratios.
Adders
We come now to a new mechanism, whose purpose is to add or subtract the amount of turning of two shafts. It is called an adder. The scheme of it is shown in [Fig. 17]: an input shaft with amount of turning a, another input shaft with amount of turning b, and an output shaft with amount of turning a + b. The adder essentially is another kind of gearbox, called a differential gear assembly. This name is confusing: the word “differential” here has nothing to do with the word “differential” in “differential analyzer.” This mechanism is very closely related to the “differential” in the rear axle of a motor car, which distributes a driving thrust from the motor to the two rear wheels of the car.
