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. [Illustration: FIG. 17. Scheme of an adder mechanism.] [Illustration: FIG. 18. Example of an adding mechanism (differential gear assembly).] A type of differential gear assembly that will add is shown in Fig. 18. This is a set of 5 gears _A_ to _E_. The 2 gears _A_ and _B_ are input gears. The amount of their turning is _a_ and _b_, respectively. They both mesh with a third gear, _C_, free to turn, but the axis of _C_ is fastened to the inside rim of a fourth, larger gear, _D_. Thus _D_ is driven, and the amount of its turning is (_a_ + _b_)/2. This gear meshes with a gear _E_ with half the number of teeth, and so the amount of turning of _E_ is _a_ + _b_. We can subtract the turning of one shaft from the turning of another simply by turning one of the input shafts in the opposite direction. Integrators Another mechanism in a differential analyzer, and the one that makes it worth while to build the machine, is called an _integrator_. This mechanism carries out the process of integrating, of adding up a very large number of small changing quantities. Figure 19 shows what an integrator is. It has three chief parts: a _disc_, a little _wheel_, and a _screw_. The round disc turns horizontally on its vertical shaft. The wheel rests on the disc and turns vertically on its horizontal shaft. The screw goes through the support of the disc; when the screw turns, it changes the distance between the edge of the wheel and the center of the disc. [Illustration: FIG. 19. Mechanism of integrator.]