Giant brains; or, Machines that think

by Edmund Callis Berkeley

Function Tables

The behavior of some physical quantities can be described only by a series of numbers or a graphic curve. For example, the resistance or drag of the air against a passing object is related to the speed of the object in a rather complicated way. Part of the relation is called the drag coefficient or resistance coefficient; a rough graph of this is shown in [Fig. 21]. This graph shows several interesting facts: (1) when the object is still, there is no air resistance; (2) as it travels faster and faster, air resistance rapidly increases; (3) when the object travels with the speed of sound, resistance is very great and increases enormously; (4) but, when the object starts traveling with a speed about 20 per cent faster than sound, the drag coefficient begins to decrease. This drawing or graph shows in part how air resistance depends on speed of object; in other words, it shows the drag coefficient as a function of speed ([see Supplement 2]).

Fig. 22. Pointer following graph.

Now we need a way of putting any function we wish into a differential analyzer. To do this, we use a mechanism called a function table. We draw a careful graph of the function according to the scale we wish to use, and we set the graph on the outside of a large drum ([Fig. 22]). For example, we can put the resistance coefficient graph on the drum; the speed (or independent variable) goes around the drum, and the resistance coefficient (or dependent variable) goes along the drum. The machine slowly turns the drum, as may be called for by the problem. A girl sits at the function table and watches, turning a handwheel that keeps the sighting circle of a pointer right over the graph. The turning of the handwheel puts the graphed function into the machine. Instead of employing a person, we can make one side of the graph black, leaving the other side white, and put in a phototube (an electronic tube sensitive to amount of light) that will steer from pure black or pure white to half and half ([see Fig. 23]).

We do not need many function tables to put in information, because we can often use integrators in neat combinations to avoid them. We shall say more about this possibility later.

We can also use a function table to put out information and to draw a graph. To do so, we disconnect the handwheel; we connect the shaft of the handwheel to the shaft that records the function we are interested in; we take out the pointer and put in a pen; and we put a blank sheet of graph paper around the drum.

Fig. 23. Phototube following graph.

We have now described the main parts of the second MIT differential analyzer. They are the parts that handle numbers. We can now tell the capacity of the differential analyzer by telling the number of main parts that it holds: