The _A_ tape contains instructions for connecting shafts in the machine. Each instruction connects a certain output of one type of mechanism (adder, etc.) to a certain input of another type of mechanism. When the machine reads an instruction on this tape, it connects electrically the transmitting angle-indicator of an output shaft to the receiving angle-indicator of another input shaft. Now the connecting part of the differential analyzer behaves as if it were very intelligent: it assigns an adder or an integrator or a gearbox, etc., to a new problem only if that mechanism is not busy. For example, if a problem tape calls for adder 3 (in the list belonging to the problem), the machine will assign the first adder that is not busy, perhaps adder 14 (in the machine), to do the work. Each time that adder 3 (in the problem list) is called for in the _A_ tape, the machine remembers that adder 14 was chosen and assigns it over again. This ability, of course, is very useful. The _B_ tape contains the ratios at which the gearboxes are to be set. For example, suppose that we want gearbox 4 (in the problem list) to change its input by the ratio of 0.2573. The machine, after reading the _A_ tape, has assigned gearbox 11 (in the machine list). Then, when the machine reads the _B_ tape, it sets the ratio in gearbox 11 to 0.2573. The answer to a differential equation is different for different starting conditions. For example, when we know speed and time and wish to find distance traveled and where we have arrived, we must know the point at which we started. We therefore need to arrange the machine so that we can put in different starting conditions (or different _initial conditions_, as the mathematician calls them). The _C_ tape puts the initial conditions into the machine. For example, reading the _C_ tape for the problem, the machine finds that 3000 should, at the start of the problem, stand in counter 4. The machine then reads the number at which counter 4 actually stands, say 6728.3. It subtracts the two numbers and remembers the difference, -3728.3. And whenever the machine reads that counter later, finding, say, 9468.4 in it, first the 3728.3 is subtracted, and then the answer 5740.1 is printed. ANSWERS Information may come out of the machine in either one of two ways: in printed numbers or in a graph. In fact, the same quantity may come out of the machine in both ways at the same time. To obtain a graph, we change a function table from input to output, put a pen on it, and have it draw the graph. The machine has 3 electric typewriters. The machine will take numerical information out of the counters at high speed even while they are turning, and it will put the information into relays. Then it will read from the relays into the typewriter keys one by one while they type from left to right across the page. HOW THE DIFFERENTIAL ANALYZER CALCULATES