Mathematical analysis of the potential variation produced by a circuit comprising two slide wire resistors (potentiometers) linked in parallel revealed the possibility of compensating the circuit so as to provide a potential varying as the product of the resistances in the individual slide wires. The problem was to counteract the fall in potential produced when a resistor is placed across a potentiometer circuit delivering an initial potential, E0. It was shown in the main report that a compensating resistor with the following characteristics would solve the problem, namely, Rx = R12 / R2 – R1 , in which R1 is the resistance operating in the first slide wire, R2 is the total resistance of the second slide wire, and is therefore, a constant, and Rx is the value of the required compensator. A suitable manner of constructing Rx was devised, with the result that when the two slide wires described are manipulated independently of each other, the output potential of the circuit varies directly as the product of the operating resistances in the slide wires. With this relationship it is possible to apply appropriate scales to the slide wire resistors, balance the output potential using a suitable measuring instrument, and hence to adapt the circuit to the type of mathematical operations involving multiplication and division.
Proceedings of the Iowa Academy of Science
©1941 Iowa Academy of Science, Inc.
"An Electrical Circuit Designed for Use in a Calculating Instrument (Abstract),"
Proceedings of the Iowa Academy of Science, 48(1), 310-311.
Available at: https://scholarworks.uni.edu/pias/vol48/iss1/91