Patent GB-684512-A (GB)
Title: Improvements relating to calculating apparatus
Inventor: LIEBMANN GERHARD
IPC: G06G7/46
Filed: 1950-07-03
Abstract: 684,512. Electric analogue calculating systems. ASSOCIATED ELECTRICAL INDUSTRIES, Ltd. May 24, 1951 [July 3, 1960], No. 16550/50. Class 37. In apparatus for solving a physical problem capable of expression as a differential equation, wherein the problem is represented by a resistance network to the respective junction points of which a current representing the independent variable is fed and the resultant voltages relative to a datum level are measured whereby the finite difference equation of the problem is obtained, a voltage bridge circuit is constituted by an indicating device connected between a nerwork junction and a variable tapping of a resistor across a voltage source and a current bridge circuit by an indicating device connected between a tapping point of a resistance in the current supply to the particular junction point and a variable tapping point of a resistance across the same or another voltage source, such that the voltage at and current into the network junction are determinable by adjustment of the appropriate tapping points. Fig. 2 shows apparatus, e.g. of the kind described in Specification 605,822, [Group XIX], for solving a physical problem whose variables are connected by the differential equation where g is a known function g(x, y) of the space variables x, y which is expressible in finite difference form, wherein a current value (R N  being the value of a network resistance unit and h the resultant resistance between network junctions) is fed to a junction and the voltage V developed thereat represents the function f. The current into a junction J<SP>1</SP> derived from the right-hand half secondary of a supply transformer secondary through a resistor RO in series with a variable regulating resistor R<SP>5</SP> is measured as the voltage drop across RO (which may be a precision resistor replaceable for the normal resistor during measurement) by a current bridge comprising variable resistors R<SP>3</SP>, R<SP>4</SP> in series across the half secondary resistors RO, R<SP>5</SP>, the network resistance between junction J<SP>1</SP> and the network boundary, and a galvanometer G<SP>2</SP> between the junctions of R<SP>3</SP>, R<SP>4</SP> and RO, R<SP>5</SP>. Similarly the voltage at junction J<SP>1</SP> is measured by a voltage bridge comprising variable resistances R<SP>1</SP>, R<SP>2</SP> across the left-hand half secondary, the resistance network, and a galvanometer G<SP>1</SP> between the junction J<SP>1</SP> and the junction of R<SP>1</SP>, R<SP>2</SP>. Switching may be provided enabling galvanometer G<SP>1</SP> and resistors R<SP>1</SP>, R<SP>2</SP> to be used for both voltage and current measurements. Further pairs of resistors, e.g. RO<SP>1</SP> and R<SP>4</SP>, are provided for the supply and measurement of currents to other junction points, e.g. J<SP>2</SP>, at which the resultant voltages are measured to enable the finite difference equation to be determined. Second order differential equations in which the second derivatives are determined not only be prescribed functions of the independent space variables but by functions of the unknown function f itself or of a previously unknown parameter p (e.g. the " Eigen value " parameter) in which g=g ( f, x, y, p), are soluble by an iteration process using the apparatus, wherein an approximate function f, and parameter p 0  are assumed such that g 0  Î g (f 0 , x, y, p 0 ) and approximate currents are fed into the junctions so that more accurate function and parameter values are determined from the measured junction voltages, and an improved value g 1 =g (f 1 , x, y, p 1 ) is obtained, which is used to derive an improved value of the junction feed current The process is iteratively repeated for all the junctions, until the obtained values for function f and parameter p show no change on further repetition. The resistances R<SP>1</SP>, R<SP>2</SP>, R<SP>3</SP>, R<SP>4</SP> may be constituted by a single logarithmic and circularly arranged tapped resistance. The sliders may be associated with mechanically interconnected pointers co-operating with plural logarithmically graduated slide-rule scales, Fig. 3 (not shown), adapted to simplify the foregoing plural iterative calculations. Automatic servomotor operation is referred to.