GB389524A - Improvements in and relating to calculating machines - Google Patents

Abstract

389,524. Calculating-apparatus. MALLOCK, R. R. M., Huccaby, Long Road, Cambridge. Sept. 18, 1931, No. 26207. [Class 106 (i).] Means for solving simultaneous linear equations, which may be adapted for evaluating mathematical expressions, and for algebraic addition, subtraction, multiplication, and division, comprises a plurality of transformers each carrying a plurality of windings the turns of which may be varied in number. To solve n simultaneous equations (n + 1) transformers each bearing n windings are necessary. For example, to solve the three equations which by substituting x1/x4 for X1, x2/x4 for X2.. (x4 being known) reduce to the symmetrical form transformers 1 .. 4, Fig. 1, corresponding respectively to the unknowns x1, x2 .. are necessary, each carrying three windings. The turns of coefficient coils 11, 21, 31, 41 are adjusted proportionally to the coefficients a11, a21, a31, a41 and connected in series to a short-circuiting lead 5, the direction of the coil connections depending on the sign of the corresponding coefficients. The coefficient coils 12, 22, 32, 42, and 13, 23, 33, 43 corresponding to the other equations are similarly connected. Under ideal conditions, there being no magnetic leakage in the transformers and the coils having no resistance, an alternating voltage applied to one of the exciting coils 14, 24, 34, 44 induces fluxes in the other transformer cores which automatically assume values satisfying the equations. The voltage per turn of the transformers, proportional to the fluxes therein and therefore to x1 .. x4, are measured by any suitable means connected across similar search coils 15,25, 35,45, and x4 being known, X1, X2, X3 may be obtained. In practice, the errors due to leakage and resistance are reduced by applying to each core 1 .. 4, the number of ampere turns required to produce the flux corresponding to the value of x1 .., the coils 14, 24, 34, 44 being connected in series and variable shortcircuiting resistances and switches to vary the turns thereof, manipulated until by successive approximation the best results are obtained. Alternatively each transformer (preferably with the exception of the one excited directly) is associated with a similar compensating transformer C1, and a thermionic amplifier A, Fig. 2. 17 and 17C are equal coils connected in opposition, the voltage produced in the former comprising the input to the amplifier A, the output of which energizes series coils 16, 16C. The flux density produced by 16C is arranged to be substantially equal to that in core 1 in which case the coils 17, 17C practically nullify the effects of each other. The flux in 1 produced by the currents in the coefficient coils 11, 12, 13 is the difference between the two fluxes and is therefore very small and similarly reduces these currents to a small value at which fairly accurate results may be obtained. The bulb B connected to series search coils 18, 18C is for roughly comparing the x1 .. values. A null method is preferred for measuring the voltages across the search coils 15, 25 .., but others are also described. By interconnecting coils of a, b .., turns on transformers 1 .. 4, as in Fig. 3, and exciting 1 such that the voltage per turn thereof is unity the voltage v4 = p.a.c.e/b.d.f . By suitably interconnecting the transformers addition, subtraction, multiplication, and division may be effected and other expressions may be evaluated. Examples are given for evaluating a<2> + b<2> +c<2> b.c and by using pairs of transformers fed from a balanced two-phase supply for evaluating expressions involving complex numbers.