In connection with the requirements of color correction discussed in the preceding paper, we found that a set of <i>n</i> simultaneous equations can be solved by using each of the <i>n</i> error signals to control one of the independent variables. Stability of this equation-solving network can be achieved by the proper interconnection. In applying this procedure to the equations for color correction, it was necessary to find the sum of eight terms, each of which is the product of either three or four independent variables. It was found that these individual products could be computed by making use of the fact that, if <i>n</i> events have probabilities of occurrence <i>a</i>, <i>b</i>, . . .<i>n</i>, respectively, the probability of their simultaneous occurrence is the product of their individual probabilities abc . . . <i>n</i>. By generating rectangular waves of irrationally related frequencies whose positive pulse widths are proportional to the values of the unknown variables, and applying these signals to the grid of a vacuum tube in such a manner that its plate current flows only when all of the signals have positive values simultaneously, the average value of the plate current is proportional to the required product. When controlled in this way, eight vacuum tubes with their plates connected in parallel deliver an average current that is proportional to the required sum.
ARTHUR C. HARDY and EDWARD C. DENCH, "An Electronic Method for Solving Simultaneous Equations1," J. Opt. Soc. Am. 38, 308-309 (1948)