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A review is made of the derivation of the basic formula for calculating the gear ratio to be employed in winding a universal coil as a function of certain coil parameters, as given in a previous paper by the author. From this basic formula a somewhat simpler, though less accurate, formula is derived merely by neglecting certain terms, and shown to be the equivalent of that evolved by Hershey. Also the nomenclature and notation originally introduced by the author are compared with those subsequently used by Hershey. The theory underlying the selection of the correct number of crossovers per turn (of the dowel) is reviewed, and rules for determining the number of crossovers per winding cycle (required in the use of the gear-ratio formulas) from the number of crossovers per turn are given. The steps in making a gear-ratio calculation are outlined and a table of useful formulas is appended. In conclusion, the details of the mathematical solution involved in the derivation of the basic formula are given.