The multiple resistances of N resistors

Mr. N. W. Lewis has shown¿ that if the values of three resistors are three consecutive terms of the geometric series in which each term is the sum of the three preceding terms, then the distribution of the 17 resistance values attainable by various combinations of the resistors is closely related to another geometric series with a common ratio not exceeding 6:5, covering approximately a decade in 16 steps. In this paper it is shown that as the number of resistors is increased the ratios between consecutive steps can be arranged to become increasingly more uniform without exceeding the same 6:5 ratio, but over an extended range. Alternatively, increased uniformity can also be obtained with more steps of lower consecutive ratio value. Tables are worked out for four and five resistors respectively. These are followed by a short summary of the results obtained and a brief analysis of the general properties of the ¿-series (¿ being the common ratio of the geometric series).