Abstract :
The "approximate" fringing capacitances C\´f0 and C\´fe are found by mapping the upper half plane into the interior of an infinite polygon bounded by an infinite rectangular bar and so infinite channel. The thickness of the bar t its spacing from the channel at one end s/2, and the width of the channel b are given in terms of two independent parameters k and a. It is shown how these relationships may be inverted and how k and a may be expressed directly in terms t/b and s/b. First, q\´= exp (-pi K/K\´) is expressed as an odd power series in exp (-pi s/b) whose coefficients are irrational functions of t/b. k is given by a well known formula in terms of q\´ from the theory of elliptic functions and an expression for a in terms of q\´ and s/b is derived. Numerical values of the coefficients of the first six terms in the expansion of q\´ in terms of exp (-pi s/b) for t/b= 0.1, 0.2, 0.3, 0.4, 0.5 are given. For this range of t/b, useable accuracy is shown for s/b as small as 0.1.
