. The Bell System technical journal . functions of the P^s, that is, 2i = Pi2 + P22 + . . P^„_i)/2, 22 = P^Pi^ + • • • + P^(n--3)/2P^(n-l)/2- The equations in p may also be written in trigonometric form asfollows: —-—= 1, cos^^ + 21COS2 = 0 r ^ fl = 2, cos^^ + 22COS2^ + 21COS2 = 0 = 3, COS 2 ^ + 23 COS 2 0 + 2i cos 2 e + 22 cos | = 0 9 7 5 3 = 4, cos ^ ^ + 24 cos - e + 2i cos ^e -\- Xa cos ^ d + 22COs|= 0. CONSTANT RESISTANCE NETWORKS 187 These equations include the root at X = — 1 corresponding to6 = T. Excluding this they will each have (n — l)/2 roots between6 = 0 and 6 = tt. The roots in p
. The Bell System technical journal . functions of the P^s, that is, 2i = Pi2 + P22 + . . P^„_i)/2, 22 = P^Pi^ + • • • + P^(n--3)/2P^(n-l)/2- The equations in p may also be written in trigonometric form asfollows: —-—= 1, cos^^ + 21COS2 = 0 r ^ fl = 2, cos^^ + 22COS2^ + 21COS2 = 0 = 3, COS 2 ^ + 23 COS 2 0 + 2i cos 2 e + 22 cos | = 0 9 7 5 3 = 4, cos ^ ^ + 24 cos - e + 2i cos ^e -\- Xa cos ^ d + 22COs|= 0. CONSTANT RESISTANCE NETWORKS 187 These equations include the root at X = — 1 corresponding to6 = T. Excluding this they will each have (n — l)/2 roots between6 = 0 and 6 = tt. The roots in p will then be given hy p = 2 cos 6. Equation (7) becomes (n-l)/2 /3i = tan~^ X -\- J^ tan —1 ymX 1-^2 (11) where the quantities pm are the roots of the above equations, withoutregard to sign. We require also the value of d^ijdx, which may be written dSidx 1 1 + X2 (n-l)/2 1+ L -1 1 p^ (4 - pj)x (1 + x^Y J (12) A possible configuration for the first network is shown in Fig. 5and for the second in Fig. 6. \AAr an-a^. Fig. 5
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