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asymptotic position becomes branch centre circle complex argument conjugate corresponding root point corresponds the lemniscate current strengths Denoting the distances differential co-efficient Differentiating both sides double point dr dz dv dx dv dy dw dz dx dx dx dz dy dy dy dz dz dw electric flow enclosing the origin entire rational function equation equipotential lines evident finite flow of heat geomet heat and electricity Hence it follows Hence the expression hn fn hyperbolas infinite extents INFINITE PLANE infinite value infinity isoclinic lines and lines lines of equipotential lines of flow locus multiple point negative electrode numerator and denominator origin corresponds orthogonally PLANE VECTOR points of outflow positive electrodes potential function pure Mathematics r d,i radii radius represent Riemann's second plane series of curves stationary flow stream lines Suppose surface theorems theory transforming function ultimately similar unit current