Spherical orthogonal coordinate system (3 dimensions)” (vixra:1106.0062, 2011) [2] Morio Kikuchi, ”Equidistant curve coordinate system (3 dimensions)” (vixra:1111.0005, 2011) [3] Morio Kikuchi, ”On coordinate systems by use of spheres (the 1st

Product of metric coefficient and radius of round line is constant in spherical orthogonal coordinate system. Coordinates and so forth are constant in the coordinate transformation from orthogonal coordinates into spherical orthogonal coordinates if the value is special. 1. Length on round line Figure 1 shows round line on xz plane. Because a round line is a figure by inversion of a line, the top N corresponds to the foot of the perpendicular dropped from origin to the line. The length s from the top N to the point P on the round line is s = K tan θ treating K as metric coefficient of round line. Differential form is ds = K sec2 θdθ 2. Case of two dimensions We find the condition for two round lines which are obtained by inversion of parallel lines on plane being parallel lines also on a sphere. In Figure 2, two sets of parallel lines cross at right angles each other, and their directions are x ′ and y′, and one side of parallel lines is on the coordinate axis in either set. Figure 3 shows round lines by inversion of them, and the figure which the four roun