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# Polyconic Projections

## meridian, central and parallel

POLYCONIC PROJECTIONS These pseudo-conical projections are valuable not so much for their intrinsic merits as for the fact that they lend themselves to tabulation. There are two forms, the simple or equidistant polyconic, and the rectangular polyconic.

The Simple Polyconic.—If a cone touches the sphere or spheroid along a parallel of lat itude 4 and is then unrolled, the parallel will on paper have a radius of v cot 4, where v is the normal terminated by the mi nor axis. If we imagine a series of cones, each of which touches one of a selected series of par allels, the apex of each cone will lie on the prolonged axis of the spheroid; the generators of each cone lie in meridian planes, and if each cone is unrolled and the generators in any one plane are superposed to form a straight central meridian, we obtain a projection in which the central meridian is a straight line and the parallels are circular arcs each of which has a different centre which lies on the pro longation of the central meridian, the radius of any parallel being v cot 4).

So far the construction is the same for both forms of polyconic. In the simple polyconic the meridians are obtained by measuring outwards from the central meridian along each parallel the true lengths of the degrees of longitude. Through corresponding

points so found the meridian curves are drawn. The resulting projection is accurate near the central meridian, but, as this is departed from, the parallels increasingly separate from each other, and the parallels and meridians (except along the equator) intersect at angles which increasingly differ from a right angle. The real merit of the projection is that each particular parallel has for every map the same absolute radius, and it is thus easy to construct tables which shall be of universal use. The simple polyconic when used for single sheets and large scales is a sufficiently close approximation to the better forms of conical projection.

At the equator this becomes simply 2CO. Let any equatorial point whose actual longitude is 2C0 be represented by a point on the developed equator at the dis tance 20) from the central meri dian, then we have the very sim ple construction (due to O'Far rell of the Ordnance Survey) (fig. 29).