Let z1 be the co-latitude of some parallel which is to be correctly represented, then 2h sin ½z1/[delta]h = sin z1, and h = cos² ½z1; putting this value of h in equation (ii.) the radius of any parallel = [rho] = 2 sin ½z sec ½z1 (iii.) This is Lambert's _conical equal-area projection with one standard parallel_, the pole being the centre of the parallels. If we put z1 = [theta], then h = 1, and the meridians are inclined at their true angles, also the scale at the pole becomes correct, and equation (iii.) becomes [rho] = 2 sin ½z; (iv.) this is the _zenithal equal-area projection_. Reverting to the general expression for equal-area conical projections [rho] = [root]{2(C - cos z)/h}, (i.) we can dispose of C and h so that any two selected parallels shall be their true lengths; let their co-latitudes be z1 and z2, then 2h(C - cos z1) = sin² z1 (v.) 2h(C - cos z2) = sin² z2 (vi.) from which C and h are easily found, and the radii are obtained from (i.) above. This is H. C. Albers' _conical equal-area projection with two standard parallels_. The pole is not the centre of the parallels. _Projection by Rectangular Spheroidal Co-ordinates._ If in the simple conical projection the selected parallel is the equator, this and the other parallels become parallel straight lines and the meridians are straight lines spaced at equatorial distances, cutting the parallels at right angles; the parallels are their true distances apart. This projection is the _simple cylindrical_. If now we imagine the touching cylinder turned through a right-angle In such a way as to touch the sphere along any meridian, a projection is obtained exactly similar to the last, except that in this case we represent, not parallels and meridians, but small circles parallel to the given meridian and great circles at right angles to it. It is clear that the projection is a special case of conical projection. The position of any point on the earth's surface is thus referred, on this projection, to a selected meridian as one axis, and any great circle at right angles to it as the other. Or, in other words, any point is fixed by the length of the perpendicular from it on to the fixed meridian and the distance of the foot of the perpendicular from some fixed point on the meridian, these spherical or spheroidal co-ordinates being plotted as plane rectangular co-ordinates.