Notes on Map Projections. 333 
If the case in hand be that involving the greatest extension of 
the method, or that of the projection of the entire spheroidal 
surface, a prime or central meridian must first be chosen, one 
half of which gives the central straight line of the development, 
and the other half cuts the zones apart, and becomes the outer 
boundary of the total developed figure. Next, the latitude of 
_the governing parallel must be assumed; thus fixing the centre 
of all the concentric circles of development. Having then drawn 
a Straight line and graduated it from 90° north latitude to 90° 
south latitude, and having fixed the vertex or centre of develop- 
ent on it, concentric arcs are traced from this centre through 
each graduation. On each parallel the longitude graduations are 
then laid off, and the meridians are traced through the corres- 
ponding points. There results from this process an oblong kid- 
ney-shaped figure, which represents the entire earth’s surface, 
and the boundary line of which is the double developed lower 
half of the meridian first assumed. If the vertex of the govern- 
ing cone be removed to an infinite distance, the equator be- 
comes the governing parallel, the parallels all fall into straight 
lines, and Flamstead’s projection results. The kidney-shaped 
figure becomes an elongated oval, with the half meridian for one 
axis, and the whole equator for the other. A somewhat similar 
figure is obtained by placing the vertex at the pole, and reducing 
the tangent cone to a plane. An indented cusp at one end, and 
a rounding out at the other, will give an approximate’ pear-shape. 
Ptolemy’s modified conic method reaches its full geometrical 
result in these forms, derived from the condition of preserving 
areas in tracing meridian curves. 
Bonue’s method is rarely applied to areas exceeding the limits 
of a State, but is invaluable for topographical maps of this de- 
scription. The projection is made at once for the whole territory 
of the map, and the rectangular system of sheets laid out on the 
projection. Each sheet is numbered, and the codrdinates of the 
Corners are determined, so that the codrdinates of intersection 
between parallels and meridians falling on each sheet are referred 
to its neat lines as axes. i 
This projection preserves in all cases the areas developed with- 
out any change. The meridians intersect the central parallel at 
right angles; and along this, as along the central meridian, the 
map is strictly correct. For moderate areas, the intersections 
approach tolerably to being rectangular. All distances alon 
parallels are correct; but distances along the meridians are in- 
creased in projection in the same ratio as the cosine of the angle 
between the radius of the parallel and the tangent to the meridian 
at the point of intersection is diminished. ‘Thus, in a full earth 
Projection, the bounding meridian is elongated to about twice its 
original length. While each quadrilateral of projection preserves 
