Notes on Map Projections. 335 
diminishes. At latitude 45° the terrestrial and development radii 
become equal. At the equator the vertex recedes to an infinite 
distance north, or the cone becomes a cylinder, and the equator 
falls in a straight line perpendicular to the meridian. On passing 
to the south the vertex approaches from an infinite distance south, 
the parallels change their concavity southward, while the curva- 
lure, increasing in an inverse order, becomes infinite at the pole, 
or the polar parallel falls in a point. ‘There results from this 
Process a biaxial figure, with four equal quadrants, the short axis 
being the rectified Washington meridian, (180° in length) and 
the long axis being the entire rectified equator, or about twice 
the length of the shorter one. A re-entering cusp marks the 
bounding curve at each pole, and the meridian, 180° from Wash- 
ington, which circumscribes each half of the figure, is elongated 
each side to more than twice its original length by the devel- 
°pment. Over the entire area of this projection all parallels and 
meridians intersect at right angles, and the diagonals of each 
Projected quadrilateral are every where nearly equal to each other. 
€ scale on N. and S. lines near the border is somewhat enlarged, 
but is very correct on E. and W. lines, while along both diagonals 
tis somewhat enlarged, though nearly equally so on each, On 
the whole there results from this method much less of local dis- 
tortion than from Bonne’s projection. Equality between the 
spheroidal and developed areas is not preserved, but the departure 
fom equivalency is not great in amount. 
