Notes on Map Projections. 329 
termined the cone which equalizes the errors and distortion on 
the central and the two limiting parallels. The use of two conic 
frustums—one for the north and one for the south half—has also 
been attempted, and advocated. 
CLASS III. 
e class of projections in which portions of the spherical 
surface are developed by being resolved into their differential ele- 
ments, which are successively developed, is characterized by a 
peculiar elegance, and is of the highest importance. By this 
means, any portion of a spherical or spheroidal surface may be 
reconstructed on a plane with the most perfect attainable preser- 
vation of the relations and dimensions of its parts. his class 
of projections is far the best for representing limited areas, and 
can even be extended with advantage in some forms to mappe- 
mondes, or maps of the entire earth’s surface. 
Cassini’s projection is made by first developing the central 
meridian of the area for projection into a straight line. A series 
of prime verticals or great circles perpendicular to their central 
meridian is passed at elementary distances along the meridian arc, 
all of which circles intersect in the spheric poles of the central 
meridian. These divide the surface into elementary rectangular 
isosceles triangles, or sectors, basing on the meridian elements. 
When the meridian is developed, these elementary triangles are 
correct relations to each other and to the central meridian. Each 
Stconp Serizs, Vol, XVIII, No. 54.—Nov., 1854. 
