C 555 ] 
middle latitude. Draw LN, In, cofines of the lati- 
tudes, the fine of the middle latitude MF, and its 
cotangent MT. Then writing unity for the radius. 
x we draw xR, xr , equal each to half the arc L/, 
and perpendicular to CM; the conical furface ge- 
nerated by the line Rr, while the figure revolves on 
the axis of the fphere, will be equal to the furface 
of the zone that is to be defcribed in the fame time 
by the arc L /; as will eafily appear by comparing 
that conical furface with the zone, as meafured by 
Archimedes. 
And, laftly, If from the point t y in which rR 
produced meets the axis, we take the angle C t V in 
proportion to the longitude of the propofed map, as 
MF the fine of the middle latitude is to radius, and 
draw the parallels and meridians as in the figure, the 
whole fpace S O QV will be the propofed part of 
the conical furface expanded into ,a plane ; in which 
the places may now be inferted according to their 
known longitudes and latitudes. 
V. Let L/, the breadth of the zone, be 50°, lying 
between io° and 6o° north latitude; its longitude 
no°, from 20 0 eaft of the Canaries to the center of 
the weftern hemifphere ; comprehending the weftern 
parts of Europe and Africa, the more known parts 
of North America, and the ocean that feparates it 
from the old continent. 
if in C M we take Cx = 
Example. 
And becaufe Cx = 
three logarithms. 
N n 
L/xMFxMT’ 
add thefe 
4 B 1 
Log. 
