62 
Mints to t^avelle^ 
the south of the 50th parallel. Number these divisions 50, 51, 52, etc.* 
and through the 51st and 55th * draw lines of an indefinite length at 
right angles to C D. Next, by the aid of the table (p. 256), ascertain the 
lengths of a degree of longitude on the parallels of 51° and 55°, which are 
shown on the diagonal scale by the lines x x, and y y. On the line drawn 
parallel to A B, from the point c, through which the first parallel is to 
pass, set off on each side of the central meridian C D the spaces c a, c a', 
each equal to the half of x x, oi half a degree of longitude in that 
parallel; and in the same way at the 55th degree of latitude, set off the 
spaces d b, d V 3 each equal to half of the line y y : then draw the lines 
a b y q! b'y and the quadrilateral figure thus formed will constitute the 
projection of half a degree of longitude upon each side of the central 
meridian. In order to carry this onward to a whole degree on either 
side, extend a pair of compasses between the points a b' , or a' b } which 
will thus measure the diagonals of an entire degree, and, fixing one leg of 
the compass at the point c, describe, with the radius a V 3 the arc e e' 3 and 
from the point d 3 with the same radius, the arc //'; then from the point c f 
with the radius a a' (= x x, see diagonal scale), and from the point d , 
with bb' ( = y y 3 see diagonal scale), as radii, describe arcs intersecting the 
others in the points /,/', e , e! ; join the points cf 3 c f, de 3 d e' 3 by straight lines, 
and draw lines passing through e /, e' f (which will represent meridians), 
and the projection will be formed for 1° on each side of C D. 
This process must be carried out on each side of C D as far as the map 
requires; thus from the points / and e 3 with the same diagonal a b' 
as a radius, the arcs g 3 h must be described and intersected by other 
arcs measuring the lines x x , y y; and in the same way from the 
corresponding points e' /'. In the present case (see Eig. 1) this is 
carried on to a distance of 4° of longitude, on each side of C D, and 
the lines cf 3 fh 3 h k 3 k n; d e 3 e g, g i 3 i m, joining the points thus found, 
will give the proper amount of curvature to the parallels which they 
represent. As these parallels include 4° of latitude, the lines e /, g 7i, 
etc., must be divided into four equal parts, and a space equal to one 
of these parts, or 1°, set off upon each of the meridians above and 
below the parallels already drawn. These divisions being then joined 
* These parallels are chosen because the errors in distance inherent to the 
projection are more nearly balanced throughout the map. 
