64 
HltfTS TO TRAVELLERS. 
by straight lines, the intermediate and extreme parallels will also bd 
obtained; and all that remains to be done is to draw the lines forming 
the border of the map, and mark on them the divisions and numbering 
of the degrees. 
In this example the meridians converge towards the top of the map 
as the latitude is north, but these rules apply equally ih south latitude, 
only the meridians will in that case be found to converge towards the 
bottoim 
When bearings taken at any station have to be shown on the map, they 
must be laid off from the meridian passing through that station . 
The following projection, which is employed in the Indian Government 
Surveys, is another modification of the conical development, and is used 
for projecting a map on a plane table sheet* It represents the parallels 
of latitude by concentric arcs, but the meridians by arcs concave to the 
central meridian, and not by straight lines as in the true conical develop¬ 
ment* A cone is assumed to roll over the spheroid tangentially to an 
adopted central parallel of latitude; the distance from the vertex of the 
cone to this parallel ( = normal x cot latitude) is the radius of projection 
of the parallel, and may be considered as the fundamental radius of the 
projection; for the radii of all other parallels are determined by adding 
to or subtracting from it the distances between those parallels and the 
central parallel. The angle subtended at the vertex of the cone by a 
longitudinal arc of 1° in length is called the “ angle of the projection” 
for the parallel of latitude to which the arc appertains; as this angle 
varies with the latitude, its value is computed for each parallel. 
The quantities given in the tables are: m = QR or PS (Fig. 3), the 
meridional distance between the parallels there stated, n ~ P Q and 
p = S R, the lengths of the corresponding portions of these parallels, 
and q = S Q or E P the diagonal of the square; m is obtained from 
Table B, and n and p from Table A by simple proportion, while q may 
be determined by proportion from Table C or as follows 
q 2 ss m 2 + n 2 — 2 m n cos P, 
and q 2 = m 2 + cos P, 
since angle E as 180° - angle P; 
therefore q 2 — m 2 -f np, 
and q - jsJ rri 2 + n p . 
