A manual of the principles and practice of road-making: comprising the location, construction, and improvement of roads, (common, macadam, paved, plank, etc.) and rail-roads. By W. M. Gillespie ...

39 APPENDIX B.
APPENDIX B.
LOCATION OF ROADS.
1. Planning the Route.
TEm true bearing or azimuth of one place from another, when
the latitude and longitude of each are given, can be found by
spherical trigonometry. But if the two places be very distant, the
"rhumb" or loxodromic line between them, i. e., the line having
the same bearing throughout its length, will not be the shortest
distance. The arc of the great circle passing through the points
must then be adopted. Its bearing, i. e., the angle which it makes
with the meridians which it crosses, will be constantly changing.
Thus, if one point be due west from another, the east and west
line, i. e., the parallel connecting them, is not the shortest line between them. For example, calling San Francisco due west from
St. Louis, the shortest line between them by an arc of a great circle
is about 9 miles shorter than the due west line following the parallel of latitude, and runs about 70 miles north of this parallel.
A similar difference exists for every other line except a due north
and south line.
For these reasons, in planning a long route, the position of points,
situated on the are of a great circle connecting the extremities,
should be determined in advance by calculating their latitude and
longitude. It would usually be impossible to follow this line perfectly, but it should be approximated to as far as possible, as is
done for a straight line for short distances, as on page 82.
Other considerations cause the line of a railroad to deviate
from the shortest line, as in common roads, in order to obtain good
grades, moderate cuttings and fillings, and to pass through certain
ruling points on the line.