**True direction and constant direction**

The concept
of direction is complicated by that fact that azimuth, or true direction, is
one thing and constant direction is another. Let's compare these two ideas,
using

The azimuth
from

Therefore,
as you follow an oblique arc, the angle at which you intercept meridians
changes with your latitude. The only great circles of constant azimuth are the
equator and the meridians.

In the
graphic below, a line of true direction from

In 1), the azimuth is
measured with respect to the prime meridian. In 2), the projection is recentered and the azimuth is measured with respect to the
30°E meridian. In 3), the projection is again recentered,
and the azimuth is measured with respect to the 60°E meridian. The arc of true
direction doesn't change; all that changes is the angle at which it intercepts
each meridian. (The projection used here is the Gnomonic, in which all great
circles project as straight lines.)

For
navigators, a line of true direction is a headache—it's the shortest way from A
to B, but you have to keep changing your compass bearings to stay on course.

A line of
constant direction (also called a *rhumb**
line* or *loxodrome*) is an alternative way
to get from A to B. It's not a great circle arc, so it's not the shortest route,
but it's easier to navigate because it crosses every meridian at the same
angle. You just follow a constant compass heading—say, 45 degrees—and
eventually you get to your destination.

The most
famous constant direction map is the Mercator. On it,
every rhumb line is projected as a straight line.

On a Mercator projection, all straight lines, like the blue line
from

On an azimuthal map, lines of constant direction are projected as
curves.

A
Gnomonic projection. The red line is azimuth; the blue line is constant
direction. The true distance from