Obtaining a Position Line
The difference between the True (TZD) and Calculated (CZD) Zenith Distances is the Intercept.
TRUE, TINY, TOWARDS
If the TZD is less than the CZD then the assumed position must be moved in the direction of the body by the amount of the Intercept. This gives a position of the correct distance from the body. It is known as the Intercept Terminal Position or ITP.
As the radius of the circle is normally very large, it is considered to be a straight line near this point. A line at 90 to the direction of the body is the Position Line.
Combining Position Lines
A single Position Line must be combined with other observations for a fix. This can be achieved using a plotting sheet and then transferring the ITP by the distance to the next sight and redrawing the Transferred Position Line in the same direction as the original.
For Sun sights, it is more usual to calculate the ITP of a morning sight and then calculate the transferred position for the Sun's Meridian Passage (Noon.) The difference between calculated and observed latitudes provides a longitude using “Plane Sailing.” With a little practice, this will be found to be a faster, not to mention more accurate method.
For Star Sights, many people use a single position and then plot the Position Lines without allowing for the vessel's movement. This may appear a sloppy practice but a few miles error mid-ocean is usually irrelevant. Even if the position at sunset was perfect, there is no guarantee that the position an hour later is within a mile. Indeed even if the position agrees perfectly with a GPS position, there is no guarantee that an intervening military operation has not thrown the GPS position out let alone a fault in the equipment/ aerial. “I am about here,” is a far safer assumption than “My wheelhouse is/ was within 10m of this position.”