The intercept method explained

The problem it solves

A sight puts you on a circle of equal altitude around the body's ground position. The circle may be thousands of miles across, so you cannot draw it on a chart. You only need the short piece near you, which is close enough to a straight line.

The idea

Pick a position near where you think you are. Calculate what the body's altitude and bearing would be from there at the time of the sight. Then compare that with what you actually measured:

• If the measured altitude is greater, the body is higher in your sky than at the chosen position, so you are closer to its ground position: toward.
• If it is less, you are farther off: away.

And by how much is simple: one minute of altitude is one nautical mile. A difference of 7′ means your line of position is 7 miles from the chosen position, along the body's bearing.

The steps

1. Ho: correct the sextant reading to the observed altitude.
2. GHA and declination of the body from the almanac, for the second of the sight.
3. LHA: the local hour angle, GHA minus west longitude or plus east.
4. Hc and Zn: the computed altitude and true bearing at the chosen position, from sight reduction tables or a formula.
5. Intercept = Ho − Hc, in minutes, which are miles. Ho greater: toward. "Ho Mo To": Ho more, toward.
6. Plot: from the chosen position, draw the bearing Zn. Step the intercept along it, toward the body or away. Draw a line at right angles there. That is your line of position.

Why an "assumed position"?

The tables list Hc only for whole degrees of latitude and of LHA. So instead of your DR, you work from an assumed position: the nearest whole degree of latitude, and a longitude within 30′ of your DR chosen so that LHA comes out whole. With a calculator you can work straight from the DR. Either way the line of position lands in the same place; only the intercept differs. The sight reduction calculator shows both side by side.

From one line to a fix

One sight gives one line: you are somewhere on it. Cross it with a second line from another body for a fix, or with a line from the same body some hours later, moved forward by the distance you sailed, for a running fix. Three stars at twilight, spread around the horizon, give a small triangle and a check on your work.