arc St. Hilaire Method, which we are to take up today, you will
learn how to get a line of position, at any hour of the day. By having
this line of position intersect your parallel of latitude, you will be
able to establish the position of your ship, both as to its latitude and
longitude.

Now you have already learned that in order to get your latitude
accurately, you must wait until the sun is on your meridian, i.e., bears
due North or South of you, and then you apply a certain formula to get
your latitude. When the sun is on or near the prime vertical (i.e., due
East or West) you might apply another set of rules, which you have not
yet learned, to get your longitude. By the Marc St. Hilaire method, the
same set of rules apply for getting a line of position at any time of
the day, no matter what the position of the observed body in the heavens
may be. Just one condition is necessary, and this condition is necessary
in all calculations of this character, i.e., an accurate measurement of
the observed body's altitude is essential.

What we do in working out the Marc St. Hilaire method, is to assume our
Dead Reckoning position to be correct. With this D. R. position as a
basis, we compute an altitude of the body observed. Now this altitude
would be correct if our D. R. position were correct and vice versa. At
the same time we measure by sextant the altitude of the celestial body
observed, say, the sun. If the computed altitude and the actual observed
altitude coincide, the D. R. position is correct. If they do not, the
computed altitude must be corrected and the D. R. position corrected to
coincide with the observed altitude. Just how this is done will be
explained in a moment. Put in your Note-Book:

_Formula for obtaining Line of Position by M. St. H. Method._

I. Three quantities must be known either from observation or from Dead
Reckoning.

1. The S. H. A., marked "t."

Note: The method for finding S. H. A. (t) differs when the sun or
star is used as follows:

(a) For the Sun:
Get G.M.T. from the corrected chronometer time. Apply
the equation of time to find the G.A.T. Apply the D.R. Lo.
(-W)
(+E) and the result is L.A.T. or S.H.A. as required.

(b) For a Star:
(Note to pupils: Leave this blank to be filled in when we
take up stars in more detail.)

2. The Latitude, marked "L."

3. The Declination of the observed body, marked "D."

II