Marc St. Hilaire Method By A Sun Sight
You have learned how to get your latitude by an observation at noon. By the Marc 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. Add together the log haversine of the S.H.A. (Table 45), the log cosine of the Lat. (Table 44), and the log cosine of the Dec. (Table 44) and call the sum S. S is a log haversine and must always be less than 10. If greater than 10, subtract 10 or 20 to bring it less than 10.
III. With the log haversine S enter table 45 in the adjacent parallel column, take out the corresponding Natural Haversine, which mark NS.