Lectures in Navigation

Friday Lecture

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 N_S.

IV. Find the algebraic difference of the Latitude and Declination, and from Table 45 take out the Natural Haversine of this algebraic difference angle. Mark it N_D±L

V. Add the N_S to the N_D±L, and the result will be the Natural Haversine of the calculated zenith distance. Formula N_ZD = N_S + N_D±L

VI. Subtract this calculated zenith distance from 90° to get the calculated altitude.

VII. Find the difference between the calculated altitude and the true altitude and call it the altitude difference.

VIII. In your Azimuth Table, find the azimuth for the proper "t," L and D.

IX. Lay off the altitude difference along the azimuth either away from or toward the body observed, according as to whether the true altitude, observed by sextant, is less or greater than the calculated altitude.

Altitude Difference along the Azimuth

X. Through the point thus reached, draw a line at right angles to the azimuth. This line will be your Line of Position, and the point thus reached, which may be read from the chart or obtained by use of Table 2 from the D. R. Position, is the nearest to the actual position of the observer which you can obtain by the use of any method from one sight only.

Example:

At sea, May 18th, 1919, A.M. Circle with line under 29° 41' 00". D.R. Latitude 41° 30' N, Longitude 33° 38' 45" W. WT 7h 20m 45s A.M. C-W 2h 17m 06s CC + 4m 59s. IE - 30". HE 23 ft. Required Line of Position and most probable position of ship.

WT	18d 7h 20m 45s A.M.
	- 12
	————————————
WT	17d 19h 20m 45s
C-W	2 17 06	Corr.	+ 9' 34"
	————————————	IE	- 30
CT	17d 21h 37m 51s		—————
CC +	4 59		+ 9' 04"
	————————————
G.M.T.	17d 21h 42m 50s	Circle with line under	29° 41' 00"
Eq. T. +	3 47		+ 9 04
	————————————		—————
G.A.T.	17d 21h 46m 37s	Circle with line through	29° 50' 04"
Lo. in T	2 14 35 (W - )
	————————————	log hav	9.48368
L.A.T.(t)	17d 19h 32m 02s	log cos	9.87446
Lat.	41° 30' N	log cos	9.97473
Dec.	19° 21' 25" N		————
		log hav S	9.33287
		N s	.21521
L ~ D	22° 08' 35"	N D ± L	.03687
			————
Calc. ZD	60° 16' 30"	N ZD	.25208
	- 90° 00 00
	——————	TZ found from table to be N 90° E.
Cal. Alt.	29° 43' 30"
Circle with line through	29° 50' 04"
	——————
Alt. Diff	6' 34" Toward.

Course.	Dist.	Diff. Lat.	Dep.	Diff. Lo.
90°	6' 34"	0	6.5	8.6

D.R. Lat.	41° 30' N	D.R. Lo.	33° 38' 45" W
Diff. Lat.	-	Diff. Lo.	8 36 E
	——————		——————
Most probable fix	Lat. 41° 30' N		Lo. 33° 30' 09" W

As azimuth is N 90° E, Line of Position runs due N & S (360°) through Lat. 41° 30' N. Lo. 33° 30' 09" W.

Assign for work in class and for Night Work examples such as the following:

1. July 11th, 1919. Circle with line under 45° 35' 30", Lat. by D. R. 50° 00' N, Lo. 40° 04' W. HE 15 ft. IE - 4'. CT (corrected) 5h. 38m 00s P.M. Required Line of Position by Marc St. Hilaire Method and most probable fix of ship.

2. May 16th, 1919, A.M. Circle with line under 64° 01' 15", D. R. Lat. 39° 45' N, Lo. 60° 29' W. HE 36 ft. IE + 2' 30". CT 2h 44m 19s. Required Line of Position by Marc St. Hilaire Method and most probable fix of ship.

Etc.