167

RULES FOR CORRECTING THE DEAD RECKONING BY AN OBSERVATION.

NOTWITHSTANDING the rules already laid down for keeping a ship's way at sea, yet by reason of the several accidents that may attend a ship in one day's run, such as swelling seas, different rates of sailing between the times of heaving the Log, want of care at the helm in letting the ship fall off, or come to, accidental currents, sudden squalls, when no account can be kept, &c. the latitude by account and latitude by observation may very often differ, then it is necessary that proper corrections be made in the difference of longitude.

When you have made all proper allowances you can, such as for leeway, variation, currents, &c. and still find that your latitude by account will not agree with your latitude by observation, then you must correct as follows:

First, consider whether you have made proper allowances for currents, heave of the sea, if the course of the helm has been carefully attended to, if the log-line and half-minute glass be just, and the log properly hove, or any sudden squalls, or proper allowances made for the leeway, &c. which of these you conjecture your error is in; make what allowances, you think meet to your difference of latitude and departure by dead reckoning, and see if that will reform your latitude by account, so as to make it agree with your latitude by observation; if it does, you have. guessed right (for you must always keep to the latitude by observation, it being the only thing to be depended on); but if it will not agree with the observed latitude, it is to be supposed that there are mistakes in your conjecture, or some other cause, which produces the error in the reckoning, and stands in need of being corrected. In this case, you are first to examine your log-line and half-minute glass, and if there be an error in hem, allow for it, as in the following Examples:

EXAMPLE I.

Yesterday at noon, we were in latitude 48° 20′ N. and till this day at noon we have sailed S. S. W. 48 miles, S. W. by S. 36 miles, N. E. 24 miles, and find by good observation that we are in latitude 47° 14′.

By the Traverse Table it appears, that by account the diff. of lat. is 57.2 S. and the departure 21.4 W.

Differing 9 miles from the true latitude by observation.

Wherefore I examine the log-line and half-minute glass, and find that the former measures 52 feet between knot and knot, and that the latter runs only 27 seconds. Now, as the log-line and half-minute glass are both faulty, I correct my difference of latitude and departure, as in Case III. and find my correct difference of latitude 66.2 S. and my departure 24.7 W.

Now from latitude left

Take diff. lat. corrected for error in dist.

Lat. in, corrected for error in dist.

48° 20' N.
1 6 S.

47 14

Agreeing exactly with my latitude by observation: I therefore conclude my reckoning sufficiently correct. Then, with the difference of latitude, 66.2, and departure 24.7, together with yesterday's latitude, I find the difference of longitude either by Middle Latitude, or Mercator's Sailing.

In the last example 57.2 and 21.4 multiplied severally by 156, thrice the measured length of a knot, and divide the two products by 135, five times the measured time of the glass, will give the difference of latitude 66,1, and departure 24.7, which is the same thing as if every course had been corrected separately.

EXAMPLE 11.

Yesterday at noon we were in lat. 36° 15′ N. and have sailed these 24 hours S. E. E. 55 miles, N. E. by N. 20 miles, W. S. W. 70 miles, S. by W. W. 20 miles, and by observation this day at noon we were in lat. 34° 56' N.

By the Traverse Table it appears, that by account the diff. of lat. is

64.2 S. and the departure 16.9 W.

. 36° 15′ N.

Difference of latitude by account 1 4S. Lat. obs.

Latitude in by account

Differing 15 miles from the latitude by observation.

I now examine the log-line and half-minute-glass, and find them both right. Next I consider whether there be any current, and I think I have reason to suspect one; upon trial I find there is one setting S. S. W. W. at the rate of 7 fathoms an hour, and judge I have been in it these 24 hours. Then 7 fathoms (or tenths of a knot) per hour, in 24 hours, makes about 17 miles: and to the dist. 17 miles, and course S. S. W. W. the diff. of lat. is 14.6 S. and departure 8.7 W.

Diff. lat.
Now by tra. table 64.2 S.
And by current 14.6 S.

Dep. |

16.9 W. Latitude sailed from
8.7 W. Diff. of lat. cor. for cur.

36° 15' N.

1 19 S.

Correct for cur. 78.8 S. 25.6 W. Lat. in, correct for cur. 34 56 N. Which agreeing with my latitude by observation, I conclude that my reckoning is right; then having the latitude left, and latitude come to, the difference of longitude may be found either by Middle Latitude or Mercator's Sailing, as before.

If, after all proper allowances are made for errors in distance, currents, &c., the latitude by account and observed latitude should disagree, then the reckoning must yet be further corrected; and to do which, the following are the common, and seem to be the most rational, methods:

CASE I.

If the Course found by Dead Reckoning be less than three Points, or thirty-three Degrees.

RULE. To the difference of latitude and departure by account find a course; with this course and the difference of latitude by observation, find the difference of longitude, either by Middle Latitude, or Mercator's Sailing.

EXAMPLE.

Yesterday at noon we were in lat. 39° 18' N. by an observation; this noon we are in lat. 37° 48' N. and our dead reckoning gives 107 miles of southing, and 64 of westing; required the true difference of longitude?

To the difference of latitude 107, and departure 64, I find the course 2 points; then with the meridional difference of latitude between the two observations 115, and the same course, I find the true difference of longitude 69 miles.

CASE II.

If the Course found by Dead Reckoning be more than three Points, or thirty-three Degrees, and less than five Points, or fifty-six Degrees. RULE. With the diff. of lat. and dep. by account, find the distance; with this distance, and diff. of lat. by observation, find another departure. Take half the sum of this dep. and dep. by account, for the true dep. with which, and the diff. of lat. by observation, find the diff. of longitude.

EXAMPLE.

Yesterday at noon we were in lat. 52° 40′ N. and are this noon in lat. 54° 22′ N. having by account made 84 miles of northing, and 76 miles of westing; required the true difference of longitude? To the diff. of lat. 84, and dep. 76, the distance is 113 miles, and the course 42o.

To dist. 113, and diff. of lat. between the two observations 102, the dep. is 49.5; then 76 added to 49.5 is 125.5, half of which is 62.7, the true dep..

To dep. 62.7, and diff. of lat. by observation 102, the course is 31o, and with the course 31° and the meridional diff. of lat. be-. tween the two observations 171, I find the diff. of long. is 103 miles.

CASE III.

If the Course by Dead Reckoning be more than five Points, or fiftysix Degrees.

RULE. With the diff. of lat, and departure by account find the distance; then with this dist. and diff. of lat. by observation find the diff. of long.

EXAMPLE.

Yesterday at noon we were in lat. 38° 52' N., to-day at noon we are in lat. 40° 18' N., and by account have made 68 miles northing, and 112 miles of westing; required the true diff. of longi

tude?

With the diff. of latitude 68, and departure 112, I find the distance 131 miles, and to distance 131, and difference of latitude by observation 86, the course is 49°, nearly; with this course, and the meridional difference of latitude between the two observations 111, the difference of longitude is 128 miles.

The reason of the above rule is plain, if we consider, that when a ship sails near the meridian, it will require a sensible error in the course, to make any considerable error in the difference of latitude; which can hardly happen if proper care is taken at the helm, and therefore it is most likely that the error is in the distance run; but when the course is near the middle of the quadrant, or between 3 and 5 points from the meridian, it is then probable the error may

be in both course and distance; and when the course is more than five points from the meridian, it is then most likely the error is in the course, as it will require a great error in the distance to make any considerable one in the difference of latitude.

NOTE. As the true place of a ship depends upon her latitude and longitude being truly ascertained, I have set these down only, the rest being of less consequence to the mariner.

To correct for several Days.

By help of the three preceding rules, the longitude may always be corrected for a single day; but if an observation has been wanted for one or more days, then mark the latitude and longitude at last observation, or if this be your first observation since leaving the land, mark the latitude and longitude of the land you left; this is the only latitude and longitude you can call certain; all the fol lowing part of the reckoning must undergo a correction, which is made as follows:

Take the northings, southings, eastings, and westings, that you have made since your last observation; or, if this be your first observation, then for every day from your leaving the land, minding not to leave out the difference of latitude and departure of the day you correct on, and bring them into the Traverse Table, by which you will have the whole difference of latitude and departure by account since the last observation; and with that same difference of latitude and departure find the course by dead reckoning; then observe which of the foregoing cases that course falls under, and correct by the rule for that case. But when an observation has been wanting for several days, then mark the latitude and longitude you were in at your last observation, or on leaving the land as before, and then you may correct with a greater degree of certainty, especially in high latitudes, by the following rules;

CASE I

Reckoning from the last certain latitude and longitude.

When the course given by the meridional difference of latitude and difference of longitude by account, taken as difference of latitude and departure, is less than three points, or 33 degrees.

RULE. To the meridian difference of latitude and difference of longitude by account (taken as difference of latitude and departure, as shown in Mercator's Sailing), find a course; with this course, and the meridian difference of latitude by observation, find a corresponding departure, which will be the correct difference of longitude.

EXAMPLE I.

Having sailed three days ago from latitude 49° 57' N., and got no observation till this day at noon, and find I am in latitude 45° 23' N., and by dead reckoning I am in 45° 12' N. having differed my longitude 183 miles; required my difference of longitude?