CASE III.

If the Courfe by Dead Reckoning be more than 5 Points, or 56o. RULE. With the Diff. of Lat. and Departure by Account find the Distance; then with this Dift. and Diff. of Lat. by Obfervation find the Diff. of Long.

EXAMPLE.
M PLE.

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 of Northing, and 112 Miles of Wefting; required the true Dif. of Longitude?

With the Diff. of Lat. 68, and Depar. 112, I find the Dift. 132 Miles, and to Distance 132, and Diff. of Lat. by Obfervation 86, the Courfe is 49° 30′ nearly; with this Courfe, and the Meridional Diff. of Lat. between the two Obfervations 111, the Diff. of Long. is 130 Milės.

The Reason of the above Rules is plain, if we confider, that when a Ship fails near the Meridian it will require a fenfible Error in the Course to make any confiderable 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 the Course and Distance; and when the Courfe 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 confiderable one in the Difference of Latitude. NOTE. As the true Place of a Ship depends upon her Lat. and Long. being truly afcertained, I have fet these down only, the rest being of lefs Confequence to the Mariner.

To correct for feveral Days.

By Help of the three preceding Rules, the Long. may always be corrected for a fingle Day, but if an Observation has been wanted for one or more Days, then mark the Lat. and Long, at laft Obfervation, or if this be your firft Obfervation fince leaving the Land, mark the Lat. and Long. of the Land you left; this is the only Lat. and Long. you can call certain; all the following Part of the Reckoning muft undergo a Correction, which is made as follows:

Take the Northings, Southings, Eaftings, and Westings, that you have made fince your laft Obfervation; or if it be your first Obfervation, then for every Day from your leaving the Land, minding not to leave out the Diff. of Lat. and Dep. of the Day you correct on, and bring them into a Traverfe Table, by which you will have the whole Diff. of Lat. and Dep. by Account fince the laft Obfervation; and with that fame Diff. of Lat. and Dep. find the Course by Dead Reckoning, then obferve which of the foregoing Cafes that Courfe falls under, and correct by the Rule for that Cafe. But

when an Obfervation has been wanting for feveral Days, then mark the Latitude and Longitude you were in at your laft Obfervation, of leaving the Land as before, and then you may correct with a greater Degree of Certainty; efpecially in High Latitudes, by the following Rules.

CASE I.

Reckoning from the laft certain Latitude and Longitude.

When the Courfe given by the Meridional Diff. of Lat. and Diff. of Long. by Account, taken as Diff. of Lat. and Dep. is lefs than 3 Points, or 33 Degrees.

RULE. To the Mer. Diff. of Lat. and Diff. of Long. by Account (taken as Diff. of Lat. and Dep. as fhewn in the Mercator's Sailing) find a Courfe, with this Courfe and the Merid. Diff. of Lat. by Obfervation, find a correfponding Dep. which will be the correct Diff. of Long.:

Having failed three Days ago from Lat. 49° 57' N. and got no Obfervation till this Day at Noon, and find I am in Lat. 45° 23' N. and by Dead Reckoning I am in 45° 12' N. having differed my Long. 173 Miles, required my true Difference of Longitude?

To Merid. Diff. of. Lat. by Acc. 423, and Diff. of Long. by Acc. 173, the Courfe is 22° 15'. Then with the Courfe 22° 15', and Meridional Diff. of Lat. between the Obfervations 407, I find the Diff. of Long. is 167 Miles.

When the Courfe given by the Meridional Diff. of Lat. and Diff. of Long. by Account (taken as before) is greater than 3 Points, and lefs than 5 Points.

RULE. To the Merid. Diff. of Lat. and Diff. of Long. by Account, taken as Difference of Latitude and Departure, find a Diftance; with this Distance, and Meridian Difference of Latitude by Obfervation, find a correfponding Departure; Half the Sum of this Departure, and the Difference of Longitude by Account, is the correct Difference of Longitude.

EXAMPLE II.

Three Days ago we were in Lat. 45° 23′ N. and have fince that Time failed between South and Weft, have by Dead Reckoning altered our Lat. 94 Miles, and our Long. 147 Miles; but by an Obfervation this Day, we find we are in Lat. 43° 34'; required the correct Difference of Longitude?

M. Parts,

M. Parts.

With the Meridian Difference of Latitude by Acc. 132, and Difference of Longitude by Acc. 147, I find the Distance 198, and Courfe 48°. Then to Distance 198, and Meridian Difference of Latitude by Obfervation 153, the Dep. is 125; now 125 added to 147 is 272, and half this Sum, viz. 136, is the correct Diff. of Lon.

CASE III.

When the Course given by the Meridian Difference of Latitude and Difference of Longitude by Account (taken as before) is more than 5 Points or 56 Degrees.

RULE. To the Meridian Difference of Latitude and Difference of Longitude by Account, taken as Difference of Latitude and Depart. find a Distance.

To this Distance and Meridian Difference of Latitude by Obfervation, find a correfponding Departure, this Departure will be the correct Difference of Longitude.

Two Days ago I was in Latitude 43° 34′ N. and have fince then made by Account 50 Miles of Southing, and 256 Miles Difference of Longitude Weft, but find by Obfervation that I am in 42° 30' N. what is my true Difference of Longitude?

2910 Lat, failed from 43° 34′
Lat. by Obfer. 42 30

M. Parts.

M. Parts.

Lat. failed from 43° 34'N.

2910

Lat. by Account 42 44 N.

2841

2822

Mer, Diff, of Lat, by Acc.

69

Mer. Diff. of Lat. by Obfer. 88

Then to Meridian Difference of Latitude by Account 69, and Diff. of Longitude by Account 256 (taken as Difference of Latitude and Departure) the Distance is 265, and Course 75 Degrees.

And to Diftance 265, and Difference of Latitude 88 (the Merid. Difference of Latitude by Obfervation) the Dep. is 250, which is the correct Diff. of Long.

Here we have given at fome Length the different Methods of correcting the Dead Reckoning by an Obfervation, which are readily done by the Table of Difference of Latitude and Departure.

The Ship's Way is generally greater than the Distance given by the Log, and it is always fafeit to have the Reckoning a-head of the Ship, that the Mariner may be looking out for Land, and not make it before he is aware of it,

When a great Sea fets after the Ship, it is common to allow one Mile over for every ten given by the Log, for the Heave of the Sea; but if the Sea be againft or athwart her, her Distance must be less than that given by the Log.

The Error in the Ship's Reckoning is frequently attributed to unknown Currents; for by various Caufes yet undetermined, there are many counter Motions of the Water in the open Seas, as well as thofe obferved near the Shores, where the Motions may be tolerably well accounted for. Some of the obferved Currents in the great Seas may perhaps be owing to the Tides following the Moon, and to the libratory Motion the Waters may have thereby, and the unfettled Setting and Drift of thefe Currents may poffibly depend on the Change in the Moon's Declination. However, it is well known from Obfervations, that the Trade Winds occafion a confiderable Current within their Limits, particularly within the Torrid Zone, where the Motion is perpetually towards the Weft, at the Rate of 8 or 10 Miles a Day, but at the Extremities of the Trade Winds, or near the Latitudes of 30° N, or S. it is likely that the Currents are compounded of the faid Western Motion, and of one towards the Equator; therefore, all Ships failing within these Limits fhould allow a Course each Day for this Current.

NOTE. When the Difference of Latitude by Account is lefs than the Difference of Latitude by Obfervation, the Ship is a-head of the Reckoning, but if lefs, the Reckoning is a-head of the Ship.

ge

When the Mariner is dubious of his Account of Longitude, he nerally runs into the Latitude of the intended Port, and then fails E. or W. if there be Sea Room, according as it is fituated, and keeps a good Look-out for the Land.

The Method I have chofen to introduce the young Mariner into the most capital Part of Navigation is, by fhewing him firft how to work a few separate Day's Works independant of each other, and then proceed to a continued Journal from London to Madeira, and back again to England, in which will be inferted most of the Occurrences that commonly happen at Sea, or in Harbour.

I have feen many young Navigators who have been taught the Prin ciples of Navigation on Shore, very deficient in keeping a Journal at Sea; and, therefore, must request the Teacher not to omit putting the Pupils over the following Journal, which will render them ready at Working a Day's Work at Sea, and confirm in their Memory thofe Rules they have been over.

Yesterday at Noon we were in the Latitude of 46° 28′N. Longitude 22° 18′W. and have failed till this Day Noon, as by the Log-board, the Tide having all the Time fet S. by E. 2 Miles per Hour: Required the Ship's Place and the direct Course and Distance made good?

The Courses and Winds on the Log-board being examined, it appears that the Ship goes large, and has no Lee-way; therefore the feveral Courfes from the Logboard are entered in the Traverfe Table without Alteration.

Next the Fathoms and Knots belonging to each Courfe are fummed up, and the Refults are put in the Column of Diftances in the Traverse Table; and to these Courses and Distances, the whole Difference of Latitude and Departure are found.

Then having the Latitude left, and the Latitude come to; find the Complement of the Middle Latitude, and with that, and the Departure, find the Course, &c. by Middle Latitude Sailing.

Or with the Courfe, and Meridional Difference of Latitude, find the Difference of Longitude, by Mercator's Sailing.

NOTE. When the odd Fathoms are above five, we allow one Knot, but, if under five, nothing is allowed.

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