The Latitude laft found, differing only one Mile from that used in the Operation, may be depended on as the true Latitude. Hence it is plain, that the Operation is repeated with very little additional Trouble, but few Alterations being neceffary.

Being at Sea in the Latitude of 60° o' North by Account, when the Sun was on the Equator, and confequently had no Declination, at I H. o M. P. M. per Watch, his Altitude was 28° 53', and at 3 H. o M. P. M. per Watch, it was 20° 42'. Required the true Lat. Lat. 60° 0' 0,30103 Dec. 000,00000

'Times.

H. M. S.

I O 0 300

Alt. N: S.

28 53=48303

20 42 35347

Nat. S. Sun's Mer. Alt. 5000730° o' Sun's Meridian Alt.

60 o Latitude

The Latitude by Computation, coming the fame with the Lati tude by Account, fhews that the Latitude by Account was right. From the foregoing Examples it is plain, that the Operation is the fame, whether the Sun hath North or South Declination. And it will be the fame whether the Ship is in a North or South Latitude. It is alfo clear, that when the Sun has no Declination, the Secant, rejecting the Index of the Latitude is the Log. Ratio.

Wanting to go through the N. Channel among the Maldives, and by Account being Latitude 7° 40' N. the Declination being then 22° 47' N. at 7 H. 25 M. 40 S. A. M. the true Altitude of the Sun's Centre was 22° 30', and at 10 H. 31 M. 48 S. A. M. it was found 63° 40'. Required the Ship's true Latitude?

Elap. T. 3 6 8

51355

Its Log.

4,71058

El. T. 1 33 04 Its Log. in Col. of Elap. Time is

0,40368

3 I 30

H. M. S.

3

I 30

5,15344

True T. 1 28 26 Its Log, in Col. of Rifing is

3,86709

T.p.W.1 28 12

Log. Ratio

0,03918

N. B. As the Tables are only calculated to 30 Seconds, the Log: for any intermediate Seconds is found by taking the Difference be tween the Log. next greater and next lefs, and faying, as 30 Seconds is to that Difference, fo is the given Seconds to the Difference of the Logarithms; or, if it be any even Part, take fuch a Part of the Difference, and apply it to the next lefs Logarithm; but in these Operations a few Seconds are not regarded.

6733 N. Nu.

N. S. Sun's M. Alt.96356=74 29.

The Latitude laft found, agreeing with that used in the Operation, it may be taken as the True Latitude; and the Operation is repeated with very little additional Trouble, but few Alterations being ne

3,86709

Log. Ratio

0,03878

ceffary. Hence it is plain, that if you are mistaken in the Latitude by Account, yet by repeating the Work two or three Times, making Ufe of the Latitude laft found in the next Operation, it will at last discover itself to be true, by being equal to the last Suppofition, which evidently fhews the Excellency of thefe Tables.

In the former Examples we have confidered both Altitudes taken at the fame Place or Station; but as that is feldom the Cafe at Sea, the neceffary Correction for any Alteration of Station may be readily made as follows:

Suppose the firft Altitude in the Forenoon at
The fecond Altitude in the Afternoon at 2 H. 43 M.
Difference of Longitude made is 30 Miles W. equal to

H. M.

10 26

14 43

0 2

14 41

10 26

4 15

Subtracted is the elapfed Time

If a Ship has been failing to the Eastward, the above two Minutes must be added; but unless the Difference of Longitude be confiderable, it is not worth Notice, as it will make a very inconfiderable Error in the Latitude.

Again, if the Ship fails or makes towards that Point of the Compass which the Sun bears upon, she must raise the Sun's Altitude as many Minutes as the Miles he has run towards it; therefore the Miles run towards the Sun must be added to the firft Altitude; but if failing from the Sun, the fame must be subtracted: If they are but few, they are not worth minding; and then the Seaman may make a very good Eftimation by looking at the Log-board only, who, by that, will be able to afcertain the Distance failed to, or from the Sun, between the Observations, which will be of fufficient Exactnefs in the Practice of Navigation; and if the Ship makes an Angle with the Sun's Bearing, it may be readily found by the Table of Difference of Latitude and Departure, and then either add or subtract, according as the Cafe requires; as may be seen in the following Examples, which are inferted for the Benefit of those who require a greater Degree of Accuracy.

Suppofe a Ship from the Bay of Biscay, bound to the English Channel, in a brifk Gale running N. by E. & E. per Compafs at the Rate of 9 Knots per Hour, at 10 H. o M. A. M. per Watch; obferved the Sun's Altitude 13° 18' bearing South E. by Compass, and at 1 H. 40 M, P. M. per Watch, the Sun's Altitude again was found 14° 15', the Latitude by Account being 49° 17' N. and the Sun's Declination 23° 28' S. Required the true Latitude.

The Correction to the firft Altitude.

The Time of the first Obfervation is 10 H. o. M. A. M. and of the fecond 1 H. 40 M. P. M. the Elapfed Time is 3 Hours 40 M. and the Rate of Sailing is 9 Miles per Hour; then fay, by the Rule of Three, as 1 H. is to 9 Miles, fo is 3 H. 40 M. to 33 Miles, the Distance run in the Elapfed Time..

Again, the Sun's Bearing at the firft Obfervation is South E. the oppofite Point to which is N. 1 W. or 4 Point, and the Ship's Courfe during the Elap. Time is N. by E. & E. 1 Points, fo the Angle of Ship's Courfe with the Sun's Bearing is 2 Points.

Now in the Table of Difference of Latitude and Departure, to the Course 2 Points, and Distance 33, the Difference of Latitude is 29, and the Ship is failing from the Sun; therefore from the first. obferved Altitude 13° 18' take 29', the Remainder 12° 49', the first Altitude corrected, which is to be used in the Operation as follows: Lat. 49° 17′ 0,18554

H. M. S. Times JO O O

Alt. Nat. S.

14°15'=24615

Decl.

23 28

0,03749

12 49 22185

Log. Ratio

0,22303

Its Log.

3,38561

1ts Log.

0,33559

Zen. Dift. 72 25 N. S. M. Alt. 30221 17 35

Decl.

23 28

But as the Latitude by Computation differs confiderably from that by Account, the Work must be repeated.

Lat.

48° 57' 0,18262

Tr. Lat. 48 55 N. 30259 N. S. Mer. Alt. 17° 37'. This Latitude differing only 2 Miles from that ufed in the Computation, it may be depended upon as the true Latitude.

A Ship failing N. E. half E. by Compass, at the Rate of 9 Knots an Hour, at o H. 31 M. 40 S. P. M. per Watch I found the Altitude of the Sun's lower Limb 28° 20′ above the Horizon of the Sea, the Eye being elevated 20 Feet above the Surface of the Water, and the Sun's Bearing by Compafs being at the fame Time S. by W. and at 2 H. 58 M. 20 S. P. M. by Watch, the Altitude of the Sun's lower Limb was 16° 41′ above the Horizon, the Eye being elevated as before, and the Latitude by Account, at the Time of the laft Obfervation, was 48° o' North, and the Declination 13° 17′ South. Required the true Latitude at taking the last Observation.

First observed Alt. of S's lower Limb 28° 20' Second ditto 16° 41' Refraction to be fubtracted

2

Correction for Refraction

28 18

3 16 38

Dip of the Horizon fubtracted

4

4

Correction for the firft Altitude.

The Time of the first Observation o H. 31 M. 40 S. P. M. of the Second 2 H. 58 M. 20 S. P. M. fo the Elapsed Time is 2 H. 26 M. 40 S. the Rate of Sailing is 9 Miles per Hour. Then as 1 H. 9 Miles 2 H. 26 M. 40 S.: 22 Miles, the Distance run in the Elapfed Time.

Again, the Sun's Bearing at the firft Obfervation is S. by W. the oppofite Point to which is N. by E. or 1 Point.

The Ship's Course during the Ela. Time is N. E. E. or 4 Pts. So the Angle of the Ship's Courfe with N. E. by N. E. 3 § Pts. the Sun's Bearing is

In the Table of Difference of Latitude and Departure, to the Course 3 Points, and Distance 22 Miles, the Difference of Latitude is 17 Miles, while the Ship fails from the Sun.