EXAM. 1. A fhip from latitude 56° 4′ N. and longitude 3° W. fails N. N. E. E. until fhe is in latitude 60° 29′ N.; required the distance failed, and the longitude come to ?

Anf. The diftance is 293.1 miles, and the fhip hath come to o° 59′E. longitude.

2. A fhip from latitude 52° 20′ N. and longitude 6° 24′ W. fails W. S. W. W. until fhe is in latitude 47° 49′ N.; what distance hath fhe failed, and what longitude hath she come to ?

Anf. Distance failed is 804.5 miles, and the longitude come to is 26° 5′ W.

CASE 4. Given the difference of latitude and diftance, to find the course and difference of longitude.

EXAM. I. A fhip from latitude 53° 14' N. and longitude 2o E. fails 256 miles between N. and E. and then is in latitude 56° N.; required her courfe and prefent longitude?

Anf. Course 49° 35' Northeastward, or N. E. E. 44 longitude 7° 37′ E.

2. A fhip from latitude 40° 25' S. and longitude 40° 25′ W. fails 413 miles between N. and E. and is then in latitude 360 19' S.; what was her course, and what longitude hath fhe come to?

Anf. Course 53° 27′, or N. E. E. and the fhip has come to longitude 33° 22' W.

When a table of meridional parts is not at hand, the defect may be fupplied by the logarithmic tangents. See Robertfon's Navigation, 2d edition, page 532.

Λ

1

1. To find the meridional parts answering to any given latitude.

To half of the given latitude add 45°; find the logarithm tangent of the fum, reject the index, and of the seven remaining figures, point off three on the right hand for decimals; then divide by 1.2633114, the quotient is the meridional parts required.

Note. 1.2633114 is the natural tangent of 51°38' 9".

EXAM. Required the meridional parts answering Anf.-4527.36.

to 60o of latitude ?

whofe logarithmic tangent is

10.5719475. This without its index, and pointed by the rule is 5719-475, and then divide it by 1.2633114.

1.2633114)5719.4750(4527.36 the answer.

2. Required the meridional parts answering to la

1.2633114)5065.9030(4010.019

2. To find the meridional difference of latitude between any two places, their latitudes being given. When the given places are both in north, or both in fouth latitude,

Take

Take the difference of the logarithm tangents of the half complements of the latitudes; account four figures of it next the index to be integers, and then divide it by 1.2633114; the quotient is the meridional difference of latitude.

EXAM. 1. Required the meridional difference of latitude between 13° 30' and 500 North latitudes?

Anf 2656.87.

The half comp. of 13° 30' is 380 15
The half comp. of 5000

is 20.00

1,2633114)3356.4570(2656.87

Log, Tan. 9.8967116

9.5610659

3356.457

2. Required the meridional difference of latitude between the Lizard, in latitude 49° 57′ N. and Cape Verd, in latitude 14° 43′ North?

Anf. 2576.93.

Half complement of 14° 43' is 37° 38'
Half complement of 49° 57' is 20° 1′

1.2633114)3255.4730(2576.93

Log. Tan. 9.8872024 9.5616551

3255-473

When one place is the North latitude and the other the South, add 90° to one of the latitudes, and take half of the fum for the half complement of that latitude; take half the complement of the other latitude, and divide the difference of the logarithm tangents of these two by 1.2633114, the quotient is the meridional difference of latitude. Or,

Take the half complements of the latitudes as before; take the fum of the logarithm co-tangents of