PRELIMINARY RULES IN NAVIGATION.

169. DEF.-The latitude and longitude of the place left are called the latitude from and longitude from; the latitude and longitude of the place arrived at are called the latitude in and longitude in.

170.

Given the latitude from and latitude in or to, to find the true difference of latitude.

To find the difference of latitude. (For definition, &c., see Nos. 149 and 150, pages 100 and 101.)

RULE XLII.

1. When the latitudes have like names-Subtract the less latitude from the greater, and multiply the degrees in the remainder by 60, adding in the minutes. The result is the true difference of latitude.

2o. When the latitudes have unlike names-Take the sum of the two latitudes, reduce it to minutes. The result is the true difference of latitude.

3°. To name the diff. lat.—If the latitude to is North of the latitude from, mark the diff. of latitude North (N.); but if latitude to is South of latitude from, mark diff. latitude South (S.)

If these different directions

Latitudes are reckoned north and south of the equator. are considered the one positive and the other negative, the difference of latitude of two places is always found by taking the algebraic difference of their latitudes.

the difference of latitude.

(a) When one of the places has no latitude, or is on the Equator, the latitude of the other place is equal to Ex. 7. A ship from a place A, lat. o, is bound to a place B, lat. 25° S.: required the diff. lat.

Ex. 8. A ship from a place A, in lat. 10° N., arrives at a place B, in lat. 0°: required the diff. lat. made."

One place being on the Equator, and the other in 10° N., the diff. of lat. is evidently 10° or 600', and is named S., because it is evident the ship must sail South to pass from 10° N. to o° N.

EXAMPLES FOR PRACTICE.

Required the difference of latitude between the place A and the place B in each of the following examples :

171. To find the meridional difference of latitude, having given the latitude from and latitude in. (For definition, see page 101, Nos. 151

RULE XLIII.

and 152).

Take the meridional parts for the two latitudes from the Table of meridional parts; take the difference if the latitudes are of the same name, but their sum if the names are unlike. The result is the meridional difference of latitude.

Find the meridional difference of latitude in each of the following examples :

I. Lat. from 34° 40' N. Lat. in. 33° 20' N. 4. Lat. from 15° 44' N. Lat. in 4° 20' 8.

60 20 S.

24 12 S.

15 18 N.

5.

49 10 S.

6.

172. To find the latitude in, having given the latitude from and true difference of latitude.

RULE XLIV.

1o. When the latitude from and true difference of latitude have a like name-To the latitude from add the true difference of latitude (turned into degrees, minutes, and seconds, if necessary): the sum will be the latitude in, of the same name as the latitude from.

2o. When the latitude from and true difference of latitude have unlike names-Under the latitude from, put the true difference of latitude (in degrees and minutes, if necessary): the remainder marked with the name of the greater is the latitude in.

173. To find the middle latitude, having given the latitude from and latitude in. (For definition see No. 153, page 101.)

RULE XLV.

The name being supposed alike, that is, both North or both South-—Add together the true latitudes, and take half the sum; the result is the middle latitude.

NOTE.-When the names are unlike, the middle latitude (which is seldom required but for obtaining the departure) should be found by means of a table; but in this case it may perhaps be as well to avoid the use of the middle latitude in any of the common problems of navigation.

Required the middle latitude in each of the following examples:

174. To find the difference of longitude, having given the longitude from and longitude to. (For definition see No. 155, page 102.)

RULE XLVI.

1o. When the longitudes are of the same name-Take their difference and reduce the same to minutes, place E. or W. against the remainder, according as the longitude to is East or West of longitude from.

2o. When the longitudes are of contrary names--Take the sum of the two longs., which sum, if less than 180°, is the diff. of long., and attach E. or W., according as the long. to is East or West of long. from; but when the sum exceeds 180° subtract it from 360°, for the diff. of long., and reduce the remainder thus found to minutes, attaching to it the contrary name to that found in the usual way.

Longitudes are reckoned East or West of the first meridian. If these different directions are considered one positive and the other negative, the difference of longitude of two places is always found by taking the algebraic difference of their longitudes.

Required the difference of longitude between a place A and a place B in each of the following examples:

175. To find the longitude in, having given the longitude from and the difference of longitude.

RULE XLVII.

1o. When the longitude from and the difference of longitude have like names-To the longitude from add difference of longitude (turned into degrees, if necessary): the sum, if not more than 180°, will be the longitude in, of the same name as the longitude from; but if the sum exceed 180°, subtract it from 360°, and the remainder is the long. in and of a contrary name to long. from.

2o. When the longitude left and difference of longitude have unlike names -Under longitude from, put difference of longitude (in degrees and minutes, if necessary); take the less from the greater; the remainder, marked with the name of the greater, is the longitude in.