through any remarkable place, and is therefore arbitrary. The meridian of the Royal Observatory at Greenwich is by the British esteemed the first meridian. In other countries, the first meridian is usually that which passes through the principal observatory or chief city of that country.

153. The LONGITUDE of any place is that portion of the equator which is contained between the first meridian and the meridian of the given place. The longitude of a place is said. to be east or west, according as the place is on the east or west side of the first meridian, and it cannot exceed 180°.

154. The DIFFERENCE of LONGITUDE between any two places is the intercepted portion of the equator between the meridians of these places.

Problem I.

155. Given the latitudes of two places, to find the difference of latitude between them.

RULE.

Subtract the less latitude from the greater, if they be both north or both south; but add them if the one be north and the other south.

Example I.

Required the difference of latitude between Edinburgh in latitude 55° 57′' N., and Brest in latitude 48° 23′ N.

Required the difference of latitude between the Lizard Light in latitude 49° 58′ N., and Bencoolen in latitude 3° 48′ S.

Exercises 10.

Find the difference of latitude between the two places A and

B in the following exercises:

(123.) A in latitude 70° 18′ N., and B in latitude 49° 45′ N.

156. Given the longitudes of two places, to find the difference of longitude between them.

RULE.

If the longitudes be of the same name—that is, both west or both east-subtract the less from the greater, and the remainder will be the difference of longitude; but if the longitudes be of contrary names, add them and their sum, if less than 180° is the difference of longitude; but if greater than 180°, subtract it from 360°, and the remainder will be the difference of longitude.

Example I.

Required the difference of longitude between Edinburgh in longitude 3° 12′ W., and Brest in longitude 4° 29′ W.

Example II.

Required the difference of longitude between Lizard Light in longitude 5° 12′ W., and Bencoolen in longitude 102° 28′ E.

Required the difference of longitude between Porto Bello in longitude 79° 43′ W., and Canton in longitude 113° 14′ E.

Find the difference of longitude between the places A and

B in the following exercises:

(131.) A in longitude 17° 13′ E., and B in longitude 23° 59′ E.

157. Given the latitude and longitude of a place sailed from, and the difference of latitude and longitude made, to find the latitude and longitude of the place arrived at.

RULE.

If the difference of latitude or longitude made be of the same name as that sailed from, add the difference, and the sum will be that arrived at; but if they be of contrary names, take their difference, and affix the sign of the greater.

158. Remark.—The latitude can in no case exceed 90°, the distance between the equator and poles; and should the sum of the longitudes so obtained exceed 180°, subtract it from 360°, and change the name of the remainder. Longitude is measured westward and eastward from the first meridian up to 180° in each direction; it would have been more convenient had it been measured only westward up to 360°; but as the former method has been universally adopted, except by Sir John Herschel in his Outlines of Astronomy, where he recommends it to be always measured westward up to 360°, it is here retained.

Example I.

If a ship sail from Cape Finisterre in latitude 42° 54′ N., longitude 9° 16′ W., towards the south-west till her difference of latitude is 160 miles, and her difference of longitude 136 miles; what is her latitude and longitude in?

If a ship sail from latitude 50° 28′ S., longitude 178° 20′ E. towards the south-east till her difference of latitude is 520, and her difference of longitude 385 miles, what is her latitude and longitude in ?

NOTE.-A clear idea may be obtained of parallax (which is the angle subtended by the earth's radius at the centre of the sun or moon), refraction, semidiameter, dip, true and observed altitudes, by examining the following diagram, in which S represents the true place of the sun, and S' the apparent

place when elevated by atmospheric refraction; AH, a parallel to CB, the rational horizon; and AD the sensible horizon as seen by an eye elevated above the earth's surface.