measure and angular measure to time. This may be done by the following rules:

Rule. - I. To convert time to angular measure, multiply the number of hours by 15; the product is so many degrees. Divide the minutes and seconds by 4 and reckon every unit of remainder as 15' if minutes be the dividend, and as 15" if seconds be the dividend.

EXAMPLE 1.-Convert 3h 14m 23s to angular measure.

II. To convert angular measure to time, multiply the degrees and minutes by 4; then the minutes of angular measure become seconds of time, and the degrees become minutes of time, which is reduced to hours by dividing by 60.

EXAMPLE 2. -Convert 137° 26' into time.

22. Both of these processes are greatly simplified by the use of the table on page 144 of the collection of tables accompanying this Course. In the first column of this table are contained degrees and minutes in angular measure, in the second column the corresponding hours and minutes, or minutes and seconds of time; the other columns are a continuation of the first and second, respectively. The use of this table will become clear by a few examples.

EXAMPLE 1.-Required the time corresponding to 54° 23′.

EXAMPLE 2.- Required the degrees and minutes corresponding to 4h 15m 205.

23. The difference of longitude of any two places is the arc of the equator contained between the meridians passing through the places. Thus, the difference of longitude between the two places G and C, Fig. 4 (a), is the arc AD of the equator E E' contained between the meridians P G P' and PC P' passing through G and C, respectively. When both places are in east, or both in west, longitude, the difference of longitude is equal to the difference between their longitudes expressed in time, arc, or nautical miles; but, if one place is in west longitude and the other in east longitude, the difference of longitude between the two is equal to the sum of their longitudes, or the remainder of that sum from 360°.

EXAMPLE 1.- Find the difference of longitude expressed in minutes of arc between a place in longitude 5° 3′ E and another in longitude 16° 39' E.

SOLUTION. - Since both places are in east longitude, the difference of longitude is equal to the difference of their longitudes; thus,

EXAMPLE 2. - Find the difference of longitude between New York and Charleston, S. C.; the former being in longitude 74° 0' W, the latter in 79° 54′ W.

SOLUTION. - Both places being in west longitude, take their difference; thus,

EXAMPLE 3. - One place is in longitude 1° 40′ W, another in 3° 20′ E. Find the difference of longitude between the two.

SOLUTION. - Since one place is in east, and the other in west, longitude, the difference of longitude is equal to the sum of their longitudes; thus,

2d Long. = 3° 20′ E

Diff. of Long. = 5° 0′

Expressed in Min. of arc = = 300'. Ans.

EXAMPLE 4. – A ship is in longitude 177° 45′ W; another is in longi. tude 175° 27′ E. Find the difference of longitude between the two positions.

SOLUTION. The sum of their longitudes subtracted from 360° will give the required difference of longitude; thus,

24. When a ship in west longitude sails west, and in east longitude sails east, she evidently increases her longitude. But when sailing toward the east in west longitude, and toward the west in east longitude, her longitude decreases. Therefore, when one longitude and the difference of longitude is known, the longitude arrived at is readily found, as shown in the following examples:

NOTE. - By longitude left is understood the longitude of the place the ship sailed from; by longitude in, the longitude of the place arrived at.

EXAMPLE 1.-A ship leaves a place in longitude 97° 45′ W; the difference of longitude sailed is 71' east. Find the longitude in.

SOLUTION. - The longitude being west and the difference of longitude toward the east, the longitude in is found by subtracting the latter from the former; thus,

--

EXAMPLE 2. – A ship in longitude 1° 20′ W changes her longitude 236' to the eastward. Required her longitude in.

SOLUTION.

Long. left 1° 20' W

Diff. of Long. 236′ = 3° 56′ E

Long. in

=

= 2° 36′ E. Ans.

In this case the ship changes her position from west to east longitude by an amount equal to the longitude left subtracted from the difference of longitude.

EXAMPLE 3.- Find the longitude in, having given the longitude left 160° 20′ W and the difference of longitude 2,480' to the westward.

It should be noted in the foregoing examples that the difference of latitude as well as the difference of longitude is denoted, the former by N or S, the latter by E or W, to indicate the direction in which the change has taken place.

1. The longitude left is 110° 42′ W, longitude in is 101° 42′ W. Find the difference of longitude. Ans. Diff. of Long. = 540′ E.

2. Longitude left is 2° 30′ E, the difference of longitude is 126′ E. Find the longitude in.

Ans. Long. in = 4° 36′ E. difference of longitude sailed is Ans. Long. left

0° 0'.

3. Longitude in is 1° 40.4' W, the 100.4' W. What is the longitude left? 4. Longitude left is 3° 10′ W, the difference of longitude is 380' E. Find the longitude in. Ans. Long. in = 3° 10′ E. 5. Longitude left is 62° 32′ E, the longitude in is 45° 51.5′ E. Find the difference of longitude. Ans. Diff. of Long. 1,000.5' W.

6. Longitude left is 178° 15' E, the longitude in is 178° 45′ W. Find the difference of longitude. Ans. Diff. of Long. = 180' E.

25.

=

Relation Between Time and Longitude. - Since the circumference of the earth is 360°, the sun in making its apparent daily circuit in 24 hours moves through 360°; hence, in 1 hour it moves through 3240, or 15°. When the

sun has attained its greatest altitude, or is on the meridian of any place, it is noon there; hence, the time at any place 15° east of that meridian will be 1 hour past noon, and at any place 15° west of that meridian, 1 hour before noon.

From this it is evident that if the navigator knows the difference between his local time and that of any standard meridian-Greenwich, for instance-he has a means of determining the longitude of his ship. The greater the difference of longitude, the greater the difference of time between any two places; from this it will be seen that the relations between time and longitude are so intimately connected that they may almost be said to be identical.

26. The ship's course, or the course steered, is the angle between a meridian and the ship's foreand-aft line.

27. The course made good is the angle between a meridian and the ship's real track, or path, on the surface of the globe. The

course is reckoned from north or south toward east or west, and is measured either in degrees and minutes or in points of 11° 15' each.

28. The Rhumb Line. - When a ship sails from one place to another in one and the same direction, her course