To find the Distance = AC:

This comes under the 6th analogy, page 237; hence,

This comes under the 10th analogy, page 237; hence,

Difference of long. = 633.8 miles, or 10.34 W.

=

Note. The difference of longitude DE may be readily found, independent of the course, by the 13th analogy, page 238.

To find the Course, Distance, and Difference of Longitude by

Inspection :

=

One-third of the difference of latitude 127, and one-third of the departure 171.3, are found to agree nearest abreast of 4 points, the course, and under distance 213: hence, 213 x 3 = 639 is the distance. sailed. Again, to the course 4 points, and one third of the meridional difference of latitude 156. 6, in a latitude column, the corresponding departure is 211.2, which, multiplied by 3, gives 633.6; and hence the longitude 19:49. west; being nearly the same as by calculation.

PROBLEM VIII.

Given One Latitude, Course, and Difference of Longitude; to find the Distance and the other Latitude.

Difference of Longitude = . : 7:20 = 440 miles.

To find the Meridional Difference of Latitude = A D

This comes under the 12th analogy, page 238; hence,

As radius.

AD:

90:0 Log. co-secant=.. 10.000000
2.643453

Is to the diff. long. 440 miles, Log. =
So is the course = 33 pts. Log. co-tangent = 10.042705

This comes under the 6th analogy, page 237; hence,

To find the Latitude come to, and the Distance Sailed by

Inspection :

To the course 33 points, and one third of the difference of longitude = 146. 7, in a departure column, the corresponding difference of latitude is 161.5, which, multiplied by 3, gives the meridional difference of latitude

484.5 miles; hence, the latitude come to is 32:10 south, and the difference of latitude 425 miles.-Now, to one third of the difference of latitude, thus found, = 141.7, and the course 32 points, the corresponding distance is .191; and this being multiplied by 3, gives the distance sailed = 573 miles.

PROBLEM IX.

To find the Course, Distance, Difference of Latitude, and Difference of Longitude made good, upon Compound Courses; and also the bearing and Distance from the Ship to her intended Port, by Inspection in the General Traverse Table.

RULE.

Make a Table of any convenient size, as that to the following example, and divide it into six columns: in the first of these place the several courses, taken from the log board, corrected for lee way, if any, and variation; and in the second, their corresponding distances. The third and fourth columns are to contain the differences of latitude, and, therefore, to be marked N. S. at top; and the fifth and sixth, the departures, which are to be marked E. W. at top also.

Find, by Problem I., page 107, the difference of latitude and departure answering to each corrected course and distance, and place them in their respective columns: then, the difference between the sums of the north and south columns will be the whole difference of latitude made good, of the same name with the greater quantity; and the difference between the sums of the east and west columns will be the whole departure, of the same name with the greater meridian distance.

Remark. The courses taken from the log board are to be corrected for variation and lee-way, if any, as thus.-If the variation be easterly, it is to be allowed to the right hand of the course steered by compass; but to the left hand if westerly. And,

If the larboard tacks be aboard, the leeway is to be allowed to the right hand of the course steered; but to the left hand if the starboard tacks be ,aboard.

To find the Course and Distance made good

To the whole difference of latitude and departure, so found, find the corresponding course and distance by Problem II, page 108, and thus the course and distance made good will be obtained.

To find the Latitude in, by Account, or Dead Reckoning :

If the difference of latitude and the latitude of the place from which the ship's departure was taken, or the yesterday's latitude, be of the same name, their sum will be the latitude in, by account; but if they are of contrary names, their difference will be the latitude in, of the same name with the greater quantity.

To find the Difference of Longitude:

With the course made good, and the meridional difference of latitude, in a latitude column, find the corresponding departure, by Problem III. page 110, and it will be the difference of longitude.

Or. With the middle latitude as a course, and the departure, in a latitude column, find the corresponding distance, by Problem V., page 111, and it will be the difference of longitude.

To find the Longitude in, by Account, or Dead Reckoning :—

If the difference of longitude and the longitude of the place from which the ship's departure was taken, or the yesterday's longitude, be of the same name, their sum will be the longitude in, by account, when it does not exceed 1809; otherwise, it is to be taken from 360°, and the remainder will be the longitude in, of a contrary name to that left :-but, if the difference of longitude and the longitude left are of contrary names, their difference will be the longitude in, of the same name with the greater quantity.

To find the Bearing and Distance from the Ship to the Port to which she is bound :

By Mercator's Sailing.

With the meridional difference of latitude, in a latitude column, and the difference of longitude, as departure, find the course, by Problem IV. page 111; then, with the course, thus found, and the difference of latitude, the distance is to be obtained by the same Problem.-Or,

By Middle Latitude Sailing.

With the middle latitude between the ship and the proposed place, as a course, and the difference of longitude, as distance, find the corresponding

meridional distance, or departure, by Problem VI. page 112; then, with this departure, and the difference of latitude, the course and distance are to be obtained by the same Problem.

Note. The true bearing or course, thus found, may be reduced to the magnetic, or compass bearing, if necessary, by allowing the value of the variation to the right hand if westerly; and to the left hand if easterly; being the converse of reducing the course steered by compass, to the true

course.

And, this rule comprises the substance of that nautical operation which is generally termed a day's work at sea.

Example 1.

A ship from Cape Espichell, in latitude 38:25 north, and longitude 9:13 west, bound for Porto Santo, in latitude 33:3 north, and longitude 16:17 west, by reason of contrary winds was obliged to sail upon the following compass courses; viz.-W. by S. 56 miles; N. W. by W. 110 miles; W. N. W. 95 miles; S. by E. † E. 50 miles; S. by W. 4 W. 103 miles, and S. S. W. 116 miles; the variation was 2 points westerly on the three first courses, and 14 point on the three last: required the course, and distance made good, the latitude and longitude at which the ship arrived; with the direct course, and distance from thence to her intended port?