if Dist. exceeds 300 miles, enter the Trav. Table with half the Dist., take out the corresponding D. Lat. and Dep., and then double them. 6. Add together the quantities in the N. column, and also in the. S. column; then, take the difference of the two sums, giving the remainder the name of the greater quantity (N. or S.) :' the result will be the Diff. Lat. made good. 7. Add together the quantities in the E. column, and also in the W. column; then, take the difference of the two sums, giving the remainder the name of the greater quantity (E. or W.) ; the result will be the Departure made. 8. For tlie Course and Distance made good, enter Trav. Tab. II. and seek out the page where the D. Lat. and Dep. made are side by side, reading headings of columns from the top if D. Lat. is greater than Dep., but from the bottom if D. Lat. is the less. The course (in degrees) is taken from the top of the page if D. Lat. is greater than Dep., but from the bottom if D. Lat. is the less. The Dist. comes from Dist. column alongside the given D. Lat. and Dep.: name the Course according to the D. Lat. and Dep., and write the result thus—Course made good N. or S. . . .° E. or W.; Dist. . . . miles. 9. For the Lat. in.—Under the Lat. left write the D. Lat.; if both have the same name (N. or S.) take their sum for Lat. in, of the same name as Lat. left: if one is N. and the other 8. take their difference for the Lat. in, of the same name as the greater. 10. For the Middle Lat.—Add together the Lat. left and Lat. in, if both have the same name (N. or S.), and divide the sum by 2; if one Lat. is N. and the other S., take their difference and divide the remainder by 2. 11. For the Diff. Long.—Enter Trav. Tab. II. with Mid. Lat. (as a course) I the Dist. (in Dist. col) is the and Dep. (in D. Lat. col) j required Diff. Long. Nate.—If Dep. exceeds 300, take the half of it, and having found the Dist. corresponding thereto, double it. At the equator, or if the Lat. in is less than 5° or 6° the Dep. may be taken as the Diff. Long. 12. For the Long. in.—Under the Long. left write the Diff. Long. with the same name as the Dep. If Long. left and Diff. Long. have the same name (E. or W.) take their sum for the Long. in, of the same name as Long. left; except this sum exceeds 180°, in which case subtract it from 360°, and mark the remainder W. when Long. left is E., but E. when Long. left is W. If Long. left and Diff. Long. have different names (one E. and the other W.), take their difference for the Long. in, of the same name as the greater. Day's Work No. I. The Courses, Leeway, and Variation being in points of the compass, you will retain them so, and use Trav. Tab. I. - ' 1st. Begin with the Departure; reverse it, and enter it as a course after correcting for variation. 2nd. Take each course in succession, correct for leeway (if any), and then for variation: also sum up the distance run on each course. 3rd. Take the current as the last course, and correct for variation. 4. Then proceed as directed in the summary, p. 40—41; or as your knowledge of the earlier part of this work assists you, without reference to the summary. Note.—This is a copy of the Log-board, divested of the hulk of the remarks. Mid. Lat. 49° and Dep. 91- 2 (in Lat. col.) in Trav. Tab. II. give 139 in Dist. col.. for l,iff. Long. Mid. Lat. 50° and Dep. 91-2 (in Lat. col.) in Trav. Tab. II. give 142 in Dist col., for Diff. Long. Take 141 for Diff. Long. corresponding to Mid. Lat. 49f°. We have refined here, which is not generally necessary: it would have been sufficient to hare taken Mid. Lat. 50°. And these results would be entered in the Log-Book in something like the following form, beneath the day's (24 hours) transactions :— Where there is no deviation of the compass, there is no absolute necessity, under ordinary circumstances, to correct the courses for variation, until you have arrived at a Diff. Lat. and Dep. from the courses corrected for leeway; it saves trouble and the result is equally accurate. The following is the Day's Work just solved ;—the courses are corrected for leeway, and with the distances, a Diff. Lat. and Dep. are found in the usual way; then this Diff. Lat. and Dep. give a Course arid Dist. (1) :—Now correct the course (just obtained) for Variation, once for all, and you get the True Course (2); —with the True Course and Dist., get the True Diff. Lat. and True Dep. (3); and the remainder of the solution is as before. This method is inapplicable where the magnetic meridians are crowded together, so that the variation at the end of the day differs 3° or more from what it was at the commencement. N.B.—The figures in this method (below) are as many as by the former one, but you remember we have not been at the trouble of correcting each course separately for variation. (1) Diff. Lat. 17-7 N. and Dep. 91-2 W. in Trav. Tab. II. give Course N. 79° W. and Dist. 93 m. (2) Then Course corrected for 2 pts. W. var. gives True Co. S. 78j° W. (3) True Co. S. 78}° W. or W. by S. Lat. left ... 49° 58'N. Day's Work No. 2. Has leeway, deviation, and variation; and the solution is by correcting the courses, 1st, for leeway (if any); then for deviation ; and lastly, for variation;— unless you correct by the error of the compass, that is, taking deviation and variation together as shown on p. 22-23. Diff. Lat. 86- 5 S. and Dep. 17-1 W. in Trav. Tab. I. give Course made good S. by W., and Dist. 88 miles. And our Log-Book form would be entered as follows :— f i I have filled in a Lat. and Long. by observation to show that at the end of the next day (24 hours), when working up the reckoning, they will be taken as onr departure Lat. and Long. Thus, suppose our Courses and Distances for the 24 hours gave us Diff. Lat. 72'-9 S., and Dep. 143'-6 W. Then, with these we get Course made good S. 63° W. and Dist. 161 miles; also— A SHIP'S RECKONING. A Ship's Reckoning is that account by which it can be known at any time where the ship is, and on what course or courses she must steer to gain her port. The basis of the reckoning is first kept on the Log-Board, and then transferred to the Log-Book. The Log-Board is a slate in a folding frame, on which is written at intervals during the day everything connected with the progress of the ship on her voyage, as well as any occurrences worthy of notice. The log-board is divided into seven columns as follows, under the headings of— | H. | K. | F. | Courses. | Winds. | Leeway. | Bemarks, Monday, April 10th. | The column on the left contains the 24 Hours from the noon of one day to the noon of the next, divided into two portions of 12 hours each. In the second and third columns are the .Knots and .Fathoms (or .Knots and |