is not termed the difference of longitude, because, owing to the meridians converging towards the poles, the proportions of this line will not truly represent the difference of longitude.

As, in our figure, b c equals 80 miles, on taking b d in our compasses and applying it to our scale, we shall find it equal to 57 miles, which is now our difference of latitude. We must now learn our difference of longitude, which is not truly represented by c d, and for which purpose we must have recourse to Table VI.

As we have sailed southerly, we must have lessened our northern latitude; therefore 57 miles, our difference of latitude, must be subtracted to give us our latitude in, the meridional parts of which being subtracted from those of the latitude left, give the meridional difference of latitude, viz. 88 miles, which, being measured in the direction of b d, give us be. From the point e draw eƒ parallel to d c; e f is our true difference of longitude in miles, which must be added to, or subtracted from, the longitude left, accordingly as we have increased or diminished our distance from Greenwich, i.e. have been sailing westerly or easterly. Here we must add the difference of longitude to the longitude left, to find the longitude in, as we have sailed westerly, and increased our distance from Greenwich (see p. 32).

We are now, I trust, prepared to deal with the foll wing day's work, noted down on the log-board ;

and had

supposing that we had left a port in Ireland, arrived at Lat. 48° 53' N., Long. 10° 19' W., which we will take as a point of departure. The meaning of the above is, that from 12 at noon until 5 o'clock the distance run was 24 miles, course S.W. with the wind N. b W. and N.W. b N., but making no leeway. From 5 o'clock until 10 the run was 18 miles, the compass course W. b S., wind still N.W. b N., and the ship making leeway to the amount of a point of the compass,--and so on with the rest of the log.

DAY'S WORK BY INSPECTION.

We will proceed to get the result of the above day's work by inspection; I will set it down in full, and afterwards explain it seriatim, in which case you can readily refer back.

Diff. lat. 17:4 S. give in Trav. Tab. 5 { Dist. 64 miles.

Dep. 42.3′ W.

Course S. 42° W.

Mid. lat. 481° as course. In Trav. Tab. 5 give 64 in "Dist."
Dep. 42-3' in "Lat." col. J

col., which is diff. long.

Finally, prick off the ship's place on the chart in lat. 48° 6' N., long. 11° 23′ W., which is the result of dead reckoning, if you have not the position by observation.

1. The courses steered have to be corrected for leeway (if any), and for variation. The first course on the logboard, p. 35, is S.W. with no leeway, but corrected for Var. 21 points W. (to left hand) gives true course

S. 6 W. W., or S. 1 pt. W.; the total distance run on that course is 24 miles. The second course steered W. b S. has pt. leeway with the wind N.W. b N., which allowed to left (from the wind) gives W. b S. & S.; and this corrected for Var. 24 pt. w, gives S.W. W., or S. 41 pt. W., with distance 18 miles; and similarly with the other courses and distances.

2. Having got the true courses, draw a tabular form as shown, and mark the headings as you see on p. 36; then enter the true courses in the first column, and the distances run on each course in the second column.

3. Enter Traverse Table 4 with the first course and distance, and take out the diff. lat. and dep. corresponding; in this case course 12 points and dist. 24, give diff. lat. 22'6 and dep. 8-l; the diff. lat. being entered in S. Col., and the dep. in W. Col., because course is S. and W. Proceed similarly with the other courses and distances, and fill in the N., S., E., and W. columns.

4. Next find the sum of each of columns marked N., S., E., and W.; after which take the difference between the N. and S. quantities for the true diff. lat. ; also take the difference between the E. and W. quantities for the true departure.

5. With the true diff. lat. and dep. just found, enter Traverse Table 5 for the course made good, and the corresponding distance (see p. 36, and also p. 27). The course must be named after the diff. lat. and dep., in this case S. and W.

6. To the lat. left apply the diff. lat. to get the lat. in or arrived at; in this case, being in lat. N., and having made southing you have decreased your lat. (see p. 15).

7. Proceed to find the middle latitude—i.e. the lat. midway between the lat. left and lat. in.

8. Enter Traverse Table 5 with the mid. lat. as if it were a course of so many degrees, and run the finger down the lat. column until you find the number corresponding to the dep. ; in the annexed column of distance you will find the number of miles that must be taken as the diff. long.

9. To the long. left apply the diff. long. to get the long. in; in this case the ship being in long. W., and having made westing, you have increased your long. from Greenwich.

This explanation, with what has previously been said in other parts of the work, will be sufficient, if you have carefully read the rules, studied the examples, and gone through the foregoing day's work in such manner as to understand its meaning. The method by inspection is that used at sea.

Other days' works will be given, but I shall merely work them out by inspection, leaving you to follow the different results step by step.

It now remains to show you the method by construction.

DAY'S WORK BY CONSTRUCTION.

Let every day's work that you intend to project be done in the following manner; and let every part of the work be put down in the same part of the paper, which will serve much to prevent confusion or mistakes.

I will first give some information as regards the scale on which the diagram is to be formed. Let your compass representation be on a large scale, and your traverses on a small one. Take, then, the protractor, and observe the notch (1) thus in the centre of its lower edge, as previously mentioned; put one point of the pencil-compasses to this, and extend the pencil to the outer extremity of the protractor. With this dis