5.-What is the third adjustment?

A. To set the index and horizon-glasses parallel when the index is at O.

6.-How would you make the third adjustment?

A.-Place the index at O, and holding the instrument vertically, look through the telescope and horizon-glass at the horizon; if the true and reflected horizons appear in one straight line, this adjustment is perfect, but if they are not in one line, move the bottom screw at the back of the horizon-glass until they are.

7. In the absence of a screw how would you proceed?

A.-I would find the index error.

8.-How would you find the index error by the horizon?

A.-Set the index near O, hold the instrument vertically, and, looking through the telescope and horizon-glass at the horizon, if the true and reflected parts of the horizon are not in the same straight line move the tangent screw until they form one line: the reading is the index error.

9.-How is it to be applied?

A.-To be added when the reading is off the arc, and to subtract when the reading is on the arc.

10.-Place the index at the error of

minutes to be added, clamp it, and leave it.

No answer to be written; the Examiner will see that it is correct.

This is a reading off the arc, i.e., on the arc of excess.

II. -The Examiner will then place the zero of the vernier on the arc, not near any of the marked divisions, and the Candidate will read it.

No answer to be written; the Examiner will see that it is correct.

In all cases the Candidate will name or otherwise point out the screws used in the various adjustments.

The above completes the examination of Second Mates.

In addition to the above Only Mates, First Mates, and Masters will be required to state in writing:

12.-How do you find the index error by the sun?

A.—Place the index at about 30' on the arc, and holding the instrument vertically, look through the telescope and the horizon-glass at the sun, two sun's will be seen; bring their upper and lower limbs in exact contact by the tangent screw, read off and mark down, then place the index at about 30 off the arc, or to the right of O, bring down the upper and lower limbs in contact as before, read off and mark down; half the difference of these two readings will be the index error.

13.—The readings being{

}: what is the index error, and how do you apply it?

A.-To be added when the greater reading is of the arc, and subtracted when the greater reading is on the arc.

14.-What proof have you that these measurements or angles have been taken with tolerable accuracy?

A.-By adding the two readings together, and dividing the sum by 4; if the measurements are correct, the result should be nearly equal to the semidiameter for the day, as given in the Nautical Almanac. If they do not so agree, repeat the observations until they do.

ON THE CHART.

208. A Chart is a map or plan of a sea or coast. It is constructed for the purpose of ascertaining the position of the ship with reference to the land, and of shaping a course to any place.

209. The use to be made of the chart in each case determines the method of projection, and the particulars to be inserted. (1) The chart may be required for coasting purposes, for the use of the pilot, &c., and then only a very small portion of the surface of the globe being represented at once, no practical error results from considering that surface a plane, and a "plane chart" is constructed in which the different headlands, lighthouses, &c., are laid down according to their bearings. The soundings on these charts are marked with great accuracy; the rocks, banks, and shoals, the channels, with their buoys, the local currents, and circumstances connected with the tides, are also noted. (2) Again, for long sea passages the seaman requires a chart on which his course may be conveniently laid down. The track of a ship always steering the same course appears as a straight line (and can at once be drawn with a ruler) on the Mercator's chart. Hence the charts used in navigation are Mercator's charts. (3) When great circle sailing is practicable, and of advantage, a chart on the "central projection," or gnomic, exhibits the track as a straight line, and is therefore convenient.*

ON MERCATOR'S CHARTS.

(See Norie, pages 126-131; or Raper's "Practice of Navigation," pages 120-127, on this subject. 210. A chart used at sea for marking down a ship's track and for other purposes, exhibits the surface of the globe on a plane on which the meridians are drawn parallel to each other, and therefore the parts BH, CI, DK, &c. (Fig. 13, page 70), ares of parallels of latitude, are increased and become equal to the corresponding parts of the equator UV, VW, &e. Now, in order that every point of this plane may occupy the same relative position with respect to each other that the points corresponding to them do on the surface of the globe, the distance between any points, A and O, and A and F must be increased in the same proportion as the distance FO has been increased. The true difference of latitude, AO, is thus projected on the chart into what is called the meridional difference of latitude, and the departure BH + CI+ DK, &c., into the difference of longitude, and the representation

• The method lately introduced by HUGH GODFRAY, Esq., M.A., St. John's College, Cambridge, deserves special mention, as its beauty and simplicity will ultimately lead to its general adoption. A chart on the central projection, as stated above, exhibits the great eircle as a straight line, and thus it is seen at once, whether the track between two places is a practicable one; hence, also, we have by inspection the point of highest latitude. An accompanying diagram then gives the different courses, and distances to be run on each, in order to keep within of a point to the great circle. This chart and diagram is fully described in the Transactions of the Cambridge Philosophical Society, vol. X, part II, and is published by J. D. Potter, Poultry.

is called a Mercator's projection (see pages 73-75, and Fig. 16). It is evidently a true representation as to form of every particular small track, but varies greatly as to point of scale in its different regions, each portion being more and more enlarged as it lies farther from the equator, and thus giving an appearance of distortion.*

(1.) In charts generally, the upper part as the spectator holds it, is the North, the lower part South, and that towards his right hand the East, that towards the left West, as on the compass card.

In a case which sometimes happens when the upper part is not the North, the North part may be known by the North part of the compass.

(2.) On Mercator's chart the parallel lines from North to South (from top to bottom) are termed meridians, and they are all perpendicular to the equator; the meridians on the extreme right and left are the graduated meridians -so called from showing the divisions for degrees and minutes. The latitude is measured on the graduated meridians, and also the distance.

(3.) The parallel lines from West to East (from left to right) are called parallels, and they are all parallel to the equator, the parallels at the top and bottom are graduated to degrees and minutes--and longitude is measured on the graduated parallels. Distance cannot be taken from them.

(4.) The depth of water is denoted, as also in some places the quality of the bottom. The numerals or figures in harbours, bays, channels, &c., indicate soundings reduced to low water ordinary spring tides. The Roman figures indicate the time of high water at full and change of the moon. Thus:

m

XI hrs. 34 F & C means that the time of high water is thirty-four minutes past eleven on days of full and new moon. The anchors on the chart denote anchorage. The small arrows show the direction of the set of the current, the current going with the arrow.

• It is plain from the principles of Mercator's projection, and from the diagram (page 131) which connects the enlarged meridian with the difference of longitude, that if a ship set out on any point on the globe, and sail on the same oblique rhumb towards the pole, it can reach it only after an infinite number of revolutions round it. For from any point to the pole, the projected meridian is infinite in length, and so, therefore, is the difference of longitude due to this advance in latitude upon an oblique course. Consequently, this latitude can be reached only after the ship has circulated round the pole an infinite number of times.

These endless revolutions, however, are all performed in a finite time, the entire track of the ship being of limited extent. This, however paradoxical it may appear, is necessarily true from the principles of plane sailing, which shows that any finite advance in latitude is diff. lat. always connected with a finite length of track, this length being Cos. course.

The apparent paradox of the infinite number of revolutions about the pole being performed in a finite time, becomes explicable when we consider that, whatever be the progressive rate of the ship along i's undeviating course, the times of performing the successive revolutions continually diminish as the ship approaches the pole, both the extent of circuit and the time of tracing it tending to zero, the limit actually attained at the pole itself; hence there must ultimately be an infinite number of such circuits to occupy a finite time.

When the pole is reached the direction all along preserved may still be continued, and a descending path will be described similar to that just considered, and which will conduct the ship to the opposite pole, after an infinite number of revolutions round it, as in the former case. In receding from this pole the track described will at length unite with that at first traced, the point of junction being that from which the ship originally departed. But for the strict mathematical proof of these latter circumstances the student may consult Professor DAVIES' curious and instructive papers on Spherical Co-ordinates in the Edinburgh Transactions, vol. XII.

(5) Lines, called Compasses, similar to those on the compass card, are drawn at convenient intervals on the chart. In charts of large seas, as the Atlantic, these compasses are generally drawn so that the line from the North to the South point corresponds with the true meridian; but in coasting charts the same line generally coincides with the correct magnetic meridian.

The Candidate's attention is drawn to the following points in connection with charts.

A strange chart being placed before you, it should be your special care to determine, before you answer any question concerning it, or attempt to make use of it, which is the North part of the chart. In the case of British charts this may be known by the fact that there is always at least one compass the true North point of which is determined by a star or other ornament.

The Examiner will hand the Candidate a Mercator's chart, and he will be required to determine whether the chart is a "true" or "magnetic" one, and whether it is for the northern or southern, and eastern and western hemisphere.

In the first place then, remember that all charts are projected true, but the compass on the chart may be true or correct magnetic. When the North and South line of the compass is on a meridian, or runs in a line parallel with the meridians, and its East or West line is either on or parallel with the parallels of latitude, such a compass is a true compass; otherwise it is intended to be correct magnetic, and the variation is usually inserted within the compass. If the distance between the parallels increases upwards, i.e., towards the top of the chart, it represents a part of the northern hemisphere, but if it increases downwards, it is part of the southern hemisphere. If the degrees and minutes on the graduated parallels (top and bottom of chart) increase toward the right the longitude represented thereby is East, if they increase toward the left the longitude is West. If the meridian of Greenwich (long. o°) comes on the chart, the longitude to the right of that meridian is East, and to the left it is West.

If the meridian of 180° comes on the chart, the longitudes to the right of that meridian will be West, and the longitudes to the left of the same meridian will be East. But the West longitudes will increase from right to left, and the East longitudes will increase from left to right, as far as that meridian.

PRACTICAL EXAMINATION ON THE USE OF THE CHART.

FOR ONLY MATES, FIRST MATES, AND MASTERS.

The Deviation Tables given below are to be used in all the questions on the use of the Chart. It should be particularly noticed that these Tables contain the Deviation of the Compass for all directions of the ship's head by compass, whereas, in the Examination, we have to find the deviation of the compass for a given direction of the ship's head correct magnetic. This may easily be found by Napier's diagram (if allowed); if not allowed it may

PP

be found by allowing the deviations from the table on the courses opposite to which they stand, the results will be the Correct Magnetic Courses corresponding to the Compass Courses or Ship's Head by Compass. We have thus a second Table of Deviations for Ship's Head Correct Magnetic (see Col. 3, Table B, page 291).

Given a correct magnetic course by the chart between two points of land, to find the course that must be steered by compass.

Having found ship's head correct magnetic (see Col. 3, Table B) by applying deviation to ship's head by compass (Rule XXXVI, page 104).