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is divided from right to left; this, however, is easily done if we remember that the line on the vernier marked 10' must be considered as the commencement of the divisions, 9' must be considered as 1', 8′ as 2', 7' as 3', &c.; thus if the coincidence of lines on the arc and vernier is at 720", we must read this as 2′ 40′′; if at 5′ 40′′ we must read this as 4' 20", and so on.
THE ADJUSTMENTS OF THE SEXTANT.
The index-glass, or central mirror, must be perpendicular to the plane of the instrument.
Place the index to about 60°-viz., to near the middle of the arc or limb. Hold the sextant with its face up, the index-glass being placed near the eye, and the limb turned from the observer. Look obliquely down the glass; then, if the part of the arc to the right, and its image in the mirror, appear as one continued arc of a circle, the adjustment is perfect; if the reflection seems to droop from the arc itself, the glass leans back; if it rises upward, the glass leans forward. The position is rectified by the screws at the back.
2nd. The horizon-glass, or fixed mirror, must be perpendicular to the plane of the instrument.
Set o on the index to o on the arc; hold the instrument horizontally -viz., with its face up; direct the sight to the horizon-glass, give the instrument a small nodding motion; then if the horizon, as seen through the transparent part of the horizon-glass, and its image, as seen in the silvered part, appear to be in a continued straight line, the adjustment is perfect; or otherwise, the instrument being held perpendicular, look at any convenient object, as the sun; sweep the index-glass along the limb, and if the reflected image pass exactly over the object itself, appearing neither to the right or left of the object, then the horizon-glass is perpendicular to the plane of the instrument; if not, turn the adjusting screw, which in some instruments is a mill-headed one at the back of the instrument, while in others it is a small screw behind and near the upper part of the glass itself, which can be turned by placing a pin in the hole.
3rd. The horizon-glass must be parallel to the index-glass. Set o on the index to o on the arc; screw the tube or telescope into its socket, and turn the screw at the back of the instrument till the line which separates the transparent and silvered parts of the horizon-glass appears in the middle of the tube or telescope. Hold the sextant vertically-that is, with its arc or limb downwards-and direct the sight through the tube or telescope to the horizon; then, if the reflected and true horizons do
not coincide, turn the tangent screw at the back of the horizon-glass till they are made to appear in the same straight line. Then will the horizon-glass be truly parallel to the index-glass.*
4th. The axis of the telescope must be parallel to the plane of the instru
Turn the eye-piece of the telescope till two of the parallel wires in its focus appear parallel to the plane of the instrument; then select two objects, as the sun and moon, whose angular distance must not be less than from 100° to 120°, because an error is more easily discovered when the distance is great; bring the reflected image of the sun exactly in contact with the direct image of the moon, at the wire nearest the plane of the sextant, and fix the index; then, by altering a little the position of the instrument, make the object appear on the other wire; if the contact still remains perfect, no adjustment is required; if they separate, slacken the screw furthest from the instrument in the ring which holds the telescope, and tighten the other, and vice versa if they overlap.
5th. To find the Index Error (1.)-Move the index till the horizon, or any distant object, coincide with its image, and the distance of o on the index from o on the limb is the index error; subtractive when o on the the index is to the left, and additive when it is to the right of o on the limb.
Example. The horizon and its images being made to coincide, the reading is 2' on the arc. Then 2' is the Index Correction to be subtracted from every angle observed. (2.) Or measure the sun's horizontal diameter, moving the index forward on the divisions until the images of the true and reflected suns touch at the edges; read off the measure which will be on the arc; then cause the images to change sides, by moving the index back; take the measure again, and read off; this reading will be off the arc; half the difference of the two readings is the index correction.
When the reading on the arc is the greater, the correction is subtractive; when the lesser, additive.
Some sextants, as Troughton's Pillar Sextants are not provided with means for making this adjustment; because it is not absolutely necessary. An allowance, called Index Error, being made for the want of parallelism of the two glasses when the zeroes coincide.
If both readings are on the arc, or both off the arc, half their sum is the index correction-subtractive when both on, additive when both off the arc.
Ex. 3. 1st reading on the arc 2nd do. on the arc
1st reading off the arc+1' 30" 2nd do. off the arc+66 50
INDEX CORR. addit.
INDEX CORR. sub. One-fourth of the sum of the two readings should be equal to the sun's semi-diameter in the Nautical Almanac for the day; but if both readings be on or both off the arc one-fourth their difference should be the sun's semi-diameter.
Thus, suppose the observations, in Example 1, to be made on September 26th, 1872, here one-fourth of the sum of the two readings is 16' o", agreeing with the semidiameter as giver in the Nautical Almanac for the given day.
This affords a test of the accuracy with which the observation has been made.
EXAMPLES FOR PRACTICE.
Ex. 1. 1872, April 17th, the reading on the arc 29′ 40′′, the reading off the arc 34' 10" required the index correction and semi-diameter.
Ex. 2. 1872, July 4th, the reading on 33' 10", off 29′ 50′′: find index correction and semi-diameter.
Ex. 3. 1872, November 13th, on 4' 40", off 60' 10": find index correction and semi-diameter.
Ex. 4. 1872, July 10th, on 32′ 45′′, off 34′ 30′′: find index correction and semidiameter,
Ex. 5. 1872, March 21st, off 1° 10′ 0′′, off 6′ 40′′: find index correction and semidiameter.
Ex. 6. 1872, January 17th, on 67′ 40′′, on 2′ 30′′: find index correction and semidiameter.
ON THE CHART.
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.
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 strait 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.)
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. p. 64), arcs of parallels of latitude, are increased and become equal to the corresponding parts of the equator UV, VW, &c. 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 (see p.p. 66, 67), and the departure BH + CI + DK, &c., into the difference of longitude, and the representation is called a Mercator's projection. It is evidently a true representation as to form of every particular small track, but varies greatly as to point of scale in
* 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 circle 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. Mr. W. C. Bergen, of Blyth, Master in the Mercantile Marine, has also published Charts on the Gnomic Projection, and claims to share with Mr. Godfray the credit of proposing the use of this projection for charts in navigation,
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, and that towards his right hand the East, as on the compass card.
(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 parallel.
(4.) The numerals in harbours, bays, channels, &c., indicate soundings reduced to low water spring tides.
*It is plain from the principles of Mercator's projection, and from the diagram (page 101) which connects the enlarged meridian with the difference of longitude, that if a ship set out from 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 always connected with a finite length of track, this length being
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 its 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.