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When observing, the instrument is to be held with one hand by the handle P placed at the back of the frame, while the other hand moves the index.


The following brief directions for reading off will be more readily understood by the learner, if he place a sextant before him for reference and examination.

It will be seen that the arc is divided into degrees and (in the best instruments) into sixths of degrees, or ten minutes. We will suppose it is an instrument of this kind before the learner. The index, up to which an arc is read off, is a line cut in a plate at the end of the moveable radius, and is generally distinguished from the other lines on the plate by a diamond-shaped mark, resembling a spear-head. Supposing this index to stand exactly at any of the lines on the are, that is, so that the two lines are in the same direction; in such a case the reading off is easily known, for it must be a certain number of divisions and sub-divisions, of which the value is seen at once. Thus, if it coincide, for example, with the second line to the left of 40°, then the reading off will be 40° 20', since each line on the arc ropresents 1o'.

But suppose the index not to stand exactly at any line whatever on the arc, but somewhere between two, as in the above example, between the second and third line from 40°, suppose it appeared to be about half-way between the second and third lines (the learner may place it in that position). But as this is a rough and imperfect way of estimating the additional minutes and seconds beyond the second division from 40°, the exact value of this small space is known by means of a few divisions on the index plate to the left of the index, and called the vernier. These divisions are made less than the arc divisions, so that the line on the plate immediately to the left of the index is somewhat nearer to the corresponding one on the arc than the small space to be determined. It is nearer thereto, as is manifest by the difference of a division on the arc and one on the index plate. In like manner the second line, reckoning from the index, must be nearer to the corresponding are line by two differences, the third by three, and so on. At length, therefore, there must be a coincidence of two lines, or nearly

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glass on the eye-end of the telescope, without using any shade, this should always be done, for the error of this dark glass does not affect the contact at all, and the distortion caused by it not magnified, whereas any fault in the dark shade between the index and horizon-glasses produces actual error in the observation, and the distortion is magnified subsequently by the telescope.

so, that is, they must appear to an eye placed directly over them to lie in the same direction, or nearly so. And since, upon the whole, the lines on the vernier have approached those upon the are through the small part the index is in advance of 20', this excess must be equal to as many times the difference of two divisions, as there are lines, reckoning from the index, before this coincidence takes place. Hence, if we know the value of a difference, we shall know the value of the small arc to be measured.

This difference is known as follows: By examining the arc of the sextant before us, it will be seen that 60 divisions of the vernier just cover or coincides with 59 divisions on the arc, or the difference between a division on the are and one on the vernier is do of a division of the arc; if, therefore, a division on the arc is 10', the difference will be do of 10' or 10". Every sixth division of the vernier being distinguished by a figure denoting minutes, and the interval between each of these figures is divided into six parts of 10" each.

To read off then on a sextant, we first examine the divisions and sub-divisions on the arc, up to the line which stands before the index. We then move the microscope on the vernier and examine the numbered lines. If any one of these coincides in direction with the opposite one on the arc, the reading off to be added will be so many minutes; if not, we observe between which numbered lines the coincidence actually takes place, and then reckon the preceding minutes as numbered, and afterwards the sub-divisions of the vernier, as so many minutes or seconds. Let us now suppose the index to stand between the second and third divisions from 40°. In reading off, first 40° 20' is noted on the arc, and then running the microscope farther on the arc it is observed that a line on the vernier and an arc line are in the same direction, between the lines on the vernier marked 5 and 6. The farther reading off is therefore 5' and some seconds. On examining the interval between 5 and 6, which is divided into six equal parts, the fourth line to the left of 5 is found to be in the same direction with the opposite one on the are. The remaining reading off is therefore 40". Hence the whole reading off is 40° 25' 40".

The sextant supposed under examination is marked to read off to the nearest 10"; some instruments are graduated to 15" or 30", &c., but the same method of reading off is to be followed as pointed out above.

As has been observed before, the graduation of the are of the sextant is usually continued to the right of o° or zero, in which case we have to read off an arc divided from left to right by means of an index which 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 7' 20", we must read this as 2' 40"; if at 5' 40" we must read this as 4' 20", and so on.

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1st. 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

a 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

o 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 instrument.

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 rice rersa 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 z' 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.

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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 tho 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, additire when both off

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INDEX CORR, addit. 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' 0", agrecing 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. 1872, April 17th, the reading on the are 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 scmi-diameter.

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.

Ex. I.

Ex. 3.



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

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