76. 1869, August 20th: find the A.M. and P.M. tides at Sheerness (Admiralty Tide Tables).

8. 1872, May 11th, at 5h P.M. apparent time at ship, latitude 38° 50' S., longitude 139° 25′ E., sun setting by compass W.N.W., variation by chart 5° 8′ E.: required the error of compass and deviation.

9. 1872, August 24th, A M. at ship, latitude at noon 37° 59′ N., observed altitude of sun's L.L. 37° 13′ 30′′, index correction + 2' 40", height of eye 18 feet, time by chronometer, August 24d 6h 8m 13a, which was 4m 6s slow on Greenwich mean noon, August 1st, and losing 119 daily, course since observation N.N.W,, 22'4 (true): required the longitude at noon.

THE SAME, AS PROPOSED AT LIVERPOOL

1872, August 24th, at about 8h 40m A.M. at ship, latitude at noon 37° 59′ N., longitude account 143° 45′ W., observed altitude sun's L.L. 37° 13′ 30′′, index correction + 2' 40", height of eye 18 feet, time by chronometer 6h 8m 13a, which was 4m 63 slow on Greenwich mean noon, August 1st, and losing 1189 daily, course since observation N.N.W., 22'‍4 (true): required the longitude at noon.

ADDITIONAL FOR FIRST MATE.

10. 1872, February 27th, mean time at ship 5h 25m P.M., latitude 37° 20′ S., longitude 14° 10' W., sun's bearing by compass W. by N. 4 N., observed altitude sun's U.L. 14° 50' 30, index correction - 1′ 3′′, height of eye 19 feet: required the variation. II. 1872, May 29th, A.M. at ship, latitude account o° 31' N., longitude 150° 40′ W., observed altitude of sun's L.L., North of observer, was 67° 41′, index correction + 1', height of eye 20 feet, time by watch 29d 3h 32m, which had been found to be 4h 28m fast on apparent time at ship, the difference of longitude made to the East was 26'9 after the error on apparent time was determined: required the latitude,

ADDITIONAL FOR MASTER ORDINARY.

12. 1872, June 17th, the longitude 98° W., observed meridian altitude of a Serpentis, zenith South of observer, was 29° 0′ 40′′, index correction + 4′ 20′′, height of eye 24 feet required the latitude.

13. At the Cape of Good Hope the variation is about 28° W., if the sun at noon bear due North by compass, what is the deviation?

A SEXTANT is constructed on the same principles as a quadrant, and furnishes the means of measuring the angle between two objects in whatever direction they may be placed, so that the angle does not exceed 140°.

DESCRIPTION OF A SEXTANT.

BC is the arc or limb which is graduated from o° to about 140° (from C towards B), and each degree in the best instruments is again sub-divided into six equal parts of 10 each, while the vernier g used in estimating the sub-divisions of the arc shows 10". The divisions are also continued a short distance on the other side of zero (o), towards C, forming what is termed the arc of excess, for the purpose of determining the index error in the manner that will be subsequently explained. The microscope M, and its reflector r secured at the point d by a movable arm dr to the index A E, may be adjusted to read off the divisions on the graduated limb and the vernier g. The index A E is secured to the arc B C by the intervention of a clamp screws at its back, which must be loosened when the index has to be moved any

considerable distance, and when the contact nearly has been made by hand, the screw is again to be fixed, and a tangent screws enables the index to be moved by a small quantity along the limb, so as to render the contact of the objects observed more perfect than could be effected by moving the index solely by the hand; the other extremity of the index has a silvered glass or reflector I fixed perpendicular to the plane of the instrument and directly over the centre; another glass b is fixed perpendicular to the plane of the instrument frame H, of which the lower half only is silvered and the upper transparent; the plane of this glass, usually termed the horizon-glass, is made parallel to the plane of the index glass I, when the vernier g is adjusted to zero on the divided arc B C, or if not so made, the want of parallelism constitutes what is termed the index error of the instrument. The telescope t is carried by a ring fastened to a stem E, which can be raised or lowered by a mill-headed screws" at the back of the frame, for the purpose of so placing the field of the telescope that it may be bisected by the line on the horizon-glass, separating the silvered from the unsilvered part, whereby the brightness of the reflected object and that seen by direct vision may be made equal, and the quality of the observations improved. It is usual to supply a direct and inverting telescope, of which the latter is to be preferred, as possessing greater magnifying power, and thus showing a better contact of the images of the objects. Two wires parallel to each other, and to the plane of the instrument, are placed in the inverting telescope, within which limit the observation should be made.

Dark glasses of different colours and shades are a necessary accompaniment to the sextant to enable the sun to be observed, and they are usually attached to a hinged joint as K. Four of these glasses or shades are placed at a, between the index and horizon-glasses, so as to admit of one or more of them being interposed between the index and horizon-glass. Three more such glasses, sometimes called back shades, are placed behind the horizon-glass at K, any one or more of which can also be turned down to moderate the intensity of the light before meeting the eye, when observing a bright object, such as the sun. There is also a dark glass, which can be placed at the eye-end t of the telescope, which method is preferable to the other, as no error in this is liable to be introduced in the passage of the rays from the index to the horizon-glass.*

With respect to the dark glasses, when it is possible (as in observing altitudes of the sun in the mercurial horizon, &c.) to make the observation with a single dark

M M

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.

READING OFF THE ANGLE.

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 arc, 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 represents 10.

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

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 is 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 arc 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 are 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 arc and one on the vernier is of a division of the arc; if, therefore, a division on the arc is 10', the difference will be 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 arc. 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 arc 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