however, a correct table to five places of decimals could be presented in about four pages, then two more pages might contain such a table as the preceding, and an analogous table of logarithmic sines, tangents, &c. A single sheet might thus be made to exhibit all the tables, precepts, and rules, necessary in the common practice of trigonometry, and in the computation of annuities and reversions. Much shall I rejoice if some of your correspondents enable you to present to the public so valuable a gift.

P. M. W.

DESCRIPTION

SECTION XXI.

AND USE OF THE SEXTANT-ITS ADJUST

MENTS-ARTIFICIAL HORIZON-METHOD OF USING IT— PARALLAX-REFRACTION-TO FIND THE VARIATION OF

THE NEEDLE.

DESCRIPTION AND USE OF THE SEXTANT.

THE large sextant differs, both in form and in its adjustments, from the pocket box-sextant, which is described in Section XIII.; it is used for measuring the altitudes of, and distances between, heavenly bodies. The following description of the sextant is principally taken from Mr. F. Simms's work on Instruments.

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The annexed figure represents a sextant of Troughton's construction, having a double frame, A A, connected by pillars, thus uniting strength with lightness. The arc, BC, is generally graduated to 10 minutes of a mencing near the end, C, and it is numbered towards B. The divisions are also continued on the other side of zero, towards C, forming what is called the arc of excess, which is useful in determining the index-error of the instrument, as will be explained hereafter. The limb is subdivided by the vernier, E, into 10", the half of which (or 5′′) can be easily estimated: this small quantity is easily distinguishable by the aid of the microscope, H, and its reflector, b, which are connected by an arm with the index, IE, at the point, c, round which it turns as a centre, affording the

means of examining the whole vernier, the connecting arm being long enough to allow the microscope to pass over the whole of it.

B

K

I

F

H

To the index is attached a clamp to fasten it to the limb, and a tangent-screw, J (in the figure the clamp is concealed from view), by which the index may be moved any small quantity, after it is clamped, to render the contact of the objects observed more perfect than can be done by moving it with the hand alone. The upper end, I, terminates in a circle, across which is fixed the silvered index-glass, F, over the centre of motion, and perpendicular to the plane of the instrument. To the frame at G is attached a second glass, called the horizon-glass, the lower half of which only is silvered: this must likewise be perpendicular to the plane of the instrument, and in such a position that its plane shall be parallel to the plane of the index-glass, F, when the

vernier is set to 0° (or zero) on the limb, BC. A deviation from this position constitutes the index-error, before spoken of.

The telescope is carried by a ring, L, attached to a stem, e, called the up-and-down piece, which can be raised or lowered, by turning the milled-screw, M: its use is to place the telescope so that the field of view may be bisected by the line on the horizon-glass that separates the silvered from the unsilvered part. This is important, as it renders the object seen by reflection, and that by direct vision, equally bright:* two telescopes, and a two telescopes, and a plain tube, all adapted to the ring, L, are packed with the sextant, one showing the objects erect, and the other inverting them; the last has a greater magnifying power, showing the contact of the images much better. The adjustment for distinct vision is obtained by sliding the tube at the eye-end of the telescope in the inside of the other: this also is the means of adapting the focus to suit different eyes. In the inverting telescope are placed two wires, parallel to each other, and in the middle of the space between them the observations are to be made, the wires being first brought parallel to the plane of the sextant, which may be judged of with sufficient exactness by the eye. When observing with the telescope, it must be borne in mind, that the instrument is to be moved in a contrary direction to that which the object appears to take, in order to keep it in the field of view.

Four dark glasses, of different depths of shade and colour, are placed at K, between the index and horizon glasses;

*This is not the case when one object is much brighter than the other, as the sun and moon; in taking the distance between which, the screw, M, should be moved more than above stated, until they are both nearly of the same brightness, as an observation can be made better when this is the case, than when otherwise.

also three more at N, any one or more of which can be turned down to moderate the intensity of the light, before reaching the eye, when a very luminous object (as the sun) is observed. The same purpose is effected by fixing a dark glass to the eye-end of the telescope: one or more dark glasses for this purpose generally accompany the instrument. They, however, are chiefly used when the sun's altitude is observed with an artificial horizon, or for ascertaining the index-error; as employing the shades attached to the instrument for such purposes would involve in the result any error which they might possess. The handle, which is shown at O, is fixed at the back of the instrument. The hole in the middle is for fixing it to a stand, which is useful when an observer is desirous of great steadiness.

OF THE ADJUSTMENTS.

The requisite adjustments are the following:-The index and horizon glasses must be perpendicular to the plane of the instrument, and their planes parallel to each other, when the index division of the vernier is at 0° on the arc; and the optical axis of the telescope must be parallel to the plane of the instrument. We shall speak separately of

each of these adjustments.

TO EXAMINE THE ADJUSTMENT OF THE INDEX-GLASS.

Move the index forward to about the middle of the limb, then, holding the instrument horizontally with the divided limb towards the observer, and the index-glass to the eye, look obliquely down the glass, so as to see the circular arc, by direct view and by reflection, in the glass at the same time; and if they appear as one continued circle, the index-glass is in adjustment. If it requires correcting,