SECTION XIII.

THE POCKET SEXTANT-ITS ADJUSTMENTS - USE IN SURVEYING, MEASURING HEIGHTS AND DISTANCES, ETC. THE REFLECTING SEMICIRCLE - OPTICAL SQUARE PLANE TABLE.

WITH a view of not distracting the attention of the student, little or no mention has been made thus far of any surveying instruments, save such as were absolutely necessary in order to illustrate our descriptions of the various methods of military surveying: but, although we have hitherto confined ourselves to the theodolite and compass, it is not to be inferred that we reject all others. The pocket sextant and the reflecting semicircle are both applicable to the purposes of military men, and may be advantageously used on many occasions instead of a theodolite or compass. I shall now proceed to give a particular description of the sextant, and to explain the several uses to which this beautiful instrument may be applied.

The pocket sextant combines numerous valuable properties; it measures an angle to one minute of a degree, requires no support but the hand, may be used on horseback, maintains its adjustment long, and is easily readjusted when put out of order. It will determine the latitude by a meridian altitude to one minute, and an approximation may even be made with it to the longitude, by means of lunar observations. Further, it is very portable, forming when shut up a circular box under 3 inches in diameter, and only 11⁄2 inch deep.

The figure given in plate XVI. represents the instrument screwed to its box, for convenience of holding in the hand, and with the telescope drawn out. A is the index arm, having a vernier adjusted to the graduated arc, B, which latter is numbered to 140°, but the sextant will not measure an angle greater than about 120°. The index is moved by the milled head, C, acting upon a rack and pinion in the interior. Two mirrors are placed inside: the large one, or index mirror, is fixed to and moves with the index; the other, called the horizon-glass, is only half silvered. The proper adjustment of the instrument depends on these glasses being parallel, when the index is at zero; while they are, at the same time, perpendicular to what is termed the plane of the instrument, represented by its upper surface or face. To observe whether the instrument is in perfect adjustment, remove the telescope by pulling it out, and supply its place with a slide for the purpose, in which is a small hole to look through; then place the index accurately at zero, and direct the instrument, holding it horizontally, towards the sharp angle of a building not less than half a mile distant, applying the eye so as to see both through the hole in the slide and also through the unsilvered part of the horizonglass; the same object ought then to be so reflected from the index-mirror to the silvered part of the horizon-glass, as to seem but one with the object seen direct: if such be not the case, a correction becomes necessary, which is thus performed:-D is a key, removeable at pleasure, that fits two keyholes, the one at a, the other at b. Apply this key at a, and gently turn until the reflected object, and the one seen direct, seem but as one. The glasses are

then parallel.

The next point is to examine whether the horizon-glass is perpendicular to the plane of the instrument. For this purpose hold the sextant horizontally, and look at the distant horizon; then, if any adjustment is wanted, two horizons will appear, and the reflected one will be higher or lower than the one seen direct: should this be the case, apply the key at b, so as to bring the two horizons together. Observe, that the large or index-mirror, being correct by construction, it can want no alteration.

By looking at the sun, we can always satisfy ourselves with respect to the adjustments; the telescope has a dark glass at the eye end, and with this on we have only to place the index at zero, and, using the telescope, to look at the sun; when, provided the instrument is in exact adjustment, one perfect orb only will be seen. If the reflected image projects beyond the other, then correction is necessary. The full moon will answer as well as the sun for this purpose, but the dark glass at the eye end of the telescope must then be removed. The instrument is provided with two other dark glasses, which sink out of the way by raising two little levers at f.

It has been mentioned above that, for trying the adjustment of the sextant, an object must be half a mile off; this is on account of what is called the parallax of the instrument, occasioned by the necessity of placing the eye of the observer on one side of the index-mirror. Could we look from the middle of it, there would be no parallax; which is the angle subtended by the point of vision and centre of the index-glass, when observing any near object: consequently, as the distance of an object is increased, this angle diminishes, and at length becomes as nothing when compared with it. Half a mile is considered sufficient for all error to vanish, but at half that distance it is scarcely perceptible.

To take an angle, the observer looks either through the telescope or hole in the slide (having previously raised the

levers of the dark glasses at f), at the left-hand object, holding the sextant horizontally in his left hand; with his right he turns the milled head, C, until the other object, reflected from the index-glass, appears upon the silvered part of the horizon-glass, exactly covering or agreeing with the left-hand object, seen direct through the unsilvered portion of the horizon-glass: the angle is then obtained by the vernier to one minute. Should circumstances render it desirable for the observer to look at the right-hand object, he has only to hold the instrument bottom upwards.

If the required angle be a vertical one, the sextant is held in a vertical position by the right hand, while the left turns the milled head, C, until the object is brought down to the horizon.

When the altitude of a celestial body is taken at sea, it is brought down, as the term is, to the natural horizon, and the measure of the angle, or height of the object, is read off upon the graduated arc; but on land the natural horizon can seldom be used, on account of its irregularity: recourse is then had to what is called an artificial horizon, such as a vessel containing water, mercury, or other fluid. The observer then places himself in a situation to see the reflected image of the sun or other body in the fluid; he has only then to bring down the image, as reflected from the index-glass, until it reaches its reflection in the fluid: the altitude will then be half the number of degrees indicated by the graduated arc, subject to certain corrections, not necessary to be explained here. [See Artificial Horizon.]

The chief, and indeed only objection to the sextant, as a surveying instrument, arises from the angles taken with it not being always, like those measured by the theodolite and compass, horizontal ones. If the theodolite be set truly level, we can take angles all round upon its circle, no matter whether one object be high and another low, and these angles will be what are termed horizontal angles; so that, were we to take angles from object to object and complete the circle, the sum of all those angles ought to be 360 degrees, or the measure of a circle. But if the same angles were to be measured by a reflecting instrument, they would not produce precisely 360 degrees, unless taken upon a perfectly level plane; owing to this circumstance, that to take an angle by the sextant, the two objects having to be brought into contact, namely, the reflected one and that seen direct, it is necessary for the observer to hold his instrument, not strictly horizontal, but in the plane of the two objects, or in such a position as will enable him to form the contact; and therefore, if one point is elevated very much above the other, the sextant must be held at a corresponding inclination with the horizon. Angles so taken require a reduction, as it is termed, to horizontal ones; that is, to what those angles would have been, had the points subtending them been on a level with the eye of the observer, which is what is understood by the term horizontal. But, as we seldom use the sextant to lay down points for a trigonometrical survey of importance, it rarely occurs that the reduction is required; indeed, to effect it with accuracy is attended with considerable difficulty, as the angles of elevation and depression must be known-a matter of no easy attainment with the sextant. It is better to avoid, if possible, the necessity of making any reductions, by selecting stations neither much elevated nor depressed; and three or four degrees either way can never affect an angle, so as to be of much consequence in military sketching. By a little management, too, a correct eye will enable us to select some spot directly under an elevated object, and at the same time nearly horizontal;