such mark may then be taken instead of the object itself: or we may take the angle between each of the objects we are observing, and some other point situated far to the right of them, and the difference will be an approximation to the angle sought. In short, a person habituated to the use of the sextant will generally be prepared with some contrivance, to obviate the necessity of having recourse to the reduction of his angles; which is performed, when requisite, by a calculation in spherical trigonometry, the formula for which will be given in another place.

An addition has lately been made to the pocket boxsextant, for the purpose of taking altitudes and depressions: it consists of two small spirit-levels, fixed at the back of the horizon-glass, at right angles to each other; so that, standing before the object, you look perpendicularly down through the plain sight, and, moving the index, bring the image of the object to appear with the levels, which must have their air-bubbles in the centre of their tubes. The reading of the instrument will then show the supplement of the zenith distance, and its complement to 90° will be the angle required; elevated, if more than 90°, and depressed, if less than 90°. A moment's consideration will show that a practised hand is here necessary to catch the bubbles of such minute spirit-levels at the happy instant. This addition has the disadvantage of increasing somewhat the depth of the box, which is rather an objection in the eyes of military men. And, after all, allowing that an approximation may be made by it towards determining an elevation or depression, when the object is very near, I feel disposed to think that with distant ones, which necessarily subtend low angles, the result can never be depended on.

I may just notice a contrivance for enabling the observer to read large angles with the box sextant, namely, by placing a second index-glass below the other, and at right angles to it; and, having the arc doubly graduated, observations are then taken by looking through a different hole, placed opposite the usual one.

For military purposes this arrangement is objectionable, as it reduces the index-glasses to half the original size, and therefore injures the instrument for distant observations.

In order to render this chapter on the sextant as useful as possible, I shall take the liberty of extracting from Mr. Burr's "Practical Treatise on Surveying and Topographical Plan-drawing," a little contrivance that military men may chance to find of use for determining heights of mountains.

" It has been said in the preceding pages, that reflecting instruments require an artificial horizon to take altitudes; but we cannot use them for small altitudes, because the rim of the vessel containing the reflecting fluid renders it impossible, nor can we take depressions by such means: yet, as a military man may have occasion for such observations, and not possess an instrument provided with a vertical arc and level, we shall see how this may be done nearly, that is to say, within two or three minutes, by a reflecting instrument. Place three strong stakes across, like the triangle used for hanging a kettle, upon the ground, binding them firmly at the junction; across two of the legs tie a fine thread tightly, and place underneath any vessel containing a fluid, as mercury or water. Now, it is plain, that when we look from above, so as to bring the thread and its reflected image into exact coincidence, our eye will be in a vertical plane; therefore, by resting upon the stakes, and bringing the reflected image of a distant object into exact contact with the thread, we shall measure the supplement of the zenith distance; and if that

is less than 90°, its complement will be the depression; but if above 90°, the surplus will be the elevation. This apparatus can be made anywhere; and we insert this expedient, in order to show that, with apparently slender means, we may do something."

I have found this simple expedient to answer very well for an approximation to the height of hills, buildings, &c., and shall add a diagram, which will assist my readers to understand it.

Let C represent the situation of the observer's eye, AB the horizon, and E the top of a hill. ED is then the zenith distance. By the method above given, we measure the angle, ECG, which is, of course, the supplement of the zenith distance, ED; and, consequently, if we deduct 90°, or the angle, ACG, measured by the arc, AG-the angle, ACE, is left, namely, the elevation of E above the horizon. Again, for the depression -- suppose our object is to obtain the depression of F-we measure the angle, FCG, the complement of which, or its difference from 90°, gives the angle, ACF, which is the depression of F.

The height and distance of objects, as walls or buildings, whether accessible or otherwise, may be obtained in a very simple and expeditious manner with the sextant, by means of the following table of tangents.

Make a mark upon the object, if accessible, equal to the height of your eye from the ground. Set the index to one of the angles in the table, and retire on level ground, until the top is brought by the glasses to coincide with the mark; then, if the angle be greater than 45°, multiply the distance by the corresponding figure to the angle in the table; if it be less, divide; and the product, or quotient, will be the height of the object above the mark. Thus, let EB be a wall, whose height we want to know; and Make a mark at D equal to

26° 34′ the angle selected. the height of the eye; then step back from the wall, until the top at E

E

from your station to the wall, and divide that distance by 2,

the figure corresponding to 26° 34', this will give the

height, DE, to which BD must be added.

The parallax of the instrument has been already mentioned and explained: it exerts an influence on measurements of this kind, from the object being near. To correct it, we have only to ascertain its amount, by placing the index at zero, and looking through the instrument at the top of the wall; when, if influenced by parallax, it will appear as a broken line; but by moving the index a little way on the arc of excess, or to the left of zero, the broken line will reunite, and the adjustment be effected. When any quantity is taken thus on the arc of excess, the amount must be considered, when setting the instrument to any of the tabular angles.

When the object is inaccessible, set the index to the greatest of the divisor angles in the table, that the least distance from the object will admit of, and advance or recede till the top of it is brought down by the sextant to a level with the eye: at this place set up a staff, equal to the height of the eye. Then set the index to one of the lesser angles, and retire in a line from the object, till the top is brought to coincide with the staff set up to indicate the height of the eye: place a mark here, and measure the distance between the two marks; this, divided by the difference of the figures opposite the angles used, will give the height of the object above the height of the eye, or mark. For the distance, multiply the height of the object by the numbers against either of the angles made use of, and the product will be the distance of the object from the place where such angle was used.

The above will be understood better by means of a diagram. Let A B be a wall, not to be approached nearer than C; and we find, upon trial, that this distance admits of our using the angle 45°: assume a point E on the wall, as the height of the eye; then the index being set to 45°, fix yourself so that the glasses shall bring the top, A, to coincide