the sight and horizon glass at the mark A, and observe whether the image is directly under the object; if not, move the index till they coincide. 4. If the index division of the nonius is on the arc of excess, the indicated quantity is to be added to the observed angle; but if it be on the quadrantal arc, the quantity indicated is to be subtracted: let us suppose five to be added. 5. Now direct the sight through the transparent part of the horizon glass to A, keep that object in view, move the index till the object C is seen by reflection in the silvered part of the horizon glass. 6. The objects being now both in view, move the index till they unite as one, or appear in one vertical line, and the index will shew the angle subtended at the eye by the two objects: suppose 75° 20′, to which add 5' for the index error, and you obtain 75° 25', the angle required; if the angle be greater than 120°, which seldom happens in practice, it may be subdivided by marks, and then measured.

No instrument can be more convenient or expeditious than the sextant, for setting of offsets. Adjust the instrument and set the index to 90 degrees; walk along the station line with the octant in your hand, always directing the sight to the farther station staff; let the assistant walk along the boundary line; then, if you wish to make an offset from a given point in the station line, stop at that place, and wait till you see your assistant by reflection, he is then at the point in the boundary through which that offset passes; on the other hand, if you wish an offset from a given point or bend in the boundary, let the assistant stop at that place, and do you walk on in the station line till you see the assistant by reflection in the octant, and that will be the point where an offset from the proposed point or bend will fall.

The manner of using this instrument for the solution of those astronomical problems that are necessary in surveying, &c. will be shewn in its proper place.

DESCRIPTION OF A NEW POCKET BOX SEXTANT, AND AN ARTIFICIAL HORIZON,* BY THE EDITOR.

Fig. 11, plate 19, is a representation of a very convenient pocket sextant, and contains a material improvement on the reflecting cross staff before described, see fig. 4, plate 14. In military operations, as well as trigonometrical ones, it has been found of very essential service. AB a round brass box three inches in diameter, and one inch deep. AC is the index turning an index glass within the box: a, a, are the two outside ends of the screws that confine an horizon glass also within the box. An angle is observed by the sight being directed through an hole in the side of the box about D, upon and through the horizon glass and the second opening at E, and the angle is read off to one minute by the divided arc and nonius F, G, II. By sliding a pin projecting on the side of the box, a dark glass is brought before the sight hole, not shewn in the figure; by pushing the pin at b, a dark screen for the sun is interposed between the index and horizon glasses. I is an endless screw, sometimes applied to give a very accurate motion, like the tangent screw to the index of a sextant. Or a racked are and pinion may be applied at about c, d, which I think in some respects better.

The following table is sometimes engraved upon the cover that goes over the box when shut up. By the sextant being set to any of the angles contained in this table, an height or distance of accessible or inaccessible objects is obtained in a very simple and expeditious manner.

Plate 19, fig. 13, represents a portable and universal brass stand for supporting occasionally a sextant or reflecting circle, which with the horizon packs into a flat portable case.

Make a mark upon the object, if accessible, equal to the height of your eye from the ground. Set the index to any of the angles from this table, and walk from the object, till 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 corre‐ sponding 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. If the object be inaccessible, set the index to the greatest angle in the table that the least distance from the object will admit of, when by moving backwards and forwards, till the top of the object is brought to a level with the eye, and at this place set up a mark equal to the height of the eye. Then set the index to any of the lesser angles, and go backwards in a line from the object, till the top is made to appear on the level with the eye, or mark before set; set here another mark, measure the distance between the two marks, and this divided by the difference of the figures in the last column, against the angle made use of, the quotient 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.

If the index is set at 45° the distance is the height

of the object, and vice versa. The index set to 90 becomes a reflecting cross staff, and is used according to the directions in page 267. See also page 204.

The sextants, as before described by the author, of the best kind, are made of brass, or other metal. The radii now most approved of are from six to ten inches, their arcs accurately divided by an engine, and the nonii shewing the angles to 30, 15, or even 10 seconds; but the fine divisions of the latter are liable to be obliterated by the frequent cleaning of the instrument.

THE ARTIFICIAL HORIZON.

In many cases it happens that altitudes are to be taken on land by the sextant; which, for want of a natural horizon, can only be obtained by an artificial one. There have been a variety of these sort of instruments made, but the kind now to be described is allowed to be the only one that can be depended upon. Fig. 12, plate 19, represents the horizon fixed up for use. A is a wood or metal framed roof containing two true parallel glasses of about 5 by 3! inches, fixed not too tight in the frames of the roof. This serves to shelter from the air a wooden trough filled with quicksilver. In making an observation by it with the sextant, the reflected image of the sun, moon, or other object, is brought to coincide with the same object reflected from the glasses of the sextant; half the angle shewn upon the limb is the altitude above the horizon or level required. It is necessary in a set of observations that the roof be always placed the same way. When done with, the roof folds up flat-ways, and, with the quicksilver in a bottle, &c. is packed into a portable flat case.

TO SURVEY WITH THE CHAIN ONLY.

The difficulties that occur in measuring with accuracy a straight line, render this method of survey

ing altogether insufficient for measuring a piece of ground of any extent; it would be not only extremely tedious, but liable to many errors that could not be detected; indeed there are very few situations where it could be used without King's surveying quadrant, or some substitute for it. The method is indeed in itself so essentially defective, that those who have praised it most, have been forced to call in some instrument, as the surveying cross and optical square, to their aid. Little more need be said, as it is evident, as well from the nature of the subject, as from the practice of the most eminent surveyors, that the measuring of fields by the chain can only be proper for level ground and small enclosures; and that even then, it is better to go round the field and measure the angles thereof, taking offsets from the station lines to the fences. That this work may not be deemed imperfect, we shall introduce an example or two selected from some of the best writers on the subject; observing, however, that fields that are plotted from measured lines, are always plotted nearest to the truth, when those lines form at their junction angles that approach nearly to a right angle.

Example 1. To survey the triangular field A B C, fig. 22, plate 9, by the chain and cross. Set up marks at the corners, then begin at one of them, and measure from A to B, till you imagine that you are near the point D, where a perpendicular would fall from the angle C, then letting the chain lie in the line A B, fix the cross at D, so as to see through one pair of the sights the marks at A and B; then look through the other pair towards C, and if you see the marks there, the cross is at its right place; if not, you must move it backwards and forwards on the

line AB, till you see the mark at C, and thus find the point D; place a mark at D, set down in your field book the distance AD, and complete the measure of A B, by measuring from D to B, 11.41.