the outer limb be divided into degrees and 6th parts of a degree, marking the degrees from the middle of the limb, both ways, 10, 20, 30, &c., to 90 at N and Z. Let also, the middle space between the outer and inner limbs, be marked from Z to N, 10, 20, 30, 40, &c., to 180 at N.

Let this semi-circle be fixed to the middle of a box ruler B D, about 3 feet long, an inch and a half broad, and of a convenient thickness. The inner breadth of half this rule must be level with the surface of the semi-circle, but the outer half must be higher about two-tenths of an inch. On the outer half there must be fixed a thin brass scale of an equal length and breadth with the box ruler, the breadth of which scale is to be divided, by lines drawn from end to end, into three equal parts, and the length into inches, half inches, and tenth of an inch; the inches are to be drawn directly across the whole breadth, and marked 1, 2, 3, 4, &c., both ways to B and D; the half inches are to be drawn across the middle and innermost third, and the 10ths only across the inner third. Let there be on one end of this scale an inch, and on the other end half an inch, each divided very

exactly into 10 equal parts diagonally, that the 10ths and centesms which may happen in the operations, on the square and indices hereafter to be described, may be exactly measured on them by a pair of dividers. The reason for raising the outer half of the box ruler above the inner half two-tenths of an inch, is to make room for the indices A b and A d, which are to be fixed to the centre of the semi-circle, and there to open and shut as occasion requires, like the legs of a sector. Those indices are about 26 inches long, threefourths of an inch broad, and about two-tenths thick; their breadth is to be divided into three equal parts, and their length into inches, half inches, and tenths, as the brass scale before mentioned. The inches are to be marked from the center A, with 1, 2, 3, 4, &c., to b and d, and the tenths drawn across the inner third. Each of those indices must have a small screw nut with a pin or bit of wire upon it, which pin may, by the screw nut, be fixed exactly to any division on them in order to suspend the label, or ruler T Y, which has a thin piece of brass with a small hole in it, exactly fitting the aforesaid pin, and is to be fixed

also to any division of the ruler, as occasion requires. Let this label, or ruler, be about two feet long, and of the same breadth and thickness as the indices A b and A d, and divided after the same manner as they are, only the tenths are to be drawn across the inner edge, as well as across the inner third of the breadth, and the inches are to be marked 1, 2, 3, 4, &c., from C to T and Y, making C T eighteen inches, and C Y six. The like divisions are to be made on the side of the square K X, beginning at the inner edge of the brass ruler at K, marking the full inches on the upper side, 1, 2, 3, 4, &c., to 24; the tenths are to be drawn across the upper third and the upper edge. Let this instrument be fixed on a tripod with a ball and socket like those of a common surveying instrument, but very strong, in order to have it very firm; and let there be sights which may, as occasion requires, be fixed on the diameter, indices, and ruler T Y, of the the same kind with those of a surveying instrument.

N. B. The ball and socket must not be fixed exactly under the center of the semi-circle, but some distance from it, on the cross-bar which goes from

the center to the middle of the limb, as well to support the head of the instrument more easily by being nearer its center of gravity, as to make room for an air level, which must be fixed exactly under the diameter or ruler A B, so that when the semicircle is turned vertically the diameter may be fixed horizontally.

The use of the Instrument in measuring distances:

EXAMPLE.

Let it be required to find the distance from the house at A to the castle, (fig. 27) or to any part thereof, as the weather-cock on the top of the spire at C.

Having set up your instrument at A, turn it about till through the sights on the diameter, you see a mark set up at B, and having fixed the diameter in that position, turn the moving index till through the narrow slit of a small sight fixed on the center, you see the hair in the other sight cut the spire at C, then fixing the index in that position to the limb of the semi-circle, measure with a four pole chain in a straight line from A to B ; and having marked the chains and links of that distance on the diameter and placed the ruler with the sights on it exactly to that distance, by means of the small pin and hole mentioned before, set up your instrument at the end of the distance you measured (which you may make full chains if you please) and turn it about till through the sights on the diameter you see a pole at the first station A, and having fixed it in that position, turn the ruler on the pin which is fixed at the former distance on