QUADRAT, a mathematical instru, ment, called also a geometrical square, and line of shadows ; it is frequently an additional member on the face of the common quadrant, as also on those of Gunter's and Sutton's quadrants ; but we shall describe it by itself, as being a dis tinct instrument.
It is made of any solid matter, as brass, wood, &c. or of any four plain rules joined together at right angles, as represented in Plate XIII. Miscell. fig. 2, where A is the centre, from which hangs a thread-with a small weight at the end, serving as a plummet. Each of the sides, B E and D E, is divided into an hundred equal parts ; or, if the sides be long enough to admit of it, into a thousand parts ; C and F are two sights, fixed on the side AD. There is, moreover, an index, G H, which, when there is occasion, is joined to the centre, A, in such a manner as that it can move freely round, and remain in any given situation ; on this instrument are two sights, K L, perpendicular to the right line going from the centre of the in strument. The side D E is called the up
right side, or the line of the direct or upright shadows ; and the inside B E is termed the reclining side, or the line of the versed or back shadows.
To measure an accessible height, A B, (fig. 3) by the quadrat, let the distance, B D, be measured, which suppose = 96 feet, and let the height of the observer's eye he 6 feet ; then holding the instrument with a steady hand, or rather resting it on a support, let it be directed towards the summit A, so that it may be seen clearly through both sights; the perpen dicular, or plumb-line, meanwhile hang ing free, and touching the surface of the instrument : let now the perpendicular be supposed to cut off on the tipper side, K N, 80 equal parts ; it is evident, that