a method of measuring angles, so called by M. de Lagny, who gave several papers on this method in the Memoirs of the Royal Acad. anno 1724, 1725, 1729. M. de Lagny's method of goniometry consists in measuring the angles with a pair of compasses, and that without any scale whatever, except an undivided semicircle. Thus, having any angle drawn upon paper to be measured, produce one of the sides of the angle backwards behind the angular point; then with a pair of fine compasses describe a pretty large semicircle from the angular point as a centre, cutting the sides of the proposed angle, which will intercept a part of the semicircle. Take then this intercepted part very exactly between the points of the compasses, and turn them successively over upon the arc of the semi-

circle, to find how often it is contained in it, after which there is commonly some remainder: then take this remainder in the compasses, and, in like manner, find how often it is contained in the last of the integral parts of the first arc, with again some remainder: find, in like manner, how often this last remainder is contained in the former; and so on continually, till the remainder become too small to be taken and applied as a measure. By this means he obtains a series of quotients, or fractional parts, one of another, which being properly reduced into one fraction, gives the ratio of the first arc to the semicircle, or of the proposed angle to two right angles, or 180 degrees, and consequently that angle itself, in degrees and minutes.

We have given this account of goniometry from Dr. Hutton, and frankly acknowledge that we had never thought of it till we perused his excellent Dictionary of Mathematics and Philosophy. To have omitted the method when pointed out to us would have been wrong; though we mistake much if mathematicians in general will not look upon it as a method of very little value.

GOTHIC ARCHITECTURE. (See Gothic Architecture in this Supplement, and Roof Encyclopaedia.)