Three points on the circumference of a circle being known, and the centre being inaccessible, the curve is drawn by the following method. If it is for workshop vise only that the curve is wanted, cut a triangular template (Fig. 1), two of whose sides touch the outer points AC and meet on the inner point B. Then pins being inserted at A and C, and a pencil or scriber at B, the template may be shifted round to describe the curve. If it is for work such as railway curves, let ABO (Fig. 2) be the three given points. Measure the lengths A B, B C, and the angle ABC; then to find radius B F, we have first Bed + Bde = 180° - dBe. L tan. 1/2 (Bed - Bde) = log. (1/2AB - 1/2BC) - log. (1/2AB + ABC) + L cot. dBe/2. whence by reference to mathematical tables (Bed -Bde) is obtained, and then B d e = (Bed+ Bde) - (Bed-Bdej and BeD = 180 - (Bde + dBe). Then de = (1/2 A B) sin dBe/sin.BeD log.de=log.(1/2 AB) + L sin. dBe - L sin.

Bed, From this edf = 90 - Bde, and def = 90o-Bed; dfe= 180° -edf- def; df= de sin.def/sindfe,log. df.= e log. de + Lsin. def - L sin. dfe. But B d f = Bde + edf - 90°; = radius B f. Now g d: d B d B: d h, or d h = (dB)2/gd, and 2 (fh) - dh = 2 (Bf) - dh = dg. If more points are required, say point i, join Ag, then Ag= ,gf =Bf,jf= and .'.ji = Bf - j f. Other points can be found in the same way.

Finding Circular Curve when Centre is Inaccessible.