Ebook The Compass

C E, Fig. 5, touch a circle, and from the point of contact A a straight line A B be drawn cutting the circle, the angles CA B and B A E, which this line makes with the line touching the circle, shall be equal to the angles A D B and A F B which are in the alternate segments of the circle. Thus, in the figure, the angle A 0 B at the centre of the curve being known 2 a, the angle in the segment A D B =c A B 180° a. Set the vernier of the instrument to the angle thus found, and taking any position, say D, supposed to be in or near to the required curve, hold up the instrument, the observer facing towards the centre of the curve. If the images of a rod at A and another rod at B coincide in the two prisms vertically, then the point D is in the required curve, but if they do not coincide, the observer must shift his position until they are brought into coincidence. In this manner, and by the simple use of the rods at A and B, any number of points in the curve may be found.