### Penciling

In laying out Plate VIII, draw the border lines and horizontal and vertical center lines as in previous plates, dividing the plate into four spaces.

## Problem 25. How To Construct A Cycloid When The Diameter Of The Generating Circle Is Given

With 0' as a center and a radius of 7/8 inch draw a circle, and, tangent to it, draw the indefinite horizontal straight line A B. Divide the circle into any number of equal parts - 12 for instance - and through these points of division C, D, E, F, etc., draw horizontal lines. Now with the dividers set so that the distance between the points is equal to the chord of the arc C D, mark off the points L, M, N, 0, P, on the line A B, commencing at the point H. At these points erect perpendiculars to the center line X O' which is the line of centers of the generating circle as it rolls along the line A B. With the intersections Q, R, S, T, etc., as centers describe arcs of circles as shown. The points on the cycloid will be the intersections of these arcs and the horizontal lines drawn through the points C, D, E, F, etc. Thus the intersection of the arc whose center is Q and the horizontal line through C is a point J on the curve. Similarly, the intersection of the arc whose center is R and the horizontal line through D is the point K on the curve. The remaining points on the left, as well as those on the right, are found in the same manner. To obtain great accuracy in this curve, the circle should be divided into a large number of equal parts, because the greater the number of divisions the less the error due to the difference in length between a chord and its arc. 