Fig. 76.
Answer: In [Fig. 76] is shown how the center of a circle may be determined without the use of compasses; this is based on the principle that a circle can be drawn through any three points that are not actually in a straight line. Suppose we take A, B, C, D for four given points, then draw a line from A to D, and from B to C; get the center of these lines, and square from these centers as shown, and when the square crosses the line, or where the lines intersect, as at x, there will be the center of the circle. This is a very useful rule.
Ed. McDonald, Cincinnati, Ohio, says: “I want to know how much can be done with the square towards setting out stair railing?”
Answer: In a previous page a few remarks on this subject will be found and the following is further submitted:
Fig. 77.
Fig. 78.
[Fig. 77] shows a plan of a stair well having three winders. The rail in this case will have two different pitches. These rails are a little more complicated than those having equal pitches, as in the latter the major axis is parallel off the diagonal line B D ([Fig. 77]). When the pitches differ the major axis ceases to be parallel; and the greater the difference in the pitches, the greater will be the difference in the axis and diagonal line. This fact can be easily demonstrated by cutting a model bed block out of 2-inch by 2-inch stuff to equal pitches. Procure a board, and draw a parallel line, say 8 inches off the edge. Now square over a line to cut the first line; set the bed block on, with the back corner touching the intersection of the lines. Lay a piece of cardboard on the inclined face of the bed block, and let it slide down until it touches the board. Make a mark along this edge, and it will be seen, on removing the card, that this line is equidistant from the corner (see [Fig. 78]). In [Fig. 78] the cardboard is shown as though it were transparent. What has just been done is that the plane in which the rail lies has been projected to intersect the horizontal plane which contains the plan of the wreath. The name by which this line is generally known is the horizontal trace (shown at C, Figs. [78] and [79]). The minor axis (Figs. [78] and [79]) is always parallel off this, and always touches A as in [Fig. 77]. The major axis (Figs. [78] and [79]) also touches this point A, and is always square off the minor axis and off the horizontal trace. It will be seen by this that the rail is pitched equally both ways; therefore the face mold will be of equal width at the ends.