. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . awing tangents to it by the method ofresultants. 131. Tangent to the spiral of Archimedes. Differentiating (1) -r = - 2tt ; where -r-, or is the ratio of the rotary and dr n dr n * the radial components of the motion of the generatrix, the former being referred to the circumference of the circle whose radius is a. The appli
. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . awing tangents to it by the method ofresultants. 131. Tangent to the spiral of Archimedes. Differentiating (1) -r = - 2tt ; where -r-, or is the ratio of the rotary and dr n dr n * the radial components of the motion of the generatrix, the former being referred to the circumference of the circle whose radius is a. The application will be better understood by an example. As we may generally make m = 1, write at once -r = —. Then let it be required to construct the tangent at 5|, in Here, n = 4, since i of the circle OA is divided into thesame number of parts as are found on the line OA. Then layoff on Fbi produced, bYn = 4, on any convenient scale; and2p = 2tt, by the same scale, on the tangent at 2 to the circle O A;reduce the rotary component as estimated with the radius P2, STONE-CUTTING. 117 to its actual value, byS, parallel to 2p, at bv by drawing theradius Pp. Then, bxt, the diagonal of the parallelogram on thecomponents, bin and b^s, is the required tangent at bx. n1-. Fig. n = 1, PcZ, and the circle of radius Fd will be divided intothe same number of equal parts, -5- = -j- and 2p would be 4 times 2p, or ^w would have been called 1 instead of 4. 132. The subnormal method. — Draw PQ perpendicular toP51? and limited at Q by the normal ^Q. Then PQ is the sub-normal. Now the triangles PQ5i and b^it are similar, and give, whence PQ = b,n X -r-*- But if bxn is made constant for each point, *2p will be so also; and hence, as we see from the figure, bys will vary as PZ^; that Vbis, the ratio ~ will be constant. Thus PQ is constant. Hence, having any one tangent, any other can be found as , for example, the point ex. Draw a perpendicular, PQx,not shown, to its radius v
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