. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let A n and C D, (fig. 1) be the two given curves fsay of 130 chains radius), an<l let it be reipiired to unite them by a third curve of less radius, tangent to A H on its concave, and to C D on its convex side. 1st case. Tlie required curve is to pass through the point G of the curve A Li. Erinn I', the centre of A B, and (hrough G, (he required point of contact, draw the straight line F (t H, equal to the sum of the radii of (he two given curves, or twice the railius I'
. The Civil engineer and architect's journal, scientific and railway gazette. Architecture; Civil engineering; Science. Let A n and C D, (fig. 1) be the two given curves fsay of 130 chains radius), an<l let it be reipiired to unite them by a third curve of less radius, tangent to A H on its concave, and to C D on its convex side. 1st case. Tlie required curve is to pass through the point G of the curve A Li. Erinn I', the centre of A B, and (hrough G, (he required point of contact, draw the straight line F (t H, equal to the sum of the radii of (he two given curves, or twice the railius I' G (both curves being sup- ]iosed to have the same radius); from H draw the straight line H <) lo the ceuire of (he curve C D; and from K, the miildle point of H O, draw the perpenflicular K (j, intersecting the straight line 1' H at (he point Q. (j will \h: the centre of the required curve, and its radius \vill be equal to Q G. .Toin tj (), and the jHiint E, where Q O inter- sects the curve C 1), will be its poiiil of con(act wi(li the required curve. For, the right angled triangles H K Cj, tj K () being eepial, tj H = Q i) ; and, if from these c-cpials we t;dve the eipials (j H and E O, the remainders (,) G, tj E will also be equal; and, since they are situated on normals to the given curves, the circular arc G E will be tangent to both these curves. 2nd case. The required curve must pass through the point E in the curve C D. From the cenfre O, and (hrough (he given point of contact E, draw the straight line () K (j ; and froiu (lie cende F draw P L parallel to U (^ and equal to the smn of the radii of the given curves i from P as a centre, and with a radius equal to P L, describe ;ui arc of u circle in the direction in which the connecting curve G E is expected to meet (he given curve A B, and from L draw the straight line L () H, inter- seciing (hat arc at (he point II; join HP. The point Q, where 11 P intersects () Q, will be the centre of (he reqinnul curve, and the )io
Size: 1434px × 1742px
Photo credit: © The Book Worm / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., boo, bookcentury1800, booksubjectarchitecture, booksubjectscience
