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Caption: Mathematical Models Catalog of a Collection of Models of Ruled Surfaces
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10 24. Conoids. T w o equal circles in parallel planes are connected by threads so as to form four surfaces. A A A A cylinder. cone. conoid. second conoid, with its director plane and line at right angles to those of the former. S a m e arrangement as N o . 23, except that the lower ring is replaced by a plane of section a little higher up. T h e section gives,— For the cone, a circle smaller than the upper ring. For the cylinder, a circle of the same size- as the upper ring. For the conoids, two ellipses turned crosswise. 25. Model exhibiting the simultaneous transformation, of a conoid into a cylinder, a cylinder into a conoid, the paraboloid touching the conoid into the tangent plane of a cylinder, and the tangent plane of a cylinder into the tangent paraboloid of a conoid, and reciprocally. T h e changes m a y be arranged as follows :—From. Into. Conoid. Tangent paraboloid. Cylinder. Tangent plane. Cylinder. Tangent plane. Conoid. Tangent paraboloid. These changes are all effected simultaneously by one movement, which can be reversed. 26. Model exhibiting the transformation, first, of a conoid into a cylinder. Second, of the tangent paraboloid of the conoid into the tangent plane of the cylinder, 27. French Skew Arch (Mais passe). T h e inner drum, of yellow thread, represents this surface. It is a skew surface, with a right line director; and its faces, the planes of the two semicircles, are usually parallel, although the model permits them to be placed obliquely to one another. T h e horizontal line joining the centres of the two large semicircles is the right line director. T h e construction for any one of the generating lines is as follows:—Draw a plane through the right line director at
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