III. MODELS. 21 



The director planes, as well as the head lines, of these conoids 

 are at right angles to one another. 



100. Conoids. 



Two equal circles in parallel planes are connected by threads so 

 as to form four surfaces. 

 A cylinder. 

 A cone. 

 A conoid. 



A second conoid, with its director plane and line at right 

 angles to those of the former. 



Same arrangement as No. 23, except that the lower ring is replaced by a 

 plane of section a little higher up. The 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. 



101. 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. 



The changes may be arranged as follows : 



From. 



Conoid. 



Tangent paraboloid. 

 Cylinder. 

 Tangent plane. 



Into. 



Cylinder. 

 Tangent plane. 

 Conoid. 

 Tangent paraboloid. 



These changes are all effected simultaneously by one movement, which can 

 be reversed. 



102. 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. 



103. French Skew Arch (biais passe}. 



The 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. The 

 horizontal line joining the centres of the two large semicircles is 

 the right line director. 



The construction for any one of the generating lines is as follows : Draw 

 a plane through the right line director at any selected obliquity. It will, of 

 course, give the radii of the outside circles, and the line joining the points 

 at which it cuts the inside semicircles will be a generator of the surface. 

 This line will evidently pass through the director line, because it is in tlje 

 game plane with it. 



