m. MODELS. 27 



be noticed that the head lines of the two conoids, that is to say, 

 the right line in which the two sheets of each conoid meet, are 

 perpendicular to one another. 



The transformation is effected by making the upper semicircle turn through 

 two right angles. 



97. Conoids. 



Intersection of two equal conoids having a common director plane. The 

 horizontal intersection is a plane ellipse. 



98. Conoid, in contact with a hyperbolic paraboloid. 



99. Conoids. Two equal circles in parallel planes, divided 

 equidistantly, are connected by threads, so as to form four surfaces. 



A cylinder. A conoid. 



A cone. A second conoid. 



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. 99, 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. 



