84 LECTURES TO SCIENCE TEACHERS. 



models are beautifully arranged. You can shift them so 

 as to change the direction of the generating lines. During 

 the movement in this particular model, the length of the 

 generating lines never varies. I say this particular model, 

 because we shall see that is not the case with the 

 others. 



Here is a very pretty model of a surface. If you come 

 to examine it, you will find it similar to the last. You 

 have here a directing line in brass, and here another, and 

 these silk generating lines are kept constantly parallel to 

 a directing plane, while remaining in contact with the 

 directing lines, so that the surface is the twisted plane. 

 Below you will see a little net- work, showing the difference 

 between such a surface as this and its horizontal projec- 

 tion ; and you will see also a set of little brass rings giving 

 peculiar intersections which give the name to the surface. 

 Of this class there are several. 



Hitherto the lengths of the threads representing gener- 

 ating lines do not vary, but in some of them the lengths vary, 

 and there is a beautiful arrangement made for the purpose. 

 This is a model intended to show the curve formed by 

 the intersection of two cones. In this, and most of the 

 models, when the figure is altered by shifting the brasses, 

 the lengths of the generating lines alter as well. And in 

 order to effect this, there are boxes below which contain 

 little weights : these are attached one to each of the 

 threads which represent generating lines ; and these fall 

 lower or rise higher in the boxes according as the curvature 

 alters. 



There is another very interesting class of surfaces 

 described here namely, the conoids. This form of conoid 

 now before you is used for arches. The line which describes 

 the surface, while always in contact with the directing 

 curve and line, remains horizontal. 



Here is a very pretty instance of the change of a 

 conoid into another figure. As at present placed, all the 

 generating lines remain in contact with this straight line, 

 and emerge again here, producing a similar conoid in an 

 opposite direction ; but letting go this string, and turning 

 the brass ring round, the figure becomes a cylinder. If it 

 were turned the other way it would become a cone. 



To render this series complete and clear, these models 



