GEOMETRICAL AND ENGINEERING DRAWING. 85 



require casts to indicate what they are intended to be, and 

 I will show you a series of these casts, not made from 

 these models, but which answer the same purpose. 



This model represents the intersection of a cylinder by a 

 plane. The yellow lines represent the plane. The simplest 

 way in which a plane is engendered is by a line moving 

 between two parallel lines. The cylinder is produced 

 by a line moving round a curve and remaining parallel 

 to its initial position. You may take any section of the 

 cylinder you please by shifting this long bar. "When 

 you come to have the plane perpendicular to all the 

 generating lines of the cylinder, you have what is called 

 the right section of the cylinder, which in this case would 

 be an ellipse. 



I have here a very beautiful illustration of the inter- 

 section of two cylinders. You may have already seen it 

 in another form. It is nothing more than a groined arch, 

 and the curve of intersection between these two is the 

 groin of the arch. In this next example of two cylinders, 

 the groin would be what is called a waving groin. These 

 intersections occur often in architecture. This figure, 

 again, can be modified by changing the position of the two 

 ends. These little rings show the form of intersection 

 of the two surfaces. 



The next model is composed of a series of lines, which 

 are constantly in contact with two curves, one above and 

 one below. A more ordinary and more useful form of this 

 surface is when the two curves are identical or similar. 

 You will see, as I turn this button, how the figure 

 changes. 



If I turn the upper curve round thus, so that these 

 generating lines tend to meet at an imaginary point above 

 the model, you have a cone ; as I turn it round further we 

 come to the hyperboloid of revolution ; and lastly, as I 

 turn still further, all the points come together at this point, 

 and we have again a cone. 



This next model is that of the hyperboloid of revolution 

 of one sheet. It is a very useful figure, for it is one 

 employed for making the teeth of skew-bevel wheels. 



Here is another example of the hyperboloid. It is 

 composed of two series of coloured lines one red, and 

 another green, inclined equally and in opposite directions, 



