19] 



THE CYLINDROID. 



That one, but only one, cylindroid can always be drawn so that two of its 

 generators shall coincide with any two given screws a and ft, and that when all 

 the generators of the surface become screws by having pitches assigned to them 

 consistent with the law of distribution characteristic of the cylindroid, the pitches 

 assigned to the generators which coincide with a and /3 shall be equal to the 

 given pitches of a. and /3. 



Thus the cylindroid must become a familiar conception with the student 

 of the Theory of Screws. A model of this surface is very helpful, and fortu 

 nately there can be hardly any surface which is more easy to construct. In 

 the Frontispiece a photograph of such a model is shown, and a plate repre 

 senting another model of the same surface will be found in Chap. XIII. 



We shall develop in Chap. V an extremely simple method by which 

 the screws on a cylindroid are represented by the points on a circle, and 

 every property of the cylindroid which is required in the Theory of Screws 

 can be represented by the corresponding property of points on a circle. 



