159] 



THE GEOMETRY OF THE CYLINDROID. 



151 



axis of the cylinder at right angles. The following table will enable the 

 work to be executed with facility. I is the angle of 13 : 



For example, when the slide has been moved 34 2 parts from the centre 

 of the cylinder, the dividing plate is to be set successively to 10, 80, 190, 

 260, and a hole is to be drilled in at each of these positions. The slide rest is 

 then to be moved on to 50 parts, and holes are to be drilled in at 15, 75, 

 195, 255. Steel wires, each about O m- 3 long, are to be forced into the holes 

 thus made, and half the surface is formed. The remaining half can be 

 similarly constructed : a length of n 066 cos 21 is to be coloured upon each 

 wire to show the pitch. The sign of the pitch is indicated by using one 

 colour for positive, and another colour for negative pitches. 



Among the various other representations of the cylindroid I can now do 

 no more than refer to an ingenious plan described by Goebel in his Neueren 

 Statik, by which a model of this surface in card-board can be made with 

 facility. There is also a model in the collection of the Cavendish Laboratory 

 at Cambridge, and another belonging to the Mathematical Society of London, 

 which, like that figured in Plate II., was made by myself. Sir Howard Grubb 

 has also made a second model with the same dimensions as that figured 

 in the frontispiece but mounted in a different manner. This exquisite 

 exhibition of a ruled surface is the property of Mr G. L. Cathcart, Fellow of 

 Trinity College, Dublin. 



A suggestive construction for the cylindroid has been also given by 

 Professor G. Minchin in his well-known book on Statics, and we have already 

 mentioned (note to 50) the construction given by Mr Lewis. 



