A Treatise on the Theory of Screws

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 :— z I 90 -I 180 + 1 270 -I 00 0 90 180 270 17-4 5 85 185 265 34-2 10 80 190 260 50'0 15 75 195 255 64-3 20 70 200 250 76'5 25 65 205 245 86-6 30 60 210 240 94-0 35 55 215 235 98-5 40 50 220 230 100-0 45 45 225 225 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°, 80c, 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 0"l’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 Ow,'O66 cos 2Z 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.