THE CYLINDROID.
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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 ß, 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 ß shall be equal to the
given pitches of a and ß.
Thus the cylindroid must become a familiar conception with the student
°f 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 cylin droid which is required in the Theory of Screws
can be represented by the corresponding property of points on a circle.