The surface of any cone or cylinder can be developed upon that of any other cone or cylinder (respectively), because the portions of surface included between infinitely near generators in corre- sponding or homologous positions vary similarly. For the same reason many other ruled surfaces can roll upon one another, their forms being such as can be developed upon each other. Thus, for example, two screw surfaces may be mutually developable, and if placed suitably, as in Fig. 32, will roll upon each other; and similarly, a screw surface and a hyperboloid, Fig. 33. Forms very closely related to these are in actual use in machines ;* the con- sideration of them is therefore of practical as well as theoretical interest.
7
Fig. 34.
Ruled surfaces which twist upon one another are also employed in machine construction; the axoids of hyperboloidal spur-wheels, as in Fig 34, belong to this class. These axoids are not themselves constructed, although in the case before us their nature is indicated by the form and position of the teeth upon the wheel. This how- ever is not the case in the pair of elements shown in Fig. 35, the worm wheel and endless screw. The axoids representing the motions of these elements are again hyperboloids, but this is not
- See for example Johnson's Imperial Cyclopaedia, "Steam Engine," Moison's
regulator, page 49.
