The Cassegrain telescope differs from the Gregorian only in the substitution of a convex hyperboloidal mirror for a concave ellipsoidal mirror as the small speculum.
For spectroscopic purposes the Cassegrain form has peculiar advantages, because in consequence of the less rapid convergence of the rays after reflection from the convex hyperboloidal mirror, the equivalent focus can be made very great in comparison with the length of the tube.
This latter carries a hyperboloidal mirror, which returns the rays towards the centre of the large mirror and causes them to converge less rapidly.
Teeth of Skew-Bevel Wheels.The crests of the teeth of a skew-bevel wheel are parallel to the generating straight line of the hyperboloidal pitch-surface; and the transverse sections of the teeth at a given pitch-circle are similar to those of the teeth of a bevelwheel whose pitch surface is a cone touching the hyperboloidal surface at the given circle.
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