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TANGENTS TO CYLINDERS.

the paste a plane, which is by turns a tangent to eachedge of the cylindrical surface of the roller.

The gardener obtains the same result for the paths andgreensward of the garden, over which he drags a rollingcylinder. As the earth is gradually levelled, it becomesa tangent to the cylinder, through the whole length of thedifferent edges of this surface.

The coachmaker suspends some carriages by a leathernbrace on each side, fig. 11. This brace is adapted to thelower and cylindrical form of the body of the carriage,and is prolonged, so that its upper surface, a plane, formsa tangent to the body of the carriage. When the body isbalanced before and behind, it advances or recedes ohthis tangent plane, which being the same on both sides,prevents the transversal shaking, which is the mostharsh and disagreeable in carriages that are not sus-pended.*

Construction of a cylinder by tangent planes .—In theLesson which treats of cylinders, the method of workinga solid body, so that its surface shall be cylindrical, hasbeen mentioned, and to it we shall now again refer.The bases are marked out on the two ends of the piece ofwood, stone, or whatever is to be made into a cylinder;and then two polygons are circumscribed about these bases,having their corresponding sides equal and parallel: witha saw, a plane, or some instrument proper for making sur-faces, small planes are worked by the parallel sides of thesepolygons. By this means, we obtain a polygonal prismcircumscribed about the cylinder ; because its variousfaces will be everywhere tangents to the surface of thecylinder. As we cut away the edges of the prism toform other planes, tangents to the cylinder, we bringthe former to resemble the latter; and the more theseplanes are multiplied, or the more frequently the edges

* This method of suspending carriages, is, we believe, no longerpractised in England, though still common on the Continent.

Tr.