188

SURFACES OF REVOLUTION.

ELEVENTH LESSON'.

Surfaces of Revolution.

Surfaces of Revolution are, with the exception of planesurfaces, the most easy to construct, and the most fre-quently employed in the arts. Their properties are call-ed perpetually into use in mechanics, and Nature in hervaried phenomena continually reproduces them before oureyes.

If we conceive any curve whatever, ABC, fig. 1, pi.11, which is made to turn round an axis AC, the sur-face formed by it is a surface of revolution. The mo-tion given to the curve, is called a circular or rotatorymotion, and when the rotation is complete, that is tosay, when the curve has revolved through 360 degrees,it is called a revolution.

In this motion every point B, B', B", describes a cir-cle. All these circles have their planes B6, B 'b', B"6",parallel to one another, and at right angles to the axisAC, on which all their centres O, O', O", are situated.In the Sixth Lesson, these various properties have beendemonstrated.

It is not necessary that the curve ABB'B"C, should be plane, inorder to produce a surface of revolution by revolving round AC. If