780

THEORY AND PRACTICE OF ENGINEERING.

Book II.

Fig 871.

it-

R

Fig 870.

J ig. 872.

Cylinders are formed by drawinga parallelogram equal to its externalface, and folding it together, addingthe top and base.

A and B show two cylindersplaced in a vertical position ; andthey are drawn by first making thecircles B C and F G equal, andafterwards uniting them by thestraight lines F B, C G, taking carethat the centres E and D are in thesame perpendicular line.

A cylinder lying in a hori-zontal position, as H, may be con-structed around the centres D, E. ina similar manner ; B F and C Gbeing drawn to unite the ends.

Columns, which differ from cy-linders by their entasis, or swellingat a certain part of their height, ordiminishing like the frustums ofelongated cones, may be formed inthe same manner; their summits Pand Q must, in that case, be madeof the dimensions calculated fortheir upper diameters.

A hollow cylinder, or one constructed in card, is commencedby drawing the parallelogram R, which has its sides ST, VX,the length of its circumference, and those of XT and V S theheight of the figure : simply bending such a card, and unitingits edges, completes the figure, and by covering the two endswith circular cards, formed of the proper dimensions, a solidcylinder may be represented. The cylinder is a solid figure,the surface of which is partly plane and partly curved, theplane portions being two equal and parallel circles, and thecurved portion such that any point being taken in the circum-ference of either circle, the straight line, which is drawnthrough it, parallel to the line joining their centres, lies whollyin the surface.

Right and Oblique Cylinders may be treatedas prisms with polygonal bases. The settingout a right cylinder is obtained by having arectangle of the height required, and also thecircumference of the circle which serves for itsbase : the twelve perpendicular lines may re-present the edges of a prism, and their distanceapart is such that the whole bend round theplan is shown at the top and bottom. In theoblique cylinder, the same principles of settingout are attended to as already described for anoblique prism.

In making plans and elevations for the con-struction of an arch or vault, we may generallysuppose that the vertical projection of a pointis above the ground line, and that the hori-zontal projection is below: if the point be abovethe horizontal and before the vertical plane,its vertical projection will be above, and its horizontal projection below, the groundline : if the point be situated before the vertical and below the horizontal plane, the twoprojections will be below the ground line : if the point be situated above the horizontaland behind the vertical plane, the two projections will be above the ground line; and if thepoint be situated above the horizontal and behind the vertical plane, the vertical projectionwill be below, and the horizontal above the ground line.

To construct a mould for a cylindrical oblique arch terminating upon the face of a wall,in a plane at oblique angles to the springing plane of a vault, so that the coursing jointsmay be in planes parallel to the lines of the intrados of the vault, we must let thevertical plane of projection be perpendicular to the axis of the intrados, and conse-

Fig. 873

Fig. 874.