792

THEORY AND PRACTICE OF ENGINEERING.

Book II.

consequently a straightedge or ruler, with a tri-angle having angles of 30,90, and 60 degrees, willenable us to set out or sub-divide a cube into anynuntbeT of parts.

The cube is containedin a circle, and its centrebecomes one angle of theupper face: lines drawnfrom the angles of thehexagon indicatethewholeof the sides. One quarterof such a cube may beshown as extracted or cutout by dividing the sidesinto two, and raising threeperpendiculars; or it maybe represented as seen fromthe other angle.

A mortise and tenon,or groove and tongue, areeasily set out, as is aGreek cross, or threesteps. By cutting a cubeinto a series of planes theinterior of a building maybe represented, and a scaleapplied, and in this exam-ple three sections arcshown, which may be sup-posed 100 feet in width,and the same in height ;consequently 50 feet a-part. Two others interven-ing would have been morein unison with the pro-portions found in churches,and could be easily in-troduced by dividing theside of the cube into fourinstead of two, and re-peating the method herelaid down of drawing therespective lines.

Where wheels are to beshown they must first beinclosed within a square,and then there is no diffi-culty in representing anycombination of them.For minerals this methodof drawing is very useful,and is becoming general.

Curved lines and surfacesmay be illustrated by thissystem and shown withgreat accuracy ; supposein the upper square wewere to trace a circle, andbeneath it in the lowerplane another, of similardimensions: uniting theseby drawing two perpen-

Fig. 906.

Fig. 908.

Fig. 909.

dicular lines, we have the representation of a cylinder ; between the planes whichits top and bottom, we may have any other number we require by setting out

express

parallel