1534

THEORY AND PRACTICE OF ENGINEERING.

Book II.

A ; draw the perpendiculars Cm,Dn, and the diagonals A G,mn, intersecting at p : throughp draw the parallel spt, and bisect it in o, which is the centre of the cutting, through

Fig. 2828.

which, if any line HoF be drawn cutting the slopes AB and EG produced, HBCwwill always be equal to wjDEF; for mnD = CDw, therefore wiwGE — CDEG. Butm»GE^sBGt = CDEG, and taking away CvtG, we have sBCv = cDEt, and thetriangles Hso and ot F are equal, having equal angles, and the side so = ou; therefore thesum Hso + s B C v=ot F+vDEtf, and taking away the part owv, there remains HBCia=w D E F; therefore, as the total breadth of the canal and bank is to the breadth of thebank added to the base of one slope, so is the depth of the canal from its # surface to thedepth below the centre of cutting, which is also the centre of cut and cover, for a linestaked out at the level of the centre of cutting will show the middle of the land requiredfor the canal.

A canal with a bench or towing-path on the upper side. Let aABCDEG be theprofile of the canal and bank; take D d=aA, and draw ab and cd parallel to the slopes;

d D

Fig. 2829.

the section a AB CDE is converted into abcd'E, which comprises the towing-path: drawthe lines a G, cd, and st, and the middle o will be the centre of cutting. The distance fromcentre of canal is equal to wj-j-DE-aA.

E</: Em : : | me : oz\ that is, as a E : E D : E D + Dd + dm : : me : oz.

To reduce the section A B C D E F with a second bench or path E F, to the equivalentsection A BIK F, with one bank only, but wider and shallower, the banking cut down, and

Fig. 2830.

filled in to the bottom. Produce BC and HF to Z, and CD to G; make DN to equalDG; draw the parallel NL; on FL describe the semicircle LMF; make ZK and ZIequal to ZM, and draw the parallel KI, and the figure is complete.

To find the Lines of Level Cutting , when the section of a canal has two banks, and theslopes are made all equal. The section ABCD must first be reduced into AHKE, and