Chap. XXVI.

CANALS AND RIVER LOCKS.

1535

the centre of the cutting must be found; each slope must be prolonged to meet in V:draw the perpendicular NV; with the radius NV and N as a centre, cut EA in p,make V a equal p Q,; then through a, parallel to E A, draw M L, which is the line oflevel cutting.

Fig. 2831.

To find any Line of Oblique Cutting _Find the line of level cutting, produce the slopes to

meet in V; draw the perpendicular VI; from L draw LN with the given slope of the

v

Fig. 2832.

ground, cutting VI in N, making N/> and p Q, equal to V I, and V R equal to p I: throughU draw KRH, which is the line of oblique cutting sought for.

Theory of Locks. — Locks with gates for the purposes of navigation are of moderninvention; those of the Canal of Martezana, in Italy , already mentioned at p. 186., werethe first executed: their date is not more than 386 years since; they were the model from■whence all others have been taken, nor does it appear that any great improvements havebeen made, nor have any rules been given for their proportion: the only difference inthe various locks hitherto constructed consists in the greater or less width and height, forthe purpose of containing one or more boats, isolating or uniting several chambers, andmaking the side walls either straight or curved. Belidor has treated on this matter, andgiven an account of various works; he has, however, only mentioned the proper pro-jection for the pointed sills, and the strength of the timber necessary for the gates, andendeavoured to show that no advantage is derived from a curvature in their plan.

The least Length that can be allowed between the Lochs should be such that 12 inches of depth,over and above what a loaded boat will draw, will only lower the water 6 inches without thenavigation being interrupted; and if it be required to draw the contents of each lock fromthe interval above, the distance for the locks must be so regulated that the quantity ofwater expended by one should not lower that of the upper interval more than 6 inches atmost; thus the distance should be greater in proportion to the contents of the chamberof the locks and the width of the canal; that is to say, when the chambers are large andthe canal is narrow, the distance between the Jocks should be greater. Chambers 110 feetin length between the gates by 17 feet in width, as those of the canal of Briare, contain1870 superficial feet; therefore 11,843 cubic feet when the fall is 6 feet 4 inches, 15,859cubic feet when it is 8 feet 6 inches, and 19,635 cubic feet when 10 feet 6 inches. If thecanal be 48 feet in width, at 3 feet below the ordinary level of the water, the length of theinterval should be 446 feet, in order that the expenditure of locks of 6 feet 4 inches of fallshould not lower the water more than 6 inches; this length should be 607 feet when thelocks are 8 feet 6 inches of fall, and 755 feet when they are 10 feet 6 inches : the distancethen between the lower gate of one lock and the upper gate of the other should be alwaysabout 624 feet for ordinary canals. If two locks of 8 feet 6 inches fall were only distant