Chap. XXVII.

CANAL AND RIVER LOCKS.

1549

three turns on the windlass, the gate is either open or shut; a rack bar is occasionally em-ployed for the same purpose. When the gates are very heavy, a roller or truck wheel isplaced under the foot ofthe head-post, and madeto run in a quadrantgroove, which assists themotion.

The Angle to be givento Double Lock Gates haslong occupied the at-tention of engineers, andthe view now taken ofthe subject may be thusdefined: - the pressure ofthe water on one of thegates, which we will call15 C, is in proportion toits breadth: the strengthof the gate being in-versely as its breadth, theeffect of the pressureupon it is as the squareof B C- The supportafforded by one gate tothe other, which we willdesignate as CA, is asa perpendicular raisedat the end of a lineB C at E, represented byA E : the strength ofthe gate is therefore asA E directly and in-versely as B C 2 ; but A Eis the sine of A B C ; theradius A B — B C is thesecant of the same angleto half the radius B D.

The strength of the gateis therefore,

A E 2 sin. ABCBC 2_ sec> ABC*

or, as the cosine is the reciprocal of the secant, as sin. x cos. 8 of A B C, the angle at the base.The maximum value of this expression is when the tangent of ABC=a/|, or = 0 * 7071 ,

|i n PTiTfT

niiiAxrrnrnu

st. Katherine’s lock-gates. .

Fig. 2866/

Fig. 2864.

Fig. 2865.

PLAN AND ELEVATION OP DOUBLE LOCK-GATES.