416 NOTES ON DOCKS AND DOCK CONSTRUCT/OX. 



The water pressure P acts throughout the extent of, and in all 

 cases normal to, the exposed surface of the back of the gate. If HIP 



W 



pressure per unit of length = p = ~T"(D 2 (Z 2 ), the magnitude of the 



resultant force P, equivalent to the whole of this pressure, is pro- 

 portional to, and may be represented by, the length of the horizontal 

 straight line ef joining the extremities of the water-bearing surface, 

 that is, P = p x e f. The direction is that of a horizontal straight 

 line D d, perpendicular to and bisecting the first-mentioned line e f. 



In the case of the reaction M of the other gate on the mitre-post, 

 assuming that the gates meet on the centre line of the passage, and 

 that this is perpendicular to a straight line A A' drawn through the 



FIG. 3G2. 



centres of the heel-posts, the natural reaction of the mitre-posts on 

 each other will be perpendicular to the centre-line of the passage, and 

 parallel to A A' ; no other direction will admit of equilibrium. It has 

 already been assumed that the mitre-posts meet so that the mutual 

 reactions are uniformly distributed throughout the width of the 

 meeting- faces, consequently the direction of the resultant force M, 

 representing the reaction of the other gate, will be that of the hori- 

 zontal straight line B D which bisects the meeting-face in B, is 

 parallel to A A', and cuts the line D d at the point D. 



The reaction of the hollow quoins on the heel-post H obviously 

 acts through the centre of the heel-post, and from the conditions of 

 equilibrium its line of direction must pass through the point of inter- 

 section of the other two forces. The line of direction of this force 

 H will therefore be represented by the line A D. If from the point e, 



