208 OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 



ds 



-W' (174). 



And exactly the same equation would arise, if the slope e remote 

 from the fluid were to vanish, and the slope c adjacent to the fluid, 

 become equal to b the whole breadth of the section; consequently, 

 the thickness of a dyke in the case of a triangular section, whether 

 the water presses on the perpendicular or hypothenuse of the tri- 

 angle, is 



In all the preceding cases, it is supposed that the section of the 

 dyke or embankment is of such dimensions, as to oppose an equipois- 

 ing resistance to the pressure of the fluid which it supports ; but in 

 the actual construction of all works of this nature, it becomes neces- 

 sary, for the sake of safety, to enlarge the dimensions considerably 

 beyond what theory assigns to them ; but it does not belong to this 

 place to determine the limits of the enlargement. 



2. OF THE PRESSURE OF FLUIDS AGAINST EMBANKMENTS OF LOOSE 



MATERIALS. 



229. The theory which we have established above, supposes that a 

 perfect connection obtains between all the parts of the dyke or 

 embankment which is opposed to the pressure of the fluid, so that any 

 one portion of it cannot be displaced or overthrown, unless the whole 

 be overthrown at the same time; the formulge thence arising, are 

 therefore, only applicable to dykes or embankments that are con- 

 structed of masonry ; in those which are constructed of earth or other 

 loose materials, and having the sides faced or fortified with stone, the 

 same connection between the component portions of the wall does not 

 exist, and consequently, although the several equations apply when 

 the whole perpendicular height of the dyke is considered, yet the dyke 

 will not resist equally at every part of the height, but is liable to 

 be separated into horizontal sections. 



In order therefore, to adapt our prin- 

 ciples to this case also, it becomes neces- 

 sary to trace out the steps of another 

 investigation ; for which purpose, 



Let ACD represent a vertical section of 

 the dyke or embankment, whose summit 

 at A is on a level with the surface of the fluid AE. 



