202 OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 



The sectional area in the one case, is 7. 804 X 20 =: 156.08 square 

 feet, and in the other, it is 8.709x20=: 174.18 square feet, being a 

 difference of 18.1 square feet in favour of magnitude in the latter 

 form, where the sloping side is adjacent to the fluid ; and this being 

 multiplied by the length of the dyke, will give the extra quantity of 

 materials necessary for obtaining the same degree of stability. 



217. If both the slopes c and e become evanescent; that is, if the 

 section of the dyke be rectangular, having both its 

 sides perpendicular to the horizon, as represented 

 by ABC D in the annexed diagram ; then, the general 

 equation (149), becomes transformed into 



sd a = 3vs'b\ (160). 



Then, by supposing the depth of the fluid, and 

 the perpendicular altitude of the dyke to become 

 equal, (the specific gravity of water being expressed by unity,) we 

 have 



3s'& 2 zrd 8 ; 



and this by division becomes 



-I- 



consequently, if the square root of both sides of this equation be 

 extracted, we shall have 



'- (161). 



218. This is indeed a very simple form of the, equation, applicable 

 to the very important case of rectangular walls ; it is however accu- 

 rate, and corresponds in form with that investigated by other writers 

 for the same purpose, and by different methods ; the mode of its 

 reduction is simply as follows. 



RULE. Divide the specific gravity of the fluid to be sup- 

 ported, by three times the specific gravity of the dyke or 

 embankment, and multiply the square root of the quotient 

 by the perpendicular altitude of the dyke, for the required 

 thickness. 



Let the perpendicular depth of the water, or the altitude of the 

 dyke be equal to 20 feet, and the specific gravity of the materials of 

 which it is built If, as in the foregoing cases; then, by proceeding 

 according to the rule, we have 



