198 OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 



In the first place then, let us take into consideration the effect 

 produced by means of the vertical pressure of the fluid ; this will 

 refer us to equation (149), but previously to the substitution of the 

 several numerical quantities, it becomes necessary to assign the nu- 

 merical value of S, which is not expressed in the question, but is 

 determinable from the perpendicular altitudes of the wall and the 

 fluid, together with the slope of that side on which the fluid presses : 

 thus, 

 '-' 30 : 24 : : 1 : 8 = of a foot. 



Let therefore, the several given numbers replace their representa- 

 tives in equation (149), and we shall have 



24 8 =24XX2K3& i)4-3X30x2J(6 1)6 30X2|(1F I 2 ), 



in which expression, b is the unknown quantity. 

 If the several terms be expanded, collected, and arranged, accord- 

 ing to the dimensions of the unknown quantity, we shall have 



2256 s 816=13956.15; 



complete the square, and we get 



2025006* 729006 X 8 1 2 = 12567096, 



and extracting the square root, it is 



4506 81= |/1 2567096 = 3545 nearly; 



therefore, by transposition and division, we get 



b 8.05 feet. 



Consequently, if from the breadth of the foundation as above 

 determined, we subtract the sum of the slopes, the remainder will be 

 the breadth of the dyke at the top ; hence, the section can be deli- 

 neated. 



212. The above is the method of performing the operation, when 

 the effect produced by the vertical pressure of the fluid is taken into 

 consideration ; but when that effect is omitted, the process is consi- 

 derably shortened ; for in the first place, there is no occasion to cal- 

 culate the value of S, that term not occurring in equation (150), and 

 in the next place, there are fewer quantities to be substituted for ; 

 this greatly abbreviates the labour of reduction ; but the equation is 

 still of the same degree, and consequently, it must be resolved in the 

 same manner. 



Let the several given quantities remain as in the preceding case, 

 and let them be respectively substituted in the equation (150), and 

 we shall obtain 



2256* 2256= 13917.75; 



