OF THE PRESSURE OF FLUIDS ON DYKES AND EMBANKMENTS. 197 



wherefore, by reducing the analogy, we obtain 

 _(e c)(3b 2c 2e) 

 6(26 c e) ' 



But by referring to the diagram, it will readily appear that scur 

 sn -\- nc ; therefore, by addition, we obtain 



.36(26 c e) + (e c)(36 2c 2e) 



6(26 c e) 



Let this value of I be substituted instead of it in the equation 

 marked (148), and we shall obtain 



and this being reduced to its simplest general form, becomes 

 sd 8 ~das(36 S} + 3bvJ(b c)-hDs'(c 8 e 2 ). (149). 



210. The general equation in the form which it has now assumed, 

 is very prolix and complicated ; but its complication and prolixity, as 

 we have before observed, are much increased by the introduction of the 

 vertical pressure; if that element be omitted, the equation becomes 



sd 3 = 3bDs'(b c) + DS'(C* e 8 ). (150). 



An expression sufficiently simple for every practical purpose ; but 

 it must be observed, that if e 2 be greater than c 2 , the term in which it 

 occurs will be subtractive. 



We shall not attempt to express these equations in words, or to 

 give practical rules for their reduction ; the combinations are too 

 complex, to admit of this being done in a neat and intelligible 

 manner; it is necessary, however, to illustrate the subject by proper 

 numerical examples, for which purpose, the following are proposed in 

 this place. 



211. EXAMPLE 1. The water in a reservoir is 24 feet deep, and the 

 wall which supports it is 30 feet in perpendicular height, the slope of 

 the side next the water being one foot, and that of the opposite side 

 one foot and a half; it is required to determine the transverse section 

 of the wall or dyke, supposing it to be built of materials whose mean 

 specific gravity is 2 J, that of water being unity ? 



By contemplating the conditions of the question as here proposed, 

 it will readily be observed, that the breadth of the section at the 

 base, is the first thing to be determined from the equation ; for since 

 the quantity of the slopes, as well as the perpendicular height are 

 given, the breadth of the dyke at top can easily be found, when the 

 breadth at the foundation is known. 



