OF THE PARALLELOGRAM AND ITS INSCRIBED PARABOLA. 71 



hence, by analogy, we obtain 



p : P :: T \bl*s : \bl*s, 

 and this, by omitting the common quantities, b, I 1 and s, becomes 



P : P : : rV : 1, 



and finally, by reducing the fractions in this analogy to a common 

 denominator, we shall obtain 



p : P : : 8 : 15. 



82. Having thus established the formula for determining the pres- 

 sure on the parabolic plane, and also the ratio which compares the 

 said pressure with that upon the circumscribing rectangular paral- 

 lelogram ; we shall in the next place deduce the rules, by which the 

 numerical process is to be performed, when the principle is applied to 

 the actual determination of the pressure in reference to cases of prac- 

 tice. The rule, as derived from the equation numbered (36), may be 

 expressed in the following manner. 



RULE. Multiply the base of the parabola by the square of 

 its vertical axis, and again by the specific gravity of the 

 fluid ; then, four fifteenths of the product will express the 

 pressure perpendicular to the surface of the parabolic plane. 



The rule for determining the pressure on the surface of a parabola, 

 as deduced from the analogy of comparison investigated above, may 

 be expressed in words in the following manner. 



Find the pressure perpendicular to the surface of the 

 circumscribed rectangular parallelogram, after the manner 

 described in the second case of the rule under the third 

 problem; then, eight fifteenths of the pressure so determined, 

 will express the pressure on the parabolic plane. 



83. EXAMPLE 15. The data remaining as in the preceding case ; 

 what will be the pressure on the parabolic plane, its axis being verti- 

 cal, and its base in contact with the surface of the fluid ? 



28 X 42 X 42 X 62J = 3087000, 



and four fifteenths of this, is 

 3087000 X 4 -r 15 zz 823200 Ibs. 



This result is derived from the first of the above rules, or that which 

 corresponds to the equation (36) ; and the process as performed by the 

 second rule, or that obtained from the ratio of comparison, will stand 

 as below. 



} X 28 X 42 X 42 X 62 X T V = 823200 Ibs. 



