OF THE PARALLELOGRAM AND ITS INSCRIBED PARABOLA. 85 



Again, the pressure perpendicular to the surface of the rectangular 

 parallelogram CEF<?, is 



and the pressure upon the inscribed parabola ECF, is four fifths of 

 the pressure on the circumscribing rectangle ; that is, 



I ' (45). 



but according to the conditions of the problem, 

 p' =. \p ; hence we have 



and by suppressing the common factors, we get 



from which, by squaring both sides, we obtain 



o: 5 -|* 5 ; 

 consequently by extracting the fifth root of both sides, we get 



x = l#1i 

 but according to the arithmetic of surd quantities 



^7=1^87 



therefore, by substitution, we shall have 



now, the sursolid, or fifth root of 8, is 1.51571 ; hence we get 



a: = .75785*. (46). 



96. The practical rule supplied by this equation is extremely 

 simple; it may be expressed in words at length in the following 

 manner. 



RULE. Multiply the axis of the given parabola by the 

 constant number .75785, and the product will give the distance 

 from the vertex through which the line of division passes. 



97. EXAMPLE 19. The axis of a parabola is 29 feet, and its plane 

 is perpendicularly immersed in a cistern of water, in such a manner, 

 that its vertex is just in contact with the surface ; through what point 



