86 OF THE PARALLELOGRAM AND ITS INSCRIBED PARABOLA. 



in the axis must a line be drawn parallel to the base, so that the pres- 

 sures on the two parts into which the parabola is divided, may be 

 equal to one another ? 



By operating according to the preceding rule derived from equation 

 (46), we shall have for the distance from the vertex 



a, .75785 X 29 = 21.97765 feet. 



In the case which we have investigated above, the parabola is 

 divided into two parts on which the pressures are equal ; but in order 

 to render the solution general, we must so arrange it, that the parts 

 of division may bear any ratio to one another, as denoted by the 

 symbols m and n ; that is, 



P ' P P' ' ' m : n. 



Now, we have seen in equation (44), that the pressure on the entire 

 parabola ACB, is 



and according to equation (45), the pressure on the parabola 

 ECF, is 



but the pressure upon the space AEFB, is manifestly equal to the 

 difference of these ; that is, 



consequently, we obtain 



: : m : n; 



and from this, by equating the products of the extreme and mean 

 terms, we shall obtain 



which, by transposing and collecting the terms, becomes 

 (m -f w) x*^/ -^- = ml\ 



from which, by division, we shall get 

 /~~x _ ml* 



X V T^r~n ; 



