54 HORIZONTAL SECTIONS CONTAINING EQUAL FLUID PRESSURES. 



GH in the points z, q, p, o and n, which points are the respective 

 centres of gravity of the several parts into which the given parallelo- 

 gram is divided, and on which the pressures are supposed to be equal 

 among themselves. 



Through the point G, and in the plane of the horizon, draw the 

 straight line or at right angles to ab, making the angle ron equal to 

 the given angle of the plane's inclination, and from the points n, o,p, 

 q and z, let fall the perpendiculars zv, qu, pt, os and nr, meeting 

 the line or respectively in the points v, u, t, s and r; then are the 

 lines zv, qu, pt, os and nr, the perpendicular depths of the centres 

 of gravity of the several portions into which the proposed rectangle is 

 divided, the points of division being estimated from the surface down- 

 wards. 



Put =iab or dc, the horizontal breadth of the given parallelogram 



abed, 

 I ad or be, the entire immersed length, or that tending down- 



wards, 



^ zzrGH, the given angle of inclination, 



d zn vz, the vertical depth of the centre of gravity of the part abme, 

 d ' zz w , the vertical depth of - e mfl, 

 d" tp, the vertical depth of 



S so, the vertical depth of -- ykhi, 

 I' rn, the vertical depth of -- iked', 

 n zzthe number of parts into which the parallelogram is divided, 

 P zzrthe entire pressure on the parallelogram abed, 

 p nz the pressure, common to each of the parts into which the 



given parallelogram is divided, 



v =n ae, the required length of the upper portion abme, 

 w ~el, the length of the second portion emfl, 

 x m Ig, the length of the third portion If kg, 

 y gi, the length of the fourth portion gkhi, 

 z zn id, the length of the fifth portion i hcd. 



Then, according to equation (7) under the third problem, the entire 

 pressure on the parallelogram abed, is 



therefore, the pressure on each part of the divided figure, is 

 bl 2 



But because the value of $, the angle of inclination, and s the 

 specific gravity of the fluid, are the same for all the parts ; those 



