ON RECTANGULAR PARALLELOGRAMS. 2l 



Therefore, by retaining the data of the preceding example, the 

 absolute pressure on the plane in the oblique position, is 



p=3* X 18 x 62.5 X \ X .92718 = 4693.84875 Ibs. 

 But when the plane is perpendicularly immersed, the absolute 

 pressure on its surface is 



p=3* X 18 X 62.5 X J = 5062Jlbs. 



COROL. 1 . Hence, the pressures on the plane in the oblique and per- 

 pendicular positions, are to one another as the numbers 4693.84875 

 and 5062 \ ; but in order to compare the pressures under the same 

 conditions, when the shorter and longer sides of the parallelogram 

 are respectively in contact with the surface of the fluid, we have as 

 follows, viz. 



2. When the shorter side of the parallelogram is horizontal, the 

 absolute pressure in the inclined position is 28163.0925 Ibs. ; but 

 when the longer side is horizontal, the absolute pressure is 4693. 84875 

 Ibs. ; consequently, the absolute pressures in the two cases are to 

 one another as 6 to 1 . 



3. Again, when the shorter side of the parallelogram is horizontal, 

 the pressure in the perpendicular position is 30375 Ibs. ; and when 

 the longer side is horizontal, the pressure is 5062 1 Ibs. ; therefore, the 

 pressures in these two cases are to one another as 6 to 1 , the same as 

 before ; from which we infer, that the quantity of inclination affects 

 only the magnitude of the pressures, and that in so far as it changes 

 the position of the centre of gravity, but it has no effect upon the 

 ratio ; therefore, if the plane were to vibrate round its shorter and 

 longer sides respectively as axes, the pressures on its surface, in the 

 two cases, would be to one another in a constant ratio. 



3. OF THE AGGREGATE PRESSURE EXERTED BY THE FLUID ON THE 

 IMMERSED PARALLELOGRAM, AND ON EACH THE CONSTITUENT 

 TRIANGLES FORMED BY ITS DIAGONAL. 



PROBLEM IV. 



38. Suppose the parallelogram to be placed under the same 

 circumstances as in the preceding problem, and let it be bisected 

 by one of its diagonals : 



It is required to determine the aggregate pressure exerted 

 by the fluid, in a direction perpendicular to the surface of 

 each triangle into which the diagonal divides the parallelo- 

 gram, and to compare the pressures on the two triangles. 



