ON DIFFERENT SECTIONS OF PARALLELOGRAMS. 29 



In the preceding values of the pressure, it is supposed, that the 

 specific gravity of the fluid in which the plane is immersed, is repre- 

 sented by unity, which is true only in the case of water ; therefore, in 

 order to render the formulae general, we must introduce the symbol 

 for the specific gravity, and then the above equations become, 



1. For the upper half of the parallelogram, 



p'=zbl 2 s sin. 0. (13). 



2. For the lower half of the parallelogram, 



pz=f bl*s sin. 0. (14). 



When the plane is perpendicularly immersed in the fluid, or when 

 90, then sin. 1, and the equations (13) and (14) become 

 p' \bl^s, andprzi&/ 2 5. 



In which equations the co-efficients or constant quantities remain ; 

 therefore, the ratio of the pressure is not varied in consequence of a 

 change in the angle of inclination, the variation takes place in the 

 magnitude of the pressures only, and not in the ratio, the magnitude 

 increasing from zero, where the plane is horizontal, to its maximum 

 where the plane is perpendicular. 



44. The practical rules for calculating the pressures, as derived by 

 the equations (13) and (14) are as follows. 



1. For the pressure on the first, or upper half of the paral- 



lelogram. 



RULE. Multiply the square of the immersed length, by the 

 breadth drawn into the specific gravity of the fluid, and again 

 by the natural sine of the angle of elevation ; then, one eighth 

 part of the product will be the pressure sought. (Eq. 13). 



2. For the pressure on the second, or lower half of the paral- 



lelogram. 



RULE. Multiply the square of the immersed length, by the 

 breadth drawn into the specific gravity of the fluid, and again 

 by the natural sine of the angle of elevation; then, three 

 eighths of the product will be the pressure sought. (Eq. 14). 



45. EXAMPLE 6. A rectangular parallelogram, whose sides are 

 respectively 20 and 30 feet, is immersed in a cistern of water, in such 

 a manner, that its breadth or shorter side is just coincident with the 

 surface ; required the pressures on the upper and lower portions of 

 the plane, supposing it to be bisected by a line drawn parallel to the 

 horizon, the inclination of the plane being 59 38' ? 



Here, by operating according to the rule, we have 

 p 30* X 20 X sin. 59 38' X i ; 



