OF THE PRESSURE OF FLUIDS ON PHYSICAL LINES. 11 



Bisect a 6 in m, and through the point m draw mn perpendicular 

 to AB, the surface of the fluid; then, because the centre of gravity 

 of, a straight line is at the middle of its length, m is the place of the 

 centre of gravity, and nm its perpendicular depth below the surface 

 AE; through b draw the straight line be parallel to mn, and cb is 

 the perpendicular depth of the lower extremity at b. 



Put Z zr a 6, the length of the line whose upper extremity is at a, 

 d~=.nm, the perpendicular depth of the centre of gravity, 

 $ ~ b a c, the angle of inclination, or the given obliquity. 

 Then, because m is the centre of gravity of the straight line a b, we 

 have a m zz \ I, and by the principles of Plane Trigonometry ,we obtain 



rad. : sin. (j> : : \ I : d, 

 and since the tabular radius is expressed by unity, we get 



d \ I sin. <j>. 



Now, the whole pressure which the line sustains in a direction 

 perpendicular to its length, according to the second inference pre- 

 ceding, 



Is proportional to its area, drawn into the perpendicular 

 depth of its centre of gravity below the upper surface of the 

 fluid. 



But the area of a physical line is simply equal to its length ; 

 therefore, if the symbol p denote the pressure, and s the specific 

 gravity of the fluid by which it is propagated, we shall have 



p = isl*sm.<t>. (3). 



and this, in the case of water, where the specific gravity is expressed 

 by unity, becomes 



p~ JZ*sin. 0. 



23. This equation, as well as the more general one from which it is 

 derived, is sufficiently simple in its form for practical application; 

 but in order that nothing may be omitted, which tends to render the 

 subject intelligible to our readers, we shall in this, and in all the 

 succeeding formulae of a practical or general nature, draw up a rule, 

 describing the manner in which the several steps of the process are to 

 be performed ; pursuant to this plan, therefore, the rule for the present 

 case will be as follows : 



RULE. Multiply the square of the length by half the specific 

 gravity of the fluid, and again by the natural sine of the 

 angle of inclination, and the product will express the required 

 pressure on the line in the oblique position. 



24. EXAMPLE 1. A physical line whose length is 36 feet, is im- 

 mersed in a cistern of water, in such a manner that the upper extremity 



