OF THE PRESSURE OF FLUIDS ON PHYSICAL LINES. 15 



depth of the centre of gravity ; then, finally, because the specific 

 gravity of water is unity, we have 



p 32.7454 X 56 = 1833.7424. 



Let the length of the line and its inclination to the horizon remain 

 as above, and suppose the depth of the lower extremity to be 56.4908 

 feet ; then, by the rule for the second case, we have 



56.4908 - 28 x .84805= 32.7454, the depth of the 

 centre of gravity, the same as above, from which the relative pressure 

 is found to be 1833.7424, as it ought to be. 



30. If the line were immersed perpendicularly, or at right angles 

 to the horizon, then sin. is equal to unity, and the formulse for the 

 pressure become 



p=l8($l + d), and^ = Z 5 (D J I), 



where it is manifest, that the parenthetical expressions are equal to 

 one another, each of them expressing the perpendicular depth of the 

 centre of gravity, or the middle point of the given line. 



PROBLEM II. 



31. Two physical lines of different given lengths, have their 

 upper extremities in contact with the surface of an incompressible 

 and non-elastic fluid in a state of equilibrium : 



It is required to compare the pressures which they sustain 

 at right angles to their lengths, supposing them to be immersed 

 at given inclinations to the horizon. 



Let A B c D, represent a vertical section of a vessel filled with 

 water, or some other incompressible and non- 

 elastic fluid, and suppose the lines a b and cdto 

 be situated in the plane of the section, in such a 

 manner that the upper extremities a and c are 

 respectively in contact with A B the surface of 

 the fluid, while their directions make with the 

 horizon the angles ba A and dc B respectively. 



Through the points b and d, the lower extre- 

 mities of the lines ab and cd, draw be and df respectively perpen- 

 dicular to A B the surface of the fluid ; and through m and r, the 

 middle points of a b and cd, draw the lines mn and rs respectively 

 parallel to the perpendiculars b e and df; then are mn and rs the 

 perpendicular depths of the centres of gravity. 



Put I zz a b, the length of the line whose upper extremity is a, 

 I' cd, the length of that whose upper extremity is c; 

 d nm, the perpendicular depth of the centre of gravity of the 

 line a b ; 



