OF THE POSITIONS OF EQUILIBRIUM. 



333 



Here then it is manifest, that the values of x and y are each expressed 

 by the same quantity ; hence we infer, that the body floats with one 

 diagonal of its vertical section perpendicular to the surface of the 

 fluid, and the other parallel to it. 



418. The practical rule afforded by the equations (261 and 262), may 

 be expressed in words at length as follows. 



RULE. Multiply the square root of twice the specific gravity 

 of the solid, by the side of the square section, and the product 

 will give the length of the immersed part , when the body is in 

 a state of rest. 



419. EXAMPLE. Suppose a square parallelopipedon, whose side is 

 equal to 18 inches, to be placed upon a fluid with one of its angles 

 immersed, and one of its diagonals vertical ; how much of the body 

 will fall below the plane of floatation, supposing its specific gravity to 

 be 0.326, that of the supporting fluid being equal to unity? 



Here, by operating according to the rule, we get 



ar= 18V 2 X0.326 zz 14.526 inches, 

 and for the corresponding value of y, we have 



, = ^ = ^6^, 



Consequently, the position of equilibrium thus indicated, is as 

 represented in the annexed 

 diagram; where IK is the 

 surface of the fluid, AC the 

 horizontal and B D the ver- 

 tical diagonal ; Dm and i>n 

 being respectively equal to 

 14.526 inches, as deter- 

 mined by the foregoing 

 arithmetical process. 



420. Take DP equal to 

 three fourths of BD, and 

 draw pm and pn meeting 



the surface of the fluid in the points m and n ; then are pm and pn 

 equal to one another ; this is one of the conditions necessary to a state 

 of equilibrium, when neither of the diagonals is vertical ; but in the 

 present instance, the condition of equality will obtain wherever the 

 point P may be taken, and consequently, the equilibrium is not in- 

 fluenced by the position of that point. 



