OF THE POSITIONS OF EQUILIBRIUM. 



329 



and 



but there are various other forms, which are not less frequent in the 

 practice of naval architecture, nor less important as subjects of theo- 

 retical inquiry : some of these we now proceed to investigate. 



PROBLEM LVIII. 



415. Suppose that a solid homogeneous body in the form of 

 a rectangular prism, floats upon the surface of a fluid of greater 

 specific gravity than itself, in such a manner, that only one of 

 its edges falls below the plane of floatation : 



It is required to determine what position the body assumes, 

 when it has attained a state of perfect quiescence. 



Let ABCD be a vertical section, at right angles to the horizontal 

 axis passing through the centre of 

 gravity of the rectangular prism, 

 and let I K be the surface of the 

 fluid, on which the body floats 

 in a state of equilibrium, 

 being the extant portion 

 mvn the part which falls below 

 the plane of floatation. 



Bisect mn in F and vn in H, 

 and draw the straight lines DF 

 and mil, intersecting each other 

 in g the centre of gravity of the 

 immersed triangle mvn. Join the 



points A, c and B, D by the diagonals AC and BD, intersecting in o 

 the centre of gravity of the rectangular section ABCD, and draw og. 



Then, because the body floats upon the surface of the fluid in a 

 state of equilibrium according to the conditions of the problem ; it 

 follows from the laws of floatation, that the straight line Gy is perpen- 

 dicular to IK. Through F the point of bisection of mn the base of 

 the immersed triangle, and parallel to go, draw FP meeting the 

 diagonal BD in the point p, and join PTW, PW; therefore, because the 

 straight line ga is perpendicular to mn the plane of floatation, it is 

 evident that FP is also perpendicular to mn, and consequently, pm 

 and PW are equal to one another. 



This is a condition of equilibrium which holds universally, and 

 another is, that the area of the immersed triangle m D n, is to the area 

 of the whole section ABCD, as the specific gravity of the solid, is to 



