OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



371 



horizon ; the body floats in equilibrio in this position ; but suppose 

 that some external force is so applied to it, as to deflect it from the 

 upright and quiescent state through an angle of 15 degrees; it is re- 

 quired to determine the stability or the momentum of restoration, the 

 parallel sides of the section being respectively 40 and 30 inches, the 

 perpendicular distance between them 20 inches, and the whole length 

 of the body 14 feet, its specific gravity when compared with that of 

 the fluid being as 270 to 1000, or as 0.27 to 1 ? 



458. For the purpose of rendering the several steps of the operation 

 perfectly clear and comprehensible, we shall refer to the annexed 

 diagram, which re- 

 presents a trans- 

 verse section of the 

 body in the inclined 

 position ; ef being 

 the line in which 

 it is intersected by 

 the water's surface 

 when it is upright, 

 and hi the corres- 

 ponding line when 

 it is deflected 

 through the angle fki. PQ is the perpendicular distance between 

 ab and cd the parallel sides of the section, QH the depth to which 

 the body sinks in the fluid as induced by the specific gravity ; o and 

 I are the centres of gravity of the triangles fki and hke; mt the 

 projected distance between them on the line hi, and Gg the distance 

 between the centre of effort and the centre of buoyancy, or the dis- 

 tance between the centre of gravity of the whole body and that of the 

 immersed part, when the body is upright. 



Now, the several parts which have to be calculated in order to 

 resolve the question, are the areas efcd, fki, and the distances mt 

 and og ; for which purpose, we have given a b, dc, PQ, the angle fk i 

 and the specific gravity of the solid. 



Therefore, according to the principles of mensuration, the area of 

 the whole section is expressed by 



20 

 |(6 -f- /3) X D =(40 -f 30) X = 700 square inches, 



and by the nature of floatation, we have 



2fi2 



