312 



OF THE POSITIONS OF EQUILIBRIUM, 



Now, it is manifest, that since the 

 whole section ABC, is divided by DE 

 the line of floatation, into the two 

 parts A DEB and DCE; it follows, 

 that the centre of gravity of the 

 section ABC, and the common centre 

 of gravity of the two parts into which 

 it is divided occur in the same point ; 

 consequently, the centres of gravity 

 of the triangular areas ABC and DEC, 

 with that of the quadrilateral space 

 A DEB, are situated in the same 

 straight line. 



But by the principles of floatation we know^ that when the solid is 

 in a state of quiescence, the centre of gravity of the whole section 

 ABC, and that of the immersed portion A DEE occur in the same verti- 

 cal line; that is, the vertical line passing through their centres of 

 gravity is perpendicular to the horizontal surface of the fluid ; and for 

 this reason, the vertical line passing through the centre of gravity of 

 the whole section ABC, and that of the extant portion DEC, is also 

 perpendicular to the horizon. 



Bisect the sides AB, BC and D E, EC in the points F, n and H, m and 

 draw the straight lines CF, ATI and CH, Din intersecting two and two 

 in the points G and g, which points are respectively the centres of 

 gravity of the triangular spaces ABC and DEC. 



Draw the straight lines Gg and FH, and because CF and CH the 

 sides of the triangle CFH, are cut proportionally in the points o and 

 g, it follows, that Gg and FH are parallel to one another; but it has 

 been demonstrated, that Gg is perpendicular to TK the horizontal 

 surface of the fluid ; therefore, FH is perpendicular to DE the line of 

 floatation; and since DE is bisected in H, it follows that FD and JE 

 are equal to one another. 



Put a AB, the immersed side of the triangular section ABC, 



b ~ AC, one of the sides of the triangular section which 



penetrate the fluid; 



c :n BC, the other penetrating side of the figure, 

 d m CF, the distance between the vertex of the section and 



the middle of the immersed side ; 

 :rz ACF, the angle contained between the side AC and the 



bisecting line c F* 



