Stability icith Draught of Water in Ships. 



211 



with the centre of buoyancy, bnt if the upper surface is bounded by a 

 plane which is parallel to, and coincident with, the water-surface, the 

 curve of metacentres does not, when produced, end in the centre of 

 buoyancy, as may be seen by fig. 3. The immersion of the plane of 

 the upper surface BC causes a point of discontinuity in the curve of 

 metacentres, which drops at once to the curve of centres of buoyancy. 

 Curves of metacentres are given in fig. 7 for prismatic bodies of 

 triangular and elliptical sections, and for a similar body the lower 

 half of whose section is elliptical and the upper half rectangular 

 (figs. 4, 5, and 6). The section in fig. 4 is an isosceles triangle with 

 the base upwards and horizontal. In figs. 5 and 6 the major axis of 

 the ellipse is horizontal. A comparison of the metacentric curves in 

 fig. 7 will show how they are affected by changes in the form of the 

 floating body. In the case of the triangular section the curve of 

 metacentres is a straight line which passes through the immersed 

 angle of the triangle. 



FIG. 4. 



FIG. 5. 



FIG. 6. 



If OS represent any draught in fig. 7, then M 1? M 2 , and M 3 are the 

 positions of the metacentres at that draught for the three bodies under 



I consideration ; OS' being the draught at which they become completely 

 immersed. 

 If the rectangular floating body shown in fig. 2 be homogeneous, 

 and the changes in its depth of flotation be caused by merely alter- 

 ing the density throughout, or by otherwise altering its weight so 

 that the position of the centre of gravity remain the same, the latter 

 will always be in the centre of the body. The locus of the centre of 

 P2 



