HYDRAULICS AND ITS APPLICATIONS 



.-. G M = G G' cot B = ~f ' 5 x cot 0. 



e may be measured by noting the change in inclination of a long pendu- 

 lum as the weights are moved. The experiment should be repeated for 

 different values of B x, measured both to the right and to the left, and a 

 curve may then be drawn on an angle base, showing values of G M. By 

 exterpolation the value of G M in the limit when = can then be 

 determined. 



Since the righting couple = W . G Msin 6, this equals 2 P B x cos 6, 

 so that the same experiment enables us to draw the Stability Curve, 

 showing the value of this righting couple for different angles of heel. 

 If the small masses be moved about, the weight, and therefore the 



volume of water displaced re- 

 maining constant, the locus of 

 the Centre of Buoyancy is 

 termed the Surface of Buoy- 

 ancy. Since, for equilibrium, 

 the vertical through the C. B. 

 must pass through the C. G., 

 and since for small displace- 

 ments, the line joining two 

 successive positions of the 

 C. B. is parallel to the surface, 

 it follows that the tangent 

 plane to the surface of buoy- 

 ancy at the C. B. is parallel to the water surface, and therefore that the 

 vertical through the C. G. of the body is normal to the surface of buoy- 

 ancy. In other words, any curve of buoyancy HI H 2 H s is an involute 

 of the corresponding curve of metacentres MI M 2 M 3 (Fig. 18). 



In general in the case of a ship, owing to the fact that the under water 

 contours are not symmetrical about an amidships section, as they are 

 about a longitudinal section, the vertical through the centre of buoyancy 

 in the displaced position will not intersect the line H G, since the C. B. 

 is now displaced in a different plane from that of the rotation of the boat. 

 By projecting the verticals through the successive centres of buoyancy 

 on to two vertical planes, one running fore and aft, and the other perpen- 

 dicular to this, we get one series of intersections on each plane, and thus 

 get two metacentric heights, the first for pitching displacements (Fig. 19), 

 and the other, previously obtained, for rolling displacements. 



The latter is in general, for the ordinary type of ship, by far the more 



FIG. 18. 



