36 HYDRAULICS AND ITS APPLICATIONS 



Since volume displaced is unaltered we have 



P' 



x y d x = 6 / x y d x 



and for this to be true the axis through must pass through the centroid 

 of the water line section. Also, due to the immersion of the wedge a o a' 

 and the emersion of b o V, we get an upward force of buoyancy trans- 

 ferred from C. G. of wedge b o b' to that of a o a', or since if w = wt of a 

 cubic foot of water, the moment of buoyancy due to the immersion of any 

 element of the wedge as shown is w. x 2 . 0. y Sx. 



x- 



. . Moment of buoyancy of ) fi I r 2 , 



-I t T 7 7 t \~ tv' t/ i U JL tl/ Jj 



wedges a o a' and b o b f I 



} J I 



= ic 6 A K* 



But by the transference of the wedge of water, the centre of buoyancy 

 is moved parallel to c c' ; c and c', being the C. G s . of the wedges ; through 

 a distance U H', where H H' . V w = iv 6 A K* (as before). 



7-7 7-7"' 



Also, if is small = very nearly. 



Knowing H M, and determining G M experimentally, H G can be 

 determined, from which, if the position of H is known, that of G may 

 then be found. H may in general be determined with comparative ease 

 since the contours of a vessel at various levels, and hence the volumes 

 displaced between these levels, are usually accurately known. The 

 problem then simply resolves itself into finding the C. G. of these volumes 

 by taking moments about the water line. 



ART. 12. TIME OF OSCILLATION OF A EOLLING SHIP IN STILL WATER. 



When a floating body is freely oscillating, the resistance of the water 

 being neglected, its motion is similar to that of a pendulum except that 

 the body does not now oscillate about a fixed axis. 



Just, however, as in the case of a pendulum, the righting couple is pro- 

 portional to the sine of the angle of displacement, so that the time of a 

 complete double oscillation is given as in the case of a pendulum by 

 j _ o ^ /Moment of inertia of body about axis of oscillation 

 * g X righting moment for unit angle of displacement. 



