396 OF THE STABILITY OF FLOATING BODIES AND OF SHIPS. 



and finally, by multiplying by three eighths of the common interval, 

 the magnitude of the volume becomes 



m = (S4-2p-f3Q)X5Xf z= 9913.85 x V = 18588.47 cubic feet 



very nearly. 



Proceeding exactly in the same manner with the areas (b -\- >'), the 

 solidity of the space comprehended between the planes passing through 

 the lines kh and ke, and the intercepted side of the vessel, becomes 



m'=. (5-f 2p 4- 3Q)X y = 18433.47 cubic feet; 



therefore, by subtraction, we obtain 

 m m'= e = 18588.47 1 8433.47 = 155. 



482. In the next place, we have to determine the area of the plane 

 passing through all the lines hki in the several vertical sections ; this 

 is effected by measuring all the ordinates in that plane, taken at the 

 common interval of 5 feet along the axis passing through k from head 

 to stern of the vessel. 



When this operation is performed in a dexterous manner, the area 

 of the plane will be found to be 7106 square feet very nearly ; that is, 



A = 7106 square feet; 

 consequently, by equation (412), we have 



Hence it appears, that the distance of the pointy from the middle 

 point k, is too small to cause any material error in the result, we shall 

 therefore suppose that the plane of floatation corresponding to both 

 positions of the vessel, intersect each other in the axis passing through 

 k from head to stern of the vessel. Taking, therefore, the mean 

 between the two foregoing solidities, we shall have 



$(ro 4- m') |(18588.47 -f 18433.47) = 18510.97 cubic feet. 



This, therefore, is the solidity of the volume which becomes immersed 

 in consequence of the inclination ; and by pursuing a similar mode of 

 procedure with respect to the areas of the twelve horizontal sections, 

 the solidity of the whole volume immersed, will be found to be 119384 

 cubic feet very nearly ; and moreover, by referring to the subsidiary 

 figure employed in the construction, and introducing the principles by 

 which the distance BR is ascertained, we shall have 

 BRzr27.32 feet; 



consequently, by Proposition XII., Chapter XIII., the distance gt in 

 the original figure is thus found, 



