Centre of Gravity in particular Bodies. 69 



centre of gravity will be at the same height in this lamina, as 

 in the trapezoid ABCD, which is a section of this lamina, 

 made by a vertical plane passing through the keel. We see, 

 therefore, that the reasoning to be made use of here, in order to 

 find the height GE, of the centre of gravity, is precisely the 

 same as that in the last case, substituting only for perpendicular 

 or ordinate, the word section ; we have, therefore, this rule ; 



(l). Take a sixth of the lowest section ; a sixth of the highest, 

 multiplied by triple the number of sections less 4; the second section 

 from the lowest, double the third, triple the fourth, and so on; and 

 call the result thejirst sum. 



(2). Take half the sum of the lowest and highest sections, and all 

 the sections between them, for the second sum. 



(3). Divide the first sum by the second, and multiply the quotient 83. 

 by the common distance between two adjacent sections. 



We may make use of the same method in finding the distance 

 of the centre of gravity from the vertical line XZ, drawn through Fig. 51. 

 a determinate point B of the stern-post, by imagining the bot- 

 tom cut by planes parallel to the midship frame ; but as it would 

 be necessary to measure the surfaces of these sections, it is better 

 to make use of those which have been already measured, in the 

 last operation ; accordingly we determine by the above method 

 the centres of gravity G', G', of the several sections parallel to'the 

 keel. Their distances from the vertical XZ wi 1 ! be each the same 

 as that of the centre of gravity G / 01 the corresponding lamina, 

 We now multiply each section by the distance of its centre of 

 gravity from the line XZ, and regarding the several products as 

 the ordinates of a curved line, like those in figure 50, we add the 

 half sum of the two extreme products, to the sum of all the 

 mean products, and divide the entire sum by the sum of all the 

 mean sections, plus half the sum of the two extreme sections, 

 the common thickness of the laminae being suppressed sa a com- 88, 

 mon factor to the dividend and divisor. 



With respect to the centre of gravity of the vessel itself, wheth- 

 er laden or not, the investigation cannot be reduced to so simple a 

 process. We must take into particular consideration, the differ- 

 ent parts which compose both the vessel and its lading. Having 



