SHIP-BUILDING. 



Area of the Upper Side of the Keel. 

 Length on the upper fide or plane of the keell 



from the aft-fide of the rudder 

 Multiplied by its thicknefs - 



Area of the upper fide of the keel 



Difplacement of the Bottom. 



Half the area of the upper water-line 

 Whole area of the fourth water-line 

 Whole area of the third water-line 

 Whole area of the fecond water-line 

 Whole area of the lower water-line 

 Half the area of the upper fide of keel 



X by diftance between the water-lines 



Area of the keel 265 ft. 9 in. x by 1 

 the depth, falfe keel included -) 



Cubic feet difplaced - - - 



X by pounds in a cubic foot of falt-water 



Ft. 



177 



I 



In. 

 2 



6 



- 265 



261 14.0729 

 3-6 



94010.6624 

 53' -5 



94542.162 



64-375 



6086151 lbs. 



As the eftimated weight of the Ihip, with every thing on 

 board, was 6,295,145 lbs. we find, by the above calculation, 

 the upper water-Hne, as parallel with the keel, is placed too 

 low, as the difplacement is only equal to 6,086,151 lbs. 

 Therefore proceed to find if the body of the (hip is con- 

 ftrufted to fail on an even keel, that is, whether the fhip 

 will be in her natural pofition when brought down to that 

 line. For this purpofe, lot the centre of cavity, or centre 

 of fupport, be next found, as then we may difcern what pro- 

 portion the difplacement of the fore-part of the (hip bears 

 to the aft-part ; for, (hould they not prove equal, the (hip 

 cannot be conftrufted to fail on an even keel. 



Method of Jtndlng the Centre of Difplacement or Support. 



The centre of gravity of a fliip, fuppofed homogeneous, 

 and in a Itate of equilibrium, is in a perpendicular fe6\ion, 

 palTing through the keel, and dividing the (hip into two 

 equal and fimilar parts, at a certain dillance from the Hern 

 and altitude above the keel. 



To afcertaiii the centre of difplacement, or centre of 

 gravity, of the immerfed part of a (hip's bottom, in a ilate 

 of equilibrium, begin by determining the centre of gravity 

 of the upper horizontal fcftion, or water-line ; and as the 

 two fidei are equal and fimilar, the middle line may be con- 

 fidered as the axis of the equilibrium, in which the centre of 

 gravity of that furface is to be found ; and as the furface of 

 the upper water-line, and fo of the others, has been already 

 divided into equal parts, and the breadths taken at the 

 feveral timbers or ordinates to find the difplacement, we 

 have only to obferve that the fpaces between thofe timbers 

 are here confidercd as fo many parallelograms, the centres 

 of gravity of which parallelograms will form a fyftem dif- 

 tributed on the middle line. 



Then to find the centre of gravity of the fyftem, in refpcft 

 to the aft-fide of the rudder, which is alfumcd for the firft 

 term of the momenta, we need not find the centre of gravity 

 of each parallelogram, but divide the whole furface into 

 three fedlions, and multiply their fums, as before, by the 

 diftance between the ordinates, and the produft will be the 

 area of each feftion. 



Then to obtain the fum of the ipomenta of all the ele- 

 mentary parts of the furface, multiply the breadth of each 

 ordinate into its diftance from the axis of the momenta, or 

 firft ordinate ; then take the film of all thefe produfts, and, 

 by multiplying this fum by tlie dillance between the ordi- 

 nates, we (hall have the fum of all the momenta of the 

 elementary parts of the (urface ; which, divided by the fum 

 of the ordinates, will quote the diltaiice of the centre of 

 gravity of the whole furface from the axis of the mo- 

 menta. 



I..aftly, the areas of the feveral planes or furfaces, and 

 their momenta, being found, divide one by the other, and 

 the quotient will be the diftance of the centre of gravity of 

 the whole feftion from the aft-fide of the rudder. 



Cpiration 



