SHIP-BUILDING. 



proof-timbers interfeft the buttock-lines and bearding-line, 

 and transfer them to the body-plan above the bafe line upon 

 each correfponding buttock-line, and half-thicknefs of the 

 dead-wood ; take alio the half breadth of the proof-timbers 

 where thev interfed the water-lines in the half-breadth plan, 

 and transfer them to their refpeftive water-lines in the body- 

 plan ; but though the proof-timbers crofs the llern-poll, their 

 heels may be fet off, as before diretted for the after-timbers ; 

 then if the fpots fo fet oft" produce fair curves, as the ticked 

 timber (hewn in the body-plan, Plate I., we may conclude 

 that the after-body is fuf&ciently proved and its fairnefs ac- 

 curate. The fore-body may be proved by vertical feftions, 

 in a limilar manner as defcribed above, only their ending will 

 be determined by fquaring up their interfeftions with the 

 main-breadth line, from the half-breadth plan to the (heer- 

 plan. 



Having completed the form of the body thus far, it will 

 be necelTary to afcertain the capacity and liability of the 

 part immerfcd, as in all fiiips of war there is a tixed height 

 for the lower fill of the midfhip port above the load-water- 

 line, allowing for fix months' llores, provifions, &c. to be 

 on board ; and the capacity fhould be fimply adequate for 

 this purpofe ; for the nearer this is approached unto, the 

 more merit is due to the conftrudor : it Ihould not be more, 

 to avoid fuperfluons expence in the building, and the addi- 

 tional men required to navigate lier ; nor (hould it be lefs, 

 from an obvious general infufficiency to anfwcr the required 

 purpofes : the bias ihould rather lead to increafe than di- 

 minifh in capacity. In fliips for commerce, an exa£l ellima- 

 tion of tlieir capacity is more frequently required to regu- 

 late the port duties, and tlie contrails between merchant 

 owners and builders, than to infure their liability, a fixed 

 line of floatation, and fall failing, as the charge may be re- 

 gulated by their ability to fupport it, and their load-water- 

 line may be confiderably varied, without any hurtful inter- 

 ference with other effential qualities. 



Let us at prefent fuppofe the 74-gun (hip, Plate I. as 

 floating upon the water in equilibrium, ar.d the upper 

 water-line upon a level with the furface of the water, by 

 which the fliip is divided into two parts, the one above and 

 the other under the water, which we call the immerfed part 

 of the body. In order to judge of this Hate of equilibrium, 

 in which we fuppofe the vell'el to be, it is ncceffary to take 

 into confideration all the forces which act upon the veflel : 

 and firlt the weight of the whole veflel prefents itfelf, by 

 which it is prelTed down vertically in a line paffing through 

 the centre of gravity of the velfel. This force mull there- . 

 fore be counterbalanced by all the efforts which the water 

 exerts upon the furface of the immerfed part, and confe- 

 quently it will be necellary to determine the preliure that 

 each particle of the immerfed lurface fullains from the water, 

 which requires refearches veiy embarrafiing, and a long feries 

 of calculations : but the following confidcrations will eaCiy 

 lead us to the defired cud. 



As the veiiel occupies in the water, by its immerfed part, 

 the cavity formed by the body under the upper water-line, 

 let us compare this cafe with another, tlie above cavity being 

 filled with water : it is at firll evident, that this mafs of 

 water will be in a perfeft equilibrium with the water that 

 furrounds it ; and it is alfo plain, that this mafs fultains 

 from the part of the furronnding water, the fame eflcirts 

 which the vedel fuffers from it. From whence we fee, tliat 

 thefe efforts of the water balance the weight of the mafs of 

 water which we have juft fubllituted in the place of the 

 veffel. Therefore, fince thefe fame efforts fullain aifo the 

 weight of the whole veflel, it follows that this weight is 

 precifely equal to the weight of the mafs of water which 

 fills the fame cavity as formed by the body of the veflel 



I 



under the upper water-line ; or rather, whofe volume 

 equal to the volume of the immerfed part of the veflel. 



Here, therefore, is the firll great principle upon whichl 

 founded the theory of the floating of bodies that fwim upq 

 the water. It is, that the immerfed part mull always \ 

 equal in volume to a mafs of water, which would have the 

 fame weight as that of the veflel : and it is from this prin- 

 ciple that we determine the true weight of a veffel, by 

 meafuring the volume of its immerfed part in the water ; 

 for then, by reckoning 64,375 lbs. avoirdupois for each 

 cubic foot, we fliall find the weight of the veffel exprcffed 

 in pounds. 



However, this prir.ciple, only, is not fuflicient to deter- 

 mine the (late of the equilibrium of the velfel ; another mull 

 be (lill joined to it, and which we fliall find with the fame 

 facility. We have only to confider in Plate I. the centre of 

 gravity of the mafs of water under the upper water-lir.c ; 

 then we fliall eafily conceive that all tlie eflorts of the furronnd- 

 ing water are in equilibrium with a force equal to the weight 

 of the mafs of water difplaced by the bottom under the 

 upper water-line, which fliould a£l in a perpendicular direc- 

 tion through the centre of gravity of the faid mafs of water 

 downwards : therefore, in order that the veffel may be in 

 equilibrium with the fame efforts, it is necefl'ary that the 

 centre of gravity of the veflel be in the fame vertical fine 

 in which the centre of gravity of the immerfed part is found. 

 For that purpofe we have only to mark within the veffel the 

 very point where the centre of gravity of the immerfed 

 part would be, if it was compofcd of an homogeneous mat- 

 ter, and this point we fliall term the centre of cavity. 



Now the ftate of the equilibrium of any velfel will be de- 

 termined from thefe two principles : i(l, that the immerfed 

 part mull be equal in volume to a mafs of water, whufc 

 weight would be equal to that of the velfel ; and, adly, that 

 the centre of gravity of the veflel, and the centre of cavity, 

 fall in the fame vertical line, which is the vertical axis of the 

 veflel. With refpeft to the centre of cavity, it is evident 

 that it mull always fall below the load-water line ; and if the 

 immerfed part (hould preferve, in defcending, every where 

 the fame furface, or that it had either a prifmatic or cylin- 

 drical figure, then the centre of cavity would fall in the 

 middle of the vertical axis between the load-water-line and 

 the keel. But if the extent dimiuiflied uniformly from the 

 load-water-line to the keel, and it at lafl terminated in a 

 right line drawn through the keel, equal and parallel to 

 the load-water-line, then the elevation of the centre of cavity 

 would be two-thirds of the immerfed part above the keel ; 

 and if the fame immerfed part fhould terminate in a point 

 at the keel as a pyramid reverfed, then the centre of cavity 

 would be three-fourths of the immerfed part above the 

 keel ; but with refpetl to the centre of gravity of the veflel, 

 it may fall either above or below the load-water-line, accord- 

 ing as the lading fhould be dillributed throughout the body 

 of the veffel. Thus in Plate I. of fliips of war in general, 

 where the guns conftitute a confiderable part of the weight, 

 fince they arc placed above the waler, the centre of gravity 

 will be fituated above its furface. 



The bottoms, or immerfed parts of veflels in general not 

 llriftly agreeing with any of the above-mentioned geome- 

 trical forms, it will be neceffary to guage the form of the 

 immerfed part of the vellel's bottom, or, which is the fame 

 thing, the quantity of water difplaced by the bottom ; the 

 weight of which, as before obferved, is equal to the weight 

 of the Ihip, its rigging, provifions, and every thing on board. 

 If, therefore, the exaA weight of the Ihip when ready for fea 

 be calculated, and alfo the number of cubic feet of water 

 difplaced by the fiiip's bottom below the lo.ad-water-line, 

 it will then be known if the lead-water-line is properly 



placed 



