SHIP.BUILDING. 



As the inclinations of the Brunfwick and Bedford are 

 omitted in the firft experiment, we fhall only compare the 

 relative itability of the other three (hips, which are quite 

 fufficient to explain everything necellary to be remarked on 

 the fubjeft. It is to be regretted that the firll inclination of 

 the Brunfwick was omitted, as it comes the neareil to 

 Plate I. 



Tons. 



The eftimated weight f Formidable 

 or difplacement of-} Barfleur* 

 the - - - (. Bombay Cadle 



* The difference of the draught of water of the Formidable 

 and Barfleur, \\\ inches, gi>es at leaft Jiotans difference 

 in the weight. Both fliips have iimilar dimcnfions nearly, 

 and are fupported on an even keel. 



Thefe three (hips have the fame number and weight of guns 

 on the lower gun-deck ; therefore the moment of the guns, 

 whether quite exact or not, does not fignify, as any error 

 will not have a partial mfluence. We fuppofe each gun and 

 carriage together to weigh three tons, and allow three feet 

 removal when the gun is run out ; and as there are 14 guns 

 run out in each fhip, the equal moments for them is 3 x 

 3 X 14, or 126 tons at three feet : the weight on one fide 

 the balance is 42 tons, at three feet diltance from the fup- 

 port ; and on the other, in the Formidable, 3150 tons, at 

 48 hundredths of an inch (lefs than half an inch), which 

 will be found to balance 42 tons at three feet : — for the 

 Barfleur 3360 tons, at 45 hundredths of an inch, which will 

 balance 42 tons at three feet ; for the Bombay Caftle 2700 

 tons, at 56 hundredths of an inch, which will balance 42 

 tons at three feet. 



Having found the diftance each centre of gravity is fe- 

 parated from the line of fupport, which is in thefe fmall 

 inclinations the fame as the fine of the angle ; the cofine, 

 or diftance of the centre of gravity from the meta-centre, is 

 eafily known, and will be found to be, for the 



Ft. In. 



^ ^Vlbelow the 



' "V f meta-centre. 

 4 StvJ 



Formidablc's centre of gravity 



Barfleur's ... 



Bombay Caltle's 



When the Formidable and Barfleur were farther inclined 

 by the men at quarters, the Barfleur continued to have one- 

 feventh more liability than the Formidable ; which proves 

 that the Formidable's centre ot gravity was above the fine 

 of floatation ; for otherwife, as herimmerfed body was bet- 

 ter calculated to feparate the line of fupport from the centre 

 of gravity than the Barfleur's, (he would have inclined lefs 

 proportionably, if the centre of gravity had not aiSed 

 againll her ftability : 100 tons of iron ballall at the keelfon 

 would have only increaled her draught of water fix inches, 

 and have given her more (lability than the Barfleur, 

 leaving her the advantage of fix inches more height for her 

 ports, and nearly 34 feet fqiiare lefs refiftance at her mid- 

 fhip-bend. Thus it is demonftrable, that thofe (hips fliould 

 have no more (liingle ballall than is necelTary for the ground 

 tier, and fhould have above 200 tons of iron ; nor would 

 there be any danger of their being labourfome, as their 

 centre of gravity would be but at the line of floatation or 

 load-watcr-linc. The fame .egulation fhoidd prevail with 

 the firft-rates. 



The Bombay Caftle is certainly ftiff enough, yet no doubt 

 her lower deck might have been placed fix inches higher 

 without any detriment whatever to the fhip, and her ports 

 would of confequence have been at a reafonable height from 

 the water. 



In Piatt I. we find, by the preceding calculations, that the 



centre of gravity of the immerfed part of the bottom was 

 above the under fide of 



Ft. Jn. 

 The keel - - - - - - 1 1 0^ 



The meta-centre above the faid centre of gravity 14 9J 



And the centre of gravity is four inches above ' 

 the load-water-line at the centre 

 which makes it - - 



25 loi 



iches above "J 

 of cavity, \ 20 



Centre of gravity below the meta-centre 



Which we find exceeds the Bombay Caftle's ; and the ports 

 in Plate I. are five feet eight inches above the water. 



By the above experiment we obferve, that the guns being 

 run out on one fide and houfed on the other, inclined the 

 fhip to a certain point, and at the fame time there was an 

 exaft equilibrium between the momenttim of the guns, and 

 the whole weight of the fhip on each fide the line of fup- 

 port in the direftion of the vertical effort of the water. The 

 centre of gravity of the fhip is in the fame vertical line with 

 the meta-centre when the fhip is in an horizontal pofition ; 

 and the more the fhip inclines, the more will the centre of 

 gravity of the fhip be removed from the vertical line of the 

 meta-centre, or line of fupport. Hence it is plam, that 

 the diftance of the centre of gravity from the line of fup- 

 port is always in proportion to the fine of the inclina- 

 tion ; at lead when the inclination is but fmall, as before 

 obferved. Now, if that dillance, and likevvife the whole 

 weight of the (hip, be known, we have alio its momentum, 

 or the relative force with which that weight afts in endea- 

 vouring to right the (hip, and bring her again into an hori- 

 zontal pofition, and which is the meafure of her flability ; 

 but fince both the fituation, and likewife the weight that 

 produces the inclination, are known, we may thence know 

 if the momentum of one be equal to that of the other, and 

 thereby eafily difcover if the centre of gravity be in that very 

 point we propofe. 



The fuccefs of the above experiment (which might be 

 rendered very ufeful if more frequently tried) depends on 

 the nicety to be obferved in taking the exaft quantity of the 

 angle of inclination : to attain this, a level line for the fen- 

 fible horizon of the fea may be ufed, or, what is much better, 

 a plumb-line fattened to the head of the matt, taking its dif- 

 tance from the heel of the maft, both when the fliip is up- 

 right, and likewife when fhe heels. The plumb-line feems to 

 be the moil convenient, becaufe we have thereby immediately 

 the proportion in which the centre of gravity recedes from 

 the vertical line of the meta-centre, which will always be in 

 proportion to the diftance of th» plumb-line from the heel 

 of the malt. During the wliole time of the operation, it is 

 neceffary to be very careful to render all the circumllances 

 abfolutely the fame, fo as to be well aCfured the inclination 

 is produced only by the momentum of the guns, &c. 



We may in this manner prove the centre of gravity of the 

 74-gun (hip, Plate I., knowing the heiglit of the meta- 

 centre ; for, having the quantity of the weight producing 

 the inclination, (which is the fame as the above,) and ex- 

 amining the dillance of the centre of gravity from the line 

 of fupport in wliich the effort of the water exerts itfclf, we 

 have alfo its momentum, or its relative force, vWiich is 

 equal to the whole fhip, fince thefe two exaftly balance one 

 another ; fo that it is only dividing this momentum by the 

 whole weight of the (hip, and the quotient will give us the 

 dillance of the centre of gravity of the (hip from the line 

 of fupport, or vertical line of the meta-centre. 



For the Bombay Caftle of 74 guns and 2700 tons, in 



eftiraating 



