326 



Mr, Major on a Digest of the 



[Noy. 



ship by moving his guns on one side. This lattei* obscurity 

 caused Mr. Charles Bonnycastle, late of the School of Naval 

 Architecture, but now Professor of Natural Philosophy at Char- 

 lotteville, near Washington, Virginia, United States, who was 

 the best mathematician belonging to our institution, to reject the 

 proposition as illegitimate in its conclusions ; and he bestowed 

 considerable time in endeavouring to find it experimentally by 

 other means. His attempts were, however, unsuccessful. The 

 difficulty is here obviated by finding the new centre of gravity 

 of the ship, and by investigating its line of transfer, we are 

 enabled to ascertain the point in the upright position of the 

 masts. 



As Chapman's mode is performed by moving the guns and 

 component weights of the ship, some naval architects have 

 regretted the inconvenience of the method. This induced me 

 to study another mode of effecting it by inclining the ship by a 

 horizontal force applied to the masts, by which the weights of 

 the ship are not disturbed, augmented, or diminished : it is here 

 appended. 



For the resolution of the problem for finding the centre of 

 gravity of the ship, by mov- 

 ing weights horizontally, let 

 C A O D B represent the bottom 

 of the ship, A B its load water- 

 line in tlie inclined position, 

 C D that in the upright one. 

 Suppose E to be the centre of 

 gravity of the displacement, G 

 that of the ship : let M be the 

 place of the guns, which are 

 transferred to N, in a direction 

 -at right angles to the masts. 



Now the new centres of gra- 

 vity of the displacement and 



ship may be found from the translations of the parts of them, 

 the guns and newly immersed part, which latter must be 

 equalto the emerged part. The lines of transfer are parallel with 

 those ofthe parts, and in distance they are inversely as the weights. 

 Suppose Q to be the new centre of gravity of the inclined dis- 

 placement, and m to be that ofthe ship. Join Q m, and produce 

 It to the plane of the masts. Now since the ship is in a state 

 of quiescence, Q m is perpendicular to A B. 



Draw G Z, E T, parallel to A B, and G R perpendicular to it. 

 Then put V for the whole volume displaced of the ship in 

 cubic feet of sea water; A for that of the immersed part by 

 inclination, in the same measure; x for E G, the unknown dist- 

 ance of G from E; W for the weight of guns in cubic feet of sea 

 water ; d for M N, A for the angle of inclination ; and b for the 



