1825.] 



Plans of Ships in the British Navy, 



transfer of immersed part. We then have G m = 

 = ^Lli^. GZis also equal to ET - ER = 



W d . COS. A __ JA 

 V 



Wd 



V 



bA 



327 



andGZ 



— xsin.A* 



Hence, 



V 



X . sin. A ==: 



bA-^W d. COS. A 



— X, sm. A. 



& A W d . COS. A 



X = 



V sm. A 



To obtain the value of 6, A and V, see Atwood's Stability* 

 • The other mode is for finding the centre of gravity of the ship 

 from knowing the force of the sails, or any given power, with 

 its. place of action on the plane of the masts. It may be also 

 used conversely. Thus, if we know the centre of gravity of the 

 ship, we can tell the inclining power of the sails at a certain 

 inclination. 



Let a power P, measured in cu- 

 bic feet of sea water, incline the 

 ship a known height from the 

 centre of gravity of the displace- 

 ment, which represent by a. Let 

 A be the angle of inclination of 

 the vessel, G the centre of gravity 

 of the ship, E that of the displace- 

 ment, Q the new centre of gravity 

 of the displacement. Then using 

 the same notation as in the last 

 proposition, GP = a — ^_,RT 



DrawGR 



or G Z = — - 



X s. 



perpendicular to A B, and PR 

 parallel to it. For this expres- 

 sion of stability, see Atwood's 

 disquisition on the subject. 



Now since the power which inclines the ship is equal to the 



buoyancy of stability, the vessel being at rest, F . a — x , sin. A 

 is equal to V . G Z. Or, 



V . G Z = P . G R 



• V 



X sin. A = P . fl — x . sin. A 



h A — X sin. AV= P«sinA— F x sin. A 

 P X sin. A — X sin. A V = P a sin. A — h A 



= F a sin. A — 6 A. 





. sin. A •— V . sin. A 



P a sin. A — J A 

 P sin. A — V sin. A * 



* The theory of Stability, which consists in finding the distance of the vertical central 

 line of buoyancy fron^ the centre of gravity of the ship, is applied to all forms of ships 

 by Atwood, in a disquisition on the subject in Phil. Trans. 1798, Part H. The inves- 

 tigation applies exactly to finding R T, which is equal to G Z aboy«. 



