394 Mode of calculating the 



whole; and is impelled upward by the re-ac"tion of the 

 fluid which fupports it, acting in the dirc&ion of a vertical 

 line paffing through the centre of gravity of the part im- 

 merfed : therefore, unlefs thefe two lines are coincident, the' 

 floating body thus impelled muft revolve round an axis,, 

 either in motion or at reft, until the equilibrium is reffored. 



Theorem III. If by any power whatever a veflel be 

 defiefted from an upright pofltion, the perpendicular di fiance 

 between two vertical lines paffing through the centres of 

 gravity of the whole, and of the part immerfed reflectively, 

 will be as theflabilityof the veflel, and which will be pofitiVe, 

 nothing, or negative, according as the metaccntre is above, 

 coincident with, or below, the centre of gravity of the veflel. 



Theorem IV. The common centre of gravity of any 

 fyflem of bodies being given in pofltion, if any one of 

 thefe bodies be moved from one part of the fvlleni to 

 another, the correfponding motion of the common centre of 

 gravity, estimated in any given direction, will be to that of 

 the aforcfaid body, efiimatcd in the fame direction, as the. 

 weight of the body moved is to that of the whole fyflem. 



From whence it is evident, that in order to afeertain the 

 liability of any veflel, the pofltion of the centres of gravity of 

 the whole, and of the part immerfed muft be determined ; with 

 which, and the dimenfions of the veflel, the line of floatation, 

 and angle of deflection, the ftability or power either to right, 

 itielf or overturn may be found. 



In fhips of war and merchandife, the calculations necef- 

 fary for this purpofe become unavoidably very operofe and 

 troublefome ; but they may be much facilitated by the experi- 

 mental method pointed out in the New Tranfa£tions of the 

 Swedifh Academy of Sciences, firft quarter of the year 1787, 

 page 48. 



In river and canal boats, the regularity and Simplicity of 

 the form of the veflel itfelf, together with the compact dif- 

 pofition and homogeneal quality of the burden, render that 

 method for them unneceifary, and make the requifite calcu- 

 lation 



