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3X. On the Principles of Equilibrium, and the Stability of 

 floating Bodies applied to River and Canal Boats of dif- 

 ferent Forms. By Mr. JOHN GrORGE ENGLISH~, Teacher 



of Mathematics and Mechanical Philofophj. Co?nmumcated 



by the Author, 



1 HE principles of dynamics in general, and of ftatics in 

 particular, have already been fo fully explained by fonie of 

 the ableft mathematicians in Europe, that little or nothing 

 of confequence is farther to be expected on thofe fubjects, 

 unleis our mode of calculus be either greatly improved or 

 totally changed. And as neither of thefe events is likely 

 foon to take place, we ought certainly, in the mean time, to 

 apply to the common concerns of life the principles of which 

 we are already in pofleffion. But fince war and merehandife 

 feem at prefent to be the chief bufinefs of all European 

 nations, and fmce neither the one nor the other can be 

 carried on to any great extent without navigation, nor can 

 any veflel with fafety be navigated without a proper degree 

 of liability; it is therefore a matter of the greater! im- 

 portance to determine with accuracy the liability of 

 nautical veflels of all kinds. 



However operofe and difficult the necelTary calculations 

 may in fome cafes become before the degree of this effcntial 

 quality can be obtained, yet they all depend upon the four 

 following Ample and obvious theorems, accompanied with 

 other well known flereometrical and Itatical principles. 



Theorem I. Every 7 floating body diiplaces a quantity of 

 the fluid in which it floats, equal to its own weight: and 

 eonfequently, the fpecific gravity of the fluid will be to that 

 of the floating body, as the magnitude of the whole is to 

 that of the part immerfed. 



Theorem II. Every floating body is impelled downward 

 by its own eflential power, acting in the 'direction of a. 

 Vertical line palling through the centre of gravity of the 



whole j 



