*4$ Mr. Atwood's Disquisition on 
A few remarks may be added in this place concerning a 
theorem delivered by M. Bouguer,* for measuring the stabi- 
lity of vessels when inclined to evanescent angles from the 
upright. The theorem is this : “ When the lengths of vessels 
“ are the same, the stabilities are as the cubes of the breadths." 
This theorem seems at first view to stand independent of, 
and not to require, any subsequent explanation : the author 
immediately applies it to the discussion of some points respect- 
ing the stability of vessels. If any person, relying on the au- 
thor for the truth of this theorem, should only pay attention 
to the proposition as it is here expressed, he would entertain 
an opinion on the subject of stability which is altogether erro- 
neous. M. Bouguer,^ in a subsequent page, gives a satisfac- 
tory account of the limitations and restrictions under which 
the theorem in question is to be understood. He observes, that 
a restriction ought to be applied to the conditions of this pro- 
position, in order to insure the exact correctness of it ; which 
is, that the whole weight of the vessel shall be concentered in 
the centre of gravity of the displaced volume ; a condition 
which may be deemed amongst the most extreme cases that 
can be devised, and such as is rarely known to exist. J The 
vessel's centre of gravity not being supposed coincident with 
the centre of the displaced volume; M. Bouguer§ gives the 
true measure of stability when the angles of inclination are 
* Traite du JSFavire, p. 299. f Ibid. p. 299 and 300. 
J In vessels of burden, the freights of which consist principally of iron, or other 
metallic bodies, or blocks of stone, the vessel’s centre of gravity may be so depressed 
as to coincide with. Or even to be situated under, the centre of the immersed volume. 
But such a disposition causes many inconveniences in the ship’s sailing ; and is never 
adopted when it is possible to raise the centre of gravity to a higher position. 
§ Traite du Navire , p. 300. 
