120 Mr. Atwood's Propositions determining the Positions 
the longer axis from their position of equilibrium through 
different angles, endeavour to regain that position, is to be 
considered in two points of view respecting the motion of a 
vessel at sea ; first, in relation to the resistance by which it 
opposes any force that may be applied to incline the ship, for 
instance, that of the wind ; in which case the ship's stability, 
and the impulse of the wind, constitute a species of equili- 
brium as long as the wind continues of the same intensity. 
Secondly, the force of stability is to be considered as operating 
on the ship, after the force by which it has been inclined 
ceases, to restore the vessel to its upright position ; the ship 
being continually impelled by the force of stability, revolves 
round an horizontal axis, passing through the centre of gra- 
vity with an increasing velocity, till it arrives at its upright 
position ; and afterwards with a velocity continually retarded, 
till it arrives at the greatest inclination on the other side. 
This rolling of the ship, with alternate acceleration and re- 
tardation of the angular velocity, will evidently depend on 
the force by which the angular motion is generated ; that is, 
on the force of stability, and its variation corresponding to 
the several angular distances of the vessel from its upright po- 
sition ; from this cause arises one of the principal difficulties 
in the practice of naval architecture ; i. e. to give a vessel a 
sufficient degree of stability, and at the same time to avoid 
the inconveniences which proceed from an angular velocity of 
rolling, increasing and decreasing too rapidly. It is certain 
that the variation of the force of stability depends principally 
on the shape given to the sides of the vessel, which admit of 
being so constructed (all other circumstances permitting) that 
the force shall increase either slowly or rapidly to its limit. 
From the preceding investigations we observe that some float- 
