634 
CONCLUSIONS APPLICABLE TO SHIP-BUILDING. 
33. If therefore some existing vessel were fixed upon whose qualities in respect to 
rolling were well known, and if it were determined by calculation from this theorem 
what amount of work must be done upon that vessel to make it roll through some 
given angle ; and this amount of work being so determined in respect to that existing 
ship, if, before all other ships of the same class were built, it were determined by a 
similar calculation, made from the drawings of those ships, whether a greater or a 
less amount of work would be necessary to make them roll through the same angle, 
then it would be known whether these ships would, under the like circumstances, roll 
more or less than that ship, and the forms proposed to be given them might be 
adopted or might be altered accordingly. 
I conceive that by this means, if duly applied, great certainty might be given to 
the construction of ships in respect to rolling, and of course to pitching, for the same 
principles which apply to the one apply also to the other, with no other difference 
than in the direction in which the inclination is supposed to take place. 
34. The force of the winds and waves, to the action of which a vessel is liable, may 
be supposed to vary as the surface she opposes to them, that is, to the area of her sails 
and the superficial dimensions of her hull. In vessels geometrically similar these vary 
as the squares of any of their similar linear dimensions, their lengths for instance. 
On the other hand, the weights of such vessels, supposed to be similarly loaded, 
varying as the cubes of their lengths ; and the depths of their centres of gravity, and 
of the centres of gravity of their immersed parts, varying as their lengths ; their 
dynamical stabilities, with reference to a given inclination, vary as the fourth powers 
of their lengths. Since, then, in reference to vessels thus geometrically similar, the 
disturbing forces, to the action of which they are subject, vary as the squares of their 
lengths and their stabilities as the fourth powers, it follows that their actual steadi- 
ness in the water will vary as the squares of their lengths, the greater vessel being 
more steady than the less in this proportion. 
35. The expedients which I have pointed out for so designing a ship as to satisfy the 
conditions of easy rolling and pitching, suppose a knowledge of the exact position of 
the centre of gravity of the ship and of the centre of gravity of her displacement. 
The determination of these however is no new question ; a knowledge of them has 
always been considered necessary to the skilful building of a ship, and the methods 
given for that purpose in books on ship-building are sufficiently aecurate for the pur- 
pose, if the data are to be relied upon ; and if not, nothing is required but the labour 
to determine these data. 
36. That form of vessel in which the surfaces subject to immersion and emersion, 
when intersected by planes perpendicular to the vessel’s length, have cireular sections, 
having their centres in a common axis, is, coeteris garihus, eminently a stable form', 
because in a vessel of sueh a form (Art. 12.) the centre of gravity of the portion of 
the displaced fluid which is included within the solid of revolution (ATB figs. 3, 4) 
formed by all these circular sections, does not in the act of rolling rise. 
