CONCLUSIONS APPLICABLE TO SHIP-BUILDING. 
635 
If it be not practicable to give to the vessel, throughout its whole length, a form 
subject to these conditions, this is practicable with regard to the midship section, 
which is the governing section. 
37 - Of vessels having this general form, those are, cceteris parihiis, the most stable 
in which the circular area, when completed, includes entirely the corresponding sec- 
tion of the ship (as shown in fig. 4), because, in respect to these ships, the centre of 
gravity of the displaced fluid descends as the ship rolls (Art. 13.); and when this is 
the case, the work necessary to incline the ship through any given angle (which 
measures its dynamical stability) is equal to that necessary to raise it bodily through 
a height equal to the sum of the vertical displacements which its centre of gravity, 
and the centre of gravity of the displaced fluid, suffer in that inclination, whilst in 
the opposite case, represented in fig. 3, it is equal to the work necessary to raise it 
through the difference of those heights*. 
Of the class of vessels represented in fig. 4, the stability of those is the greatest, 
other things being the same, in respect to which the space STD between the circum- 
ference of the circular area and the hull of the vessel is the greatest. 
38. It is not necessary to these results, taken in a general sense, that the sections 
of the vessels should be accurately circular as to their parts subject to immersion and 
emersion. If on the midship section of a ship a circle can be described, having its 
centre in the vertical axis of the section so as nearly to coincide with the parts of the 
periphery subject to immersion and emersion, then the ship may be distinguished as 
to whether it belongs to the class in which the centre of gravity of the immersion 
ascends or descends, by observing whether this circular area is wholly or only partly 
included within the section. The midship sections of Her Majesty’s ships Vanguard, 
Bellerophon and Canopus present illustrations of this principle. They are represented 
in figs. 8, 9, 10. It will be observed, that if a circular area be struck on each section 
according to the conditions stated above, that area will in the Bellerophon and 
Canopus entirely include the corresponding sections of the hulls of the two ships, a 
wider space intervening between the two areas in the Canopus than the Bellerophon. 
Other things being the same, the former ought therefore to be the more stable ship. 
In the Vanguard the circular section does not wholly include that of the hull. This 
should therefore be the least stable ship of the three. These conclusions are, I be- 
lieve, in accordance with the known qualities of the ships. If there be any ship whose 
midship section resembles that represented in fig. 3, the centre of gravity of its dis- 
placement will ascend in the act of rolling, and, cceteris paribus, it cannot but be an 
unstable ship. 
* The hull may be so shaped as to cause the centre of gravity of the vessel to descend in the act of rolling. 
In this case AHj, equation 6, must be taken negatively. If the centre of gravity of the immersed part ascends, 
U(9) -will in this case be negative, and the position ■will be one of unstable equilibrium. If the centre of gravity 
of the immersion descends, AHj, in equation 6, must be taken positively ; and if it exceeds AHi, the equilibrium 
will be stable. 
4 M 2 
