636 
CONCLUSIONS APPLICABLE TO SHIP-BUILDING. 
In all these comparisons it has been supposed that the ships do not otherwise differ as 
it regards their stability, than in their approximation to the typical forms represented 
in figs. 3 and 4. It has been supposed therefore (see equation 17) that the depths of 
their centres of gravity and of the centres of gravity of the fluid they displace in a 
vertical position are the same, and that the moments of inertia of their planes of flota- 
tion are equal. This cannot be the case ; and it is impossible to know to what extent 
this error in the hypothesis may in any particular case affect the measure of the dyna- 
mical stability, except by calculating it by formula 1/. The problem is far too com- 
plicated to render the application of any general principle — except with this preeau- 
tion — safe. It is not — in this respect as in others — more practicable to dispense with 
the resources of mathematical reasoning and of calculation, in building the ship, than, 
after she is built, in sailing her. 
39. It is a deduction of theory (equation 24.), and is confirmed by experiment, 
that, within the ordinary limits of rolling, the Time of a vessel’s rolling is independent 
of the angle through which it roils, being dependent only upon the form of the vessel, 
its weight, the position of its centre of gravity, and its moment of inertia about an 
axis passing through that point (see equation 24) ; so that ev^ery different vessel, 
when loaded in a given manner, has a time of rolling proper and peculiar to it, and 
which may be said to characterize it. x4.nd the same is true of the time of pitching. 
40. This time of the oscillations of the ship may have such a relation to the times 
of oscillation of the waves ^ as to cause the blows of the sea to be received by the ship 
at those instants when they will produce the greatest effect on the amplitude of her 
oscillations (Art. 25.), and thus a little sea may, under certain circumstances, produce 
very heavy rolling. 
If there be not this relation between successive oscillations of the ship and of the 
waves, then there wall be, during a certain number of oscillations, an antagonism of 
the two, until the times of the one class of oscillations have so gained upon those of 
the other as to bring about an interference. The vessel will then probably be com- 
paratively at rest. Then will follow a series of oscillations of the waves and the ship, 
which will in various degrees concur to produce heavy rolling, until it reaehes a maxi- 
mum, when the same cycle of changes will be gone through again-f'. 
41. The straining of the ship in the act of rolling, is dependent upon the time of 
its oscillations. This straining takes place in every part of it, but more parti- 
cularly (by reason of their elasticity) in the masts. When the rolling begins, the 
higher parts of the masts, by reason of their inertia, remain behind the lower por- 
tions, and the masts bend ; as the rolling proceeds they receive an independent motion 
* If the ship be under sail, the rate at which she sails and the distances of the waves from one another, mea- 
sured in the direction in which she sails, are also among the conditions on which her rolling depends. 
f This cyclical antagonism and concurrence of the independent oscillations of the waves and the ship will 
interfere, to a certain extent, with the tautochronism of the ship’s oscillations. 
