CONCLUSIONS APPLICABLE TO SHIP-BUILUING. 
633 
of that plane and not in the same vertical with the centre of gravity of the ship, will 
cause, in addition to that vertical oscillation, a pitching or a rolling motion. 
30. All the planes of flotation of the ship, when it is made to roll through small angles 
from its vertical position, should have their centres of gravity in the midship section 
(supposed to be that which contains the centre of gravity of the ship), and the centre 
of gravity of the displaced fluid should also always remain in this plane ; for if that 
be not the case, it is obvious, from Art. 28, that the axis about which the vessel rolls 
cannot be parallel to its length, so that every rolling must be accompanied also by a 
pitching motion. 
31. The angle through which a ship rolls under the action of a gust of wind, is 
essentially different from that at which it would be held inclined by the steady action 
of the same force of the wind, so that when the inclination which a given pressure 
would give to the ship, if applied to the centre of effort of the wind on the sails, is 
calculated (as is customary) by the formula known as that of Atwood, it is erro- 
neous to conclude that the vessel, if subjected suddenly to that force of the wind, 
would incline only through that angle. 
The experiments of Messrs. Fincham and Rawson, of which the results are stated 
in the Table, p. 615, show that it will roll through nearly double that angle, confirm- 
ing, in this respect, the deductions of theory (Art. 2). 
Neither can calculations, made by means of the theorem of Atwood, as to the re- 
spective pressures which would hold different ships inclined at the same given angle, 
be considered as determining with certainty their relative stabilities in respect to 
rolling; for the amplitude of each oscillation depends upon the stiffness of the vessel, 
not only in respect to that given inclination, but upon its stiffness at every other in- 
clination which it must have passed through to reach that angle, and at every in- 
clination which by reason of its acquired momentum it may pass through afterwards. 
The same observation is applicable to the effect of disturbances in the water-line and 
to blows of the waves. 
32. All the causes which produce the rolling motion of a ship, whether they be 
gusts of wind, disturbances of the water-line, or blows of the waves, are measured in 
their effect upon it under the form of worh (travail), so that according as a ship re- 
quires a greater or a less amount of work to be done upon her to cause her to roll 
through a given angle, there is a greater or less probability that, when at sea, she will 
roll through so great an angle as that. The angle through which the ship will be 
made to roll under the action of a given amount of worh, is measured (Art. 7) by the 
product of her weight, by the difference or the sum of the vertical displacements of 
her centre of gravity, and the centre of gravity of her immersed part whilst she is in 
the act of rolling through that angle; the difference being taken or the sum accord- 
ing as these centres of gravity both ascend, or as the one ascends and the other de- 
scends ; or in other words, it is the work necessary to raise the vessel bodily through 
the difference or the sum of these vertical displacements. 
MDCCCL. 4 M 
