CONCLUSIONS APPLICABLE TO SHIP-BUILDING. 
637 
from their elasticity, influenced, besides this cause, by their weight and length, and 
this motion assumes the form of an independent oscillation, affecting more or less 
the oscillatory motion of the vessel itself. 
If, at the instant when the ship would otherwise begin to roll back, the elasticity 
of its masts is in the act of carrying them forwards, there will be a violent strain of 
the ship, which would not take place in a ship so constructed or so loaded as to 
create that synchronism of the independent oscillations of the vessel and its masts, 
which is implied in the flict that she does not strain herself in rolling. 
42. The properties of different ships with regard to the strain they suffer in rolling, 
and whether, in respect to the seas which are of most frequent occurrence, they roll 
easily or heavily, are probably ^vell known, so that it would be possible to fix upon 
some ship of each class w^hich might in this respect serve as a standard with which 
other ships of that elass might be compared. The time of oscillation proper and 
peculiar to this ship might also be ascertained by experiment. It would then become 
possible to build and load all other ships of that class so as to oscillate in the same 
time as that ship, and thereby ensure, supposing them to be masted in the same way, 
very nearly the same qualities in regard to the strain they suffer in rolling. 
The form of the ship so constructed need not however in any respect resemble that 
of the standard ship ; all that is required is, that — in respect to the dimensions of its 
parts and the distribution of its weights when loaded — it should satisfy the condi- 
tions implied in assigning a given value to ^(^j) in equation 24. In all other re- 
spects full latitude is allowed to the builder*. 
43. I have shown (Art. 19.) that the axis about which the ship may at any instant 
be conceived to roll is perpendicular to two straight lines, one of which is drawn 
horizontally from the vessel’s centre of gravity parallel to the direction in which it is 
rolling, and the other vertically through the centre of gravity of its plane of flotation 
at that instant. 
Its vis viva, when rolling or pitching, is therefore greater as its weights are placed 
at a greater distance from this axis, and less as they are nearer to it. 
Whence it follows as a general principle (equation 24.), that the ship is made to roll 
more slowly by moving its weights to a greater distance from this axis, as when the 
yards are run up; and more quickly by bringing them nearer to it, as when the guns 
are run back in a heavy sea to diminish the strain on the ship’s timbers. 
44. The form under which l\ enters equation 24, shows that the greater the depth 
of the centre of gravity of the ship’s displacement the more slowly (other things 
being the same) will she roll, provided that she be a ship of that class of which fig. 3 
is the type, in which this quantity (/. e. the depth of the centre of gravity of the dis- 
placement) diminishes as the vessel rolls ; but that if, on the contrary, she belongs to 
* Taking a ship, whose form may indeed (within certain assignable limits) be any whatever, it is in his 
power, guided by that equation, so to load it as that it shall oscillate in the same time with any other ship 
whose form may be in all respects different. 
