of floating Bodies, and the Stability of Ships. 123 
blem seems to imply both .that the pendulum sought, and 
the vessel itself, shall vibrate in arcs that are extremely small ; 
for otherwise the analogy altogether fails : no oscillating 
body can describe arcs of unequal lengths in equal times, un- 
less it is impelled by forces which are in the direct ratio of 
the distances from the quiescent point ; and therefore the os- 
cillations of a vessel vibrating in different finite angles are evi- 
dently not isochronal with each other, since the force of stabi- 
lity varies in a proportion so different from that of the distances 
from quiescence ; nor can they be isochronal with any pendu- 
lum, unless the arcs of vibration are of evanescent magnitude ; 
in which case the force of stability being in the direct propor- 
tion of the angles of inclination from the upright, has the effect 
of producing an equality in the times of oscillation : to ascer- 
tain a pendulum vibrating in small arcs which is isochronal to 
the oscillations of a vessel, under these restrictions, is a problem 
which may be solved with sufficient exactness; but unless the 
limitation that has been mentioned should be specified, it is a 
question without the necessary conditions. Mons. Bouguer* 
in his chapter intituled, que les Oscillations sont Isochrones, does 
not expressly mention this limitation, but we must allow it 
probable that he conceived it to be implied. 
From the reasons that have been stated it seems to follow, 
that in order to form a satisfactory opinion of the qualities and 
performance of a vessel at sea as depending on the plan of its 
construction, the forces of stability at the several angles of in- 
clination from o to the greatest limit ought to be ascertained, 
particularly the measure of the greatest stability, and the angle 
of heeling at which it takes place. 
Liv. i. sect. iii. chap. vii. 
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