[ 609 ] 
XXX. On the Dynamical Stability and on the Oscillations of Floating Bodies. 
By the Rev. Henry Moseley, M.A., F.R.S., 
Corresponding Member of the Institute of France. 
Received January 24, — Read June 13, 1850. 
If a body be made, by the action of certain disturbing forces, to pass from one posi- 
tion of equilibrium into another, and if in each of the intermediate positions these 
forces are in excess of the forces opposed to its motion, it is obvious that, by reason 
of this excess, the motion will be continually accelerated, and that the body will 
reach its second position with a certain finite velocity, whose effect (measured under 
the form of vis viva) will be to carry it beyond that position. This however passed, 
the case will be reversed, the resistances will be in excess of the moving forces, and 
the body’s velocity being continually diminished and eventually destroyed, it will, 
after resting for an instant, again return towards the position of equilibrium through 
which it had passed. It will not however finally rest in this position until it has 
completed other oscillations about it. Now the amplitude of the first oscillation of 
the body beyond the position in which it is finally to rest, being its greatest amplitude 
of oscillation, involves practically an important condition of its stability; for it may 
be an amplitude sufficient to carry the body into its next adjacent position of 
equilibrium, which being, of necessity, a position of unstable equilibrium, the motion 
will be yet further continued and the body overturned. Different bodies requiring 
moreover different amounts of work to be done upon them to produce in all the same 
amplitude of oseillation, that is (relatively to that amplitude) the most stable which 
requires the greatest amount of work to be so done upon it. It is this condition of 
stability, dependent upon dynamical considerations, to which, in the following paper, 
the name of dynamical stability is given. 
I cannot find that the question has before been considered in this point of view, 
but only in that which determines whether any given position be one of stable, un- 
stable or mixed equilibrium ; or which determines what pressure is necessary to 
retain the body at any given inclination from such a position. 
1. To the discussion of the conditions of the dynamical stability of a body the 
principle of vis viva readily lends itself. That principle^, when translated into a 
language which the labours of M. Poncelet have made familiar to the uses of prac- 
tical science, may be stated as follows : — 
* See Poisson, Mecanique, chap. ix. Art. 565 ; Poncelet, Mecanique Industrielle, passim ; Mechanical Prin- 
ciples of Engineering by the author of this paper. Art. 129. 
MDCCCL. 4 I 
