WEIGHT AND SUPPORT IN SHIPS. 
445 
the rapid changes in the positions occupied by ships relatively to the crests and hollows 
of the waves, by which most unequal distributions of the weight and buoyancy are, 
under some circumstances, produced and the straining forces are increased ; and the 
pitching and ascending motions of ships, which further modify the strains, both by means 
of the accelerating forces thus developed, and by the percussive forces, shocks, and 
resistance of the water. These causes I propose to notice very briefly ; it is to the 
quantitative investigation of the second, however, that I have given special attention, 
with detailed results, which I will presently record. 
First, as to the modification. of strain that may result from the heaving or vertical 
motion of a ship floating among waves. It is obvious that such motion must produce 
changes of strain ; for when a vessel in moving downwards receives a check, the effect is 
to increase the straining-forces acting upon her ; and when, in moving upwards, she 
reaches her highest position, and is for the moment partially abandoned by the water 
support, the strains upon the hull will be diminished. If the abandonment were total 
(that is, in the hypothetical case when the ship is left up in the air), all bending- and 
shearing-strains would, in fact, disappear ; for then every particle in the ship would, for 
the moment, have impressed upon it the accelerating force of gravity, acting equally 
and in parallel directions throughout her. 
Mr. W. Froude and Professor Kankine have both referred to this subject when dealing 
with the strains of ships at sea ; and the latter gentleman has attempted to fix the limit- 
ing maximum increase of strain produced by vertical motion. This he considers to be 
about one fourth of the still-water strains (for both shearing and bending), this estimate 
being based upon two or three assumptions (see ‘ Shipbuilding, Theoretical and Prac- 
tical,’ pages 151, 152). The fundamental assumption made is that the ship may be 
considered so small in proportion to the waves as to closely accompany their motion, 
just as a float would do. This obviously differs from the condition likely to be fulfilled 
by any actual ship. A ship cannot be expected to closely accompany the wave-motion, 
and her heaving cannot be regarded as the result of the passage of one wave only, but 
of a succession of waves differing, in all probability, in sizes and forms. For these 
reasons I cannot adopt Professor Pankine’s estimate (which doubtless has, however, 
a certain theoretic value) as a basis of practical calculation, nor am I prepared to sub- 
stitute one of my own. 
The practical deduction which should be kept in mind is the general one, that the 
heaving motion in ships at sea will, under some circumstances, produce increased strains. 
It seems probable that these strains are not so severe, in most cases, as those which 
result from variations in the wave supports and from pitching motions ; but it must 
not be forgotten that all three causes may be operating simultaneously, and that their 
combined effect measures the actual strain on the structure. 
Next, as to the additional strains resulting from the changing wave supports on a 
ship at sea. In dealing with this question I shall consider the two extreme positions of 
support illustrated by figs. 14 & 15. In the first of these a ship is supported on a single 
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