446 
ME. E J. EEED ON THE UNEQUAL DISTEIBUTION OF 
wave-crest, at or about the middle of her length ; in the second she is situated in a wave- 
hollow, and has her extremities immersed in the adjacent wave-slopes. The first posi- 
tion obviously tends to develop hogging-strains of considerable amount, and the second 
to develop sagging-strains. It becomes necessary, therefore, to attempt some approxi- 
mation to the amounts of these strains in various classes of ships, in order to compare 
them with the permanent still- water strains previously calculated ; and for this purpose 
two or three assumptions must be made : — 
(1) That for the moment the effect of the ship’s vertical motion may be neglected. 
(2) That for the moment the ship may be regarded as occupying a position of 
hydrostatical equilibrium. 
(3) That the methods of calculating bending- and shearing-strains previously used 
for still water may be employed here also in order to approximate to the 
momentary strains. 
Investigations based on these assumptions, although confessedly imperfect, will give 
us a better idea of the limits between which the strains produced by changing wave 
supports lie than we could otherwise obtain. 
I have referred to the positions of support illustrated by figs. 14 & 15 as extreme, and 
it may be proper to state briefly my reasons for doing so. I will take the case of fig. 15, 
and suppose the ship to be moved forward some distance so that her bow comes nearer 
to the wave-crests, and her stern moves further down into the wave-hollow. The effect 
of this change will obviously be that a greater length of the vessel will be supported on 
one wave-slope than on the other, and that the ship as a whole will rest upon a flatter 
portion of the wave-form than it did before, as the curvature is much greater in the 
central part of the hollow than it is further up the slope. Hence, when the vessel has 
taken up her new position of equilibrium, it seems certain that the water-level will not 
sink so much below the height amidships corresponding to still water as it does in fig. 15, 
nor rise so much above that height at the bow and stern ; consequently the bending- 
strains will be less. Similar considerations render it evident that the position shown in 
fig. 14 is the other extreme. 
Without further preface I shall proceed to consider the strains brought upon our three 
