460 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OE 
case were slightly severer than even the strains corresponding to the exceptional position 
afloat which we have considered. It is proper to add, however, that they were purely 
statical strains and acted only in one direction, whereas the strains of waves are, as we 
have seen, constantly changing in character and intensity, and are therefore very much 
more trying to the structure. The result of careful observations showed, however, that 
there was scarcely any change of form in this iron-built ship, the maximum amount of 
breakage being inch only in a length of 342 feet, and this becoming reduced to ^ 
inch when the ship was floated. 
The very various positions which ships occupy when they ground may all be supposed 
to lie between the position where the only support is found at the middle of the length, 
and that where there are supports only at the extremities. Mr. Fairbairn has chosen 
these extreme positions as those by which the provision of longitudinal strength in a 
ship should be regulated ; and while I cannot entirely agree with this choice, on account 
of the fact that such positions are never occupied except by a few ships, and by them 
only in consequence of accidents, I am prepared to admit that there are cases on record 
which show that such positions may be occupied. Ships have, for example, grounded 
on rocky bottoms and on causeways, and have been left by the tide with their ends un- 
supported ; and others have grounded in such a manner as to be supported at the extre- 
mities only. Under these circumstances it may be well, therefore, to attempt an approxi- 
mation to the limiting values of the strains incidental to the extreme positions of support 
ashore, and to compare them with the statical strains which have been calculated for 
ships at sea. 
The most severe strains to which a ship aground can be subjected are those incidental 
to support at the bow and stern only. In this position the heavy-weighted amidship 
portion, of course, tends to make the ship sag ; and as it is a very simple mechanical 
problem to determine the amounts of the upward pressures at the points of support, as 
w 7 ell as the weights of the various portions of the ship between the points of support, it 
is possible to calculate the shearing-forces and the bending-moments at various stations 
by a method similar to that previously used for ships afloat. The graphical method of 
representing shearing-forces and bending-moments might also be applied to this case 
were it considered necessary : but this has not been done, on account of the fact that 
we are principally interested in determining an approximate value for the maximum 
bending-strain, and therefore care but little about the other values, which have no prac- 
tical importance. Before giving quantitative examples, taken from actual ships, of the 
maximum sagging-strains that may occur in this position, it will be only proper to call 
attention also to the obviously great increase in the maximum shearing-forces which a 
ship then experiences. Roughly speaking, we may say that one half a ship’s weight is 
taken at the bow, and the other half at the stern when the middle is unsupported ; so 
that near the points of support the shearing-force is approximately one half the ship’s 
weight. In preceding investigations it has been showrn that for still water the shearing- 
force has an approximate maximum value of ^ P ai ’t of the total weight ; and that for 
