448 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OE 
are met with. Its transverse sections are so fine, and its weight is so great, that the 
increased immersion does not suffice to entirely do away with the excess of weight 
existing in still water ; in fact on the first 20 feet of length there is a small excess of 
weight (about 50 tons) still remaining; and we thus meet for the first time with a case 
where the conditions of the two extremities of a ship differ, an excess of buoyancy 
existing at one end simultaneously with an excess of weight at the other. In actual 
ships at sea this must often be so, since the pitching and ascending motions are sure to 
produce a deep immersion at one extremity simultaneously with the emersion of the 
other extremity. Reverting to the ‘ Minotaur’ in the wave-hollow, I need only state that 
the maximum shearing-force is found to be almost the same as that for still water (470 
instead of 450 tons), and that the maximum bending-moment is also of nearly identical 
amount with that for still water (44,000 instead of 45,000 foot-tons), only it is a sagging- 
strain instead of a hogging-strain. In fact for five-sixths of her length the ‘ Minotaur’ 
is subjected to sagging-strains when in the wave-hollow; and as the small excess of 
weight at her bow can only be expected to exist in armoured ships of her extreme length 
and fineness, under such circumstances we are quite warranted in assuming that, as a 
rule, ships of this type will sag throughout the whole length when floating in wave- 
hollows. In such ships also, so far as this example enables us to judge, the sagging- 
strain in a wave-hollow is likely to fall below one half of the hogging-strain on a 
wave-crest. 
Within certain limits the strains of a ship of the ‘Minotaur’ type will be increased 
when the lengths of the waves become decreased and their steepness increased. For 
instance, I have previously supposed the ‘Minotaur’ to be balanced on waves 600 feet 
long, while her own length is only 400 feet ; but if the waves were decreased in length, 
the strains would usually be increased so long as the decrease is not sufficient to cause 
the extremities of the ship to be immersed in the slopes of adjacent waves. The latter 
consideration roughly fixes the limit of decrease in the length of the wave by the condi- 
tion that the wave and the ship shall be of equal lengths ; and consequently to find the 
limiting values of the bending- and shearing-strains corresponding to the extreme posi- 
tions of support, we will suppose our typical ships to be balanced on waves of their own 
length, and of such steepness as is likely to be met with in ocean-waves. The results 
of calculations made on these bases, and with the foregoing assumptions, I shall now 
briefly describe, as well as those for the corresponding wave-hollows. 
First I will take the case of the ‘ Minotaur’ on a wave 400 feet long and 25 feet high, 
instead of 600 feet long and 30 feet high. The results are graphically recorded in Plate 
XIX. figs. 19 & 20, and Plate XX. fig. 21. On the crest of such a wave the excesses 
of weight at the bow and stern respectively are found to be no less than 1275 tons and 
1365 tons. The maximum shearing-force is 1365 tons, and the maximum hogging- 
moment is 140,300 foot-tons. By changing the dimensions of the wave, therefore, the 
maximum shearing-force has been increased by 435 tons, about one half, and the 
maximum hogging-moment by 35,000 foot-tons. The latter now equals 3-^ times the 
