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ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OE 
building,’ where he refers to the results of a series of experiments on the endurance of 
iron-jointed beams when subjected to changes in the loads put upon them. He says 
“ the joints of an iron-rivetted beam sustained upwards of three million changes of one 
fourth the weight that would break it, without any apparent injury to its ultimate 
powers of resistance. It broke, however, with 313,000 additional changes when loaded 
to one third the breaking-weight, evidently showing that the construction is not safe when 
tested with alternate changes of a load equivalent to one third the weight that would 
break it.” In the case of ships, however, Mr. Fairbairn thinks the strain brought upon 
the material should not exceed one fourth or one fifth its ultimate strength, on account of 
the fact that the changes of strain are not merely effective as regards its amount, but 
also as regards its direction. His final conclusion is that in iron ships “ it seems highly 
probable that a strain of 5 tons per square inch on the material acting alternately in 
opposite directions would at least injure, if it did not ultimately fracture, the material 
after a great number of alterations.” Professor Rankine, I may add, also considers that 
the strain on the material in iron ships should not exceed one fifth of the ultimate 
strength, and thus provides for the changes of strain of which I have been speaking. 
It has sometimes been taken for granted, by writers on this subject, that while the 
straining-actions in smooth water become greater as the figure of the vessel becomes 
finer and sharper, the additional straining-actions produced by waves become less, and 
that these two opposite changes in a rough way compensate for each other. This con- 
clusion is based, however, upon hypothetical cases, and not upon actual ships. On 
turning to our typical ships we find that it is by no means always correct. Take, for 
instance, the cases of the ‘ Minotaur ’ and ‘ Bellerophon,’ one a long fine ship, and the 
other a comparatively short ship with fuller water-lines. In still water we have seen 
that the maximum hogging-moment in the ‘ Minotaur’ is about -g 1 ^ of the product of the 
displacement by the length, while the corresponding moment in the 4 Bellerophon ’ is 
about jyq- of the corresponding product — that is to say, the hogging-moment in the 
short ship is about one half as great in proportion as that in the long ship. This is, so 
far, quite in accordance with the view that the bending-actions in smooth water become 
greater as the figure of the vessel becomes finer and sharper ; but when we pass to the 
case of the wave-crests, we find that the long fine ship is still much more severely strained 
than the short one. The maximum hogging-moment in the 4 Minotaur’ then equals 
of the product of the displacement by the length ; that in the 4 Bellerophon ’ is less than 
fs of the corresponding product — that is to say, is about as great, in proportion, as the 
4 Minotaur’s’ maximum strain. We see, then, that in no sense is there such a compensation 
for the additional strains due to wave-support as has been supposed. In the two ships 
I have here taken the distributions of the weight are, of course, very different, as well as 
the forms of their immersed bodies, and this helps to make the strains less severe in the 
shorter ships ; but even after allowing for this it appears that the adoption of finer lines 
does not produce the mitigating effect in waves which has been supposed. 
I must next refer briefly to the subject of the bending-strains resulting from the 
