WEIGHT AND SUPPORT IN SHIPS. 
435 
follows from the fact, that in a ship which sags there must be an excess of weight amid- 
ships as well as at the extremities, and there must consequently be some intermediate 
portions at which there is an excess of buoyancy, and at which hogging-strains will 
result from the moment of the unsupported weights at the bow and stern. The curve 
of moments (MM in fig. 7) for the 4 Victoria and Albert’ illustrates these remarks; in 
the fore-and-after bodies we find considerable hogging-moments, while amidships, as I 
have shown, there are sagging-strains. While sagging alone cannot take place in still 
water, it may, however, occur at sea, or in exceptional positions ashore. 
The various conditions of strain of ships floating in still water may, I think, be grouped 
under the following types: — First, the ‘Minotaur’ type, including the greater number of 
vessels, in which the weights are pretty evenly distributed, and the buoyancy is in defect 
at the extremities only. In some vessels which might be included in this class the 
weight and buoyancy are equal for a considerable length of middle body ; but it will be 
obvious that in such cases the bending-moment is of uniform amount throughout the 
middle body, and that the length of middle body might be increased or diminished 
without affecting the vertical bending-strains. Second, the ‘Bellerophon’ or 4 Audacious ’ 
type, in which there is a defect of buoyancy amidships as well as at the extremities, but 
the bending-moments throughout the length produce hogging-strains, having a mini- 
mum value amidships. Third, the 4 Victoria and Albert’ type, which has a greater pro- 
portionate defect of buoyancy amidships, and is there subject to sagging-strains, while 
in the fore-and-after bodies hogging-strains are experienced. Besides these there may 
be, and doubtless are, many special cases, wherein, to revert to the graphical method, 
the curve of loads would have a greater number of loops than in any of the ships we 
have considered ; but the preceding classifications will, as I have said, probably include 
by far the greater number of ships. 
The determination of the positions of those sections of a ship at which the maximum 
and minimum bending-strains are experienced has been satisfactorily performed by Dupin 
and later writers. Among these later writers I may particularly refer to Professor Rankine, 
who has done much to advance the application of scientific principles to the determina- 
tion of the strength and strains of ships. At page 136 of his 4 Shipbuilding, Theoretical 
and Practical,’ are given a mathematical demonstration and a graphical representation 
of the theorem which Dupin first established, viz. that maximum and minimum bending- 
moments are experienced by, what I have termed previously, sections of water-borne 
division. Those who are desirous of following out these investigations will be repaid by 
a study of Professor Rankine’s method ; but that sections of water-borne division do 
possess this property may be shown by the following simple method. 
