464 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OE 
The maximum shearing-force is a little greater in this case than in the case of support 
at the ends ; and the maximum hogging-moment is considerably over two thirds the 
maximum sagging-moment. It may also be interesting to compare these exceptional 
hogging-strains with the strains incidental to support on a wave-crest. These are : — 
hogging-moment 140,300 foot-tons, shearing-force 1365 tons. 
The ‘ Bellerophon ’ is divided into two parts by the transverse plane containing her 
centre of gravity, such that the foremost or heavier part weighs 3825 tons, and has its 
centre of gravity 54 feet before the plane of division. The maximum shearing-force for 
support at the middle is therefore 3825 tons, a little greater than in the previous posi- 
tion, and we have 
Maximum hogging-moment=3825 tons X 54 ft. 
= 206,500 foot-tons (in round numbers); or about 
= displacementXii} of the length. 
This moment is considerably under two thirds of the maximum sagging-moment pre- 
viously found for this ship ; and we have in this fact an illustration of the statement 
made above respecting the difference existing between the exceptional hogging- and 
sagging-strains in ships with concentrated weights amidships as compared with other 
ships. In the ‘ Victoria and Albert ’ we should expect to find a more striking illustra- 
tion, and we really do so. Her after body is heavier than the fore body, and its weight, 
1330 tons, constitutes the maximum shearing-force, while the centre of gravity is 46 
feet abaft the centre of gravity of the whole ship. Hence we have 
Maximum hogging-moment = 1330 tons X 46 ft. 
= 61,200 foot-tons (in round numbers) ; or about 
=displacementXr 2 of the length. 
The maximum sagging-moment in this ship is therefore not very much less than double 
the maximum hogging-moment experienced by the ship ashore ; when compared with 
the ‘ Minotaur,’ the case of the ‘ Victoria and Albert ’ appears still more striking. 
These three examples lead to the conclusion that the limiting maximum values of the 
strains experienced by ships supported only at the middle may be fixed as follows : — 
for shearing-forces between one half and two thirds of the displacement ; for bending- 
moments between one ninth and one eleventh of the product of the displacement by the 
length. As in the other extreme position of support, these limits can never be approached 
closely in actual ships, on account of the more or less extended base of support which is 
pretty certain to be found under ships ashore. 
In order to facilitate a comparison between the various strains experienced by the 
three typical ships under different circumstances, the following tabular statement of the 
results arrived at in the preceding pages is given. 
