432 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OF 
and to take account of the moments of the resultant vertical forces representing the excess 
and defect of buoyancy of the part on the other side of that section. The algebraical 
sum of these moments represents the bending-moment required. We have in the curves 
of loads, previously constructed, graphical representations of these resultant vertical forces, 
both in magnitude and direction, as well as in position, and consequently can find with 
ease the bending-moments at various stations. The operation simply consists in finding 
the moments about the various stations of those parts of the curve of loads which lie 
on one side. I will again take the case of the ‘ Victoria and Albert,’ for which the curve 
of loads is shown byLL in Plate XVI. fig. 7. It will appear on consideration that the 
most convenient stations at which to calculate the bending-moments are those (midway 
between the dotted ordinates of the curve of loads) which have already been used as ordi- 
nates of the curve of shearing. Let a (fig. 7) be the station at which the bending-moment 
is to be determined; then starting from A (which is nearer a than B is, and which is 
therefore more convenient) the vertical pressure represented by each loop of the curve of 
loads between A and a must be multiplied by the distance of the centre of gravity of 
that loop from a; and the difference between the sums of the moments of the upward 
forces and the sums of the moments of the downward forces will equal the bending-mo- 
ment at a. At this station the moments of the downward forces are greater than those 
of the upward forces, and the bending-moment consequently tends to produce hogging, 
to represent which a length a a! is set off above A B, showing, on a certain scale of foot- 
tons per inch, the hogging-moment at a. A similar method is followed at all the other 
stations, and where (as at b , fig. 7) the resultant moment tends to produce sagging, the 
ordinate representing its amount is set off below A B. As the result of this process, a 
series of ordinates is determined for the curve of bending-moments M M, the approxi- 
mation to accuracy being sufficient for all practical purposes. We have previously 
seen that for curves of weight, buoyancy, loads, and shearing-forces the graphical me- 
thod does not cause any important error even in extreme cases, such as the ‘ Bellero- 
phon’s;’ and I may add here that for bending-moments the errors resulting from distri- 
buting weights that are really concentrated are very much less in proportion than they 
are in the cases previously considered. 
There are one or two matters of practical interest connected with the construction of 
the curves of moments to which I may briefly refer. The first has already been men- 
tioned, viz. that in calculating the moments it is always better to start from the end of 
the ship nearer to the section, although the same value would obviously be obtained by 
starting from the other end, this being one of the hydrostatical conditions of the ship’s 
equilibrium. Another point is, that in working from one end of the ship to the other, 
the moment at the end towards which we are working should always be zero, since 
there can be no bending-moment at either end ; this constitutes a check on the accuracy 
of the calculation. 
This graphical method of representing bending-moments has also been applied to the 
<• Minotaur,’ ‘ Bellerophon,’ and ‘ Audacious ’ (the latter when laden and when light), the 
