442 
ME. E. J. REED ON THE UNEQUAL DISTRIBUTION OF 
the amount and the line of action of the resultant fluid pressure, the determination of 
the bending-moment due to it is very simple. 
I will now consider the cases of some actual ships, in order to give a more definite 
idea of the amounts of the bending-moments due to the longitudinal pressure, and the 
proportions they may bear to the bending-moments resulting from the action of vertical 
forces. Taking first the ‘ Minotaur,’ it has been found by calculation that the fluid 
pressure on the midship section amounts to 405 tons. The total depth of the ship being 
41 feet, the centre of gravity of the section has been taken 20 feet above the keel, and 
the centre of pressure of the immersed midship section has been found to be about 9^- 
feet below it ; so that the bending-moment due to longitudinal pressure has in this ship 
a maximum value of 3780 foot-tons. The bending-moment due to vertical forces has 
been fixed at 45,000 foot-tons, and is therefore twelve times as great; in other words, 
the bending-moment due to the longitudinal pressure is only one twelfth of that due to 
the vertical forces. This seems a very small proportion, but it is obtained from a ship 
in which the overburdening at the ends and the length are both excessively great, so 
that the bending-moment due to vertical forces is very large. In ships of more mo- 
derate dimensions, having a less excess of weight over buoyancy at the extremities, and 
of buoyancy over weight amidships, the proportion of the horizontal force is much 
greater. Taking the case of the ‘ Bellerophon,’ for example, the fluid pressure on her 
midship section is a little over 350 tons, and the distance between the centre of pressure 
and the centre of gravity of the section is about 8^ feet, so that the bending-moment 
due to this pressure equals 3120 foot-tons. This is the maximum value occurring at 
the midship section, where we have seen the hogging-moment due to the vertical forces 
to be 100 foot-tons only, so that at that section the former bending-moment is that which 
virtually fixes the limit of strain. Greater interest attaches, however, to the comparison 
between the two maximum values of the bending-moment. The absolute maximum 
moment produced by the vertical forces has been found to be 12,000 foot-tons, and the 
moment produced by the longitudinal pressure is therefore a little more than one fourth 
of this amount. As compared with the 4 Minotaur,’ we find, then, that the bending-mo- 
ment due to longitudinal pressure is very much less in actual amount for the 4 Bellero- 
phon ;’ but that, in proportion to the moment resulting from the unequal distribution of 
the weight and buoyancy, it is much larger in the shorter ship. This fact prepares us for 
the conclusion arrived at by Dr. Young in his Keport on the diagonal system, — that in the 
short full ships of war in use at the commencement of this century the moment due to 
longitudinal pressure sometimes amounted to more than one third of the maximum mo- 
ment produced by vertical forces. Dr. Young’s method was incorrect, but his estimate 
of the relative magnitude of the bending-moments is probably not very far from the 
truth. 
One other example must suffice for this branch of the subject. In the ‘Audacious,’ 
when afloat in still water, the pressure on the midship section has been found to be 
about 295 tons, and the distance between the centre of pressure and the centre of gravity 
