430 
ME. E. J. SEED ON THE UNEQUAL DISTEIBUTION OF 
but between IP R 4 and the stern they are altogether different. At R 4 R 4 in fig. 12 the 
upward or positive shearing-force has a maximum value of 45 tons ; and as the excess of 
weight between R 4 R 4 and R 5 R 5 has been reduced to 40 tons, the shearing-force at R 5 R 5 
will still act upward, and have there a maximum value of 5 tons. After passing through 
this minimum value, the shearing-force gradually increases again until it passes through 
a maximum value at R 6 R fl of 230 tons, and then decreases to its zero value at B. Hence 
it will be seen that the chief differences between the curves of shearing in Plate XVII. 
figs. 11 & 12 consist in the facts that the latter has only three instead of five sections of 
water-borne division, and that at R 5 R 5 a minimum positive shearing-force takes the place 
of a small maximum negative shearing-force. 
It is interesting to remark, further, that by another slight alteration in the distribution 
of the weight we can convert the small positive maximum shearing-force at R 2 (fig. 12) 
into a small negative minimum shearing-force, doing away at the same time with the 
two sections of water-borne division a a! and b b'. For example, if the excess of weight 
(40 tons) still remaining between IP R 4 and R 5 R 5 be diminished by one half, and 8 tons 
be placed before R 1 R 1 while 12 tons are placed abaft R 6 R 6 in such a manner as to pro- 
duce equal moments and keep the trim unaltered, we shall have the following values 
for the shearing-forces at the balanced sections: — at R 1 R 1 a force of 183 tons acting 
downwards, being a maximum value, at R 2 a minimum shearing-force of 3 tons, also 
acting downwards, at R 3 R 3 another maximum value (158 tons acting downwards), at 
IP IP a maximum force acting upwards of 37 tons, at IP R 5 a minimum upward force of 
17 tons, and at IP IP a maximum upward force of 242 tons. The only section of water- 
borne division, where the shearing-force is zero and the curve crosses the axis, will ob- 
viously be a little nearer to R 4 R 4 than cc' is in fig. 12. 
From these examples, then, it will be seen that by slight changes in the distribution 
of the weights in a ship we may, while keeping the same total weight and the same 
number of balanced sections, have different numbers of sections of water-borne division 
and of zero shearing-force ; and at the same time it is evident that these changes may 
turn a maximum value of the shearing-force in one direction into a minimum value in 
the opposite direction. It becomes necessary, therefore, to add to our previous rules for 
the sections of maximum and zero shearing-forces. Before doing this it will be conve- 
nient to repeat what was said respecting the number of balanced sections in a ship float- 
ing in still water. The general laws deduced from various cases are as follows : — if there 
be, as there generally is, an excess of weight at both the extremities, the curve of loads 
will cross the axis in an even number of points, and consequently the number of balanced 
sections is even. Hence it follows that the number of sections of maximum or minimum 
shearing must also be even ; and it is obvious that between two maximum ordinates of 
the curve of shearing, both of which lie upon the same side of the axis, there must occur 
either a minimum ordinate also lying upon the same side, or a maximum ordinate lying 
upon the other side of the axis. Since these conditions hold, and we know in addition 
that the curve of shearing must cross the axis in at least one point, on account of the fact 
