WEIGHT AND SUPPOKT IN SHIPS. 
429 
where the curves of shearing-forces (V V, Plate XVI. fig. 7, Plate XVII. figs. 9 &10) 
cross the axis A B ; and in the 4 Audacious,’ when she has only her engines and boilers 
on board, there are no less than five such sections (see Plate XVII. fig. 11). All these 
cases, therefore, give an odd number of sections of water-borne division and of zero 
shearing-forces; and the number of these sections is one less than the number of water 
borne sections where the curves of loads cross the axis and the shearing-forces are 
maxima. It may be assumed that in most ships having an excess of weight at the 
extremities, when floating in still water, the number of sections of no shearing-forces 
will be odd. 
The rules here laid down for the number of sections of maximum and zero shearing- 
force must not be regarded, however, as universally binding, nor necessarily true ; they 
are rether indications of what may be expected to be conformed to in very many ships. 
To render this clear we will again take the case of the 4 Audacious’ when she has only 
her engines and boilers on board, her curve of loads corresponding to that condition 
being LL in Plate XVII. fig. 11. Between the water-borne sections B 4 and B 5 there 
is an excess of weight of 80 tons only, but within those limits there falls a section of 
water-borne division (d d’), and the ordinary rule is conformed to as regards the number 
of sections of water-borne division being one less than that of the balanced sections. 
Now suppose 40 tons out of the 80 tons were removed from this space, 25 tons being- 
placed 90 feet abaft its present position, between the stern and the water-borne section 
R 6 , and 15 tons being placed 150 feet before its present position on the fore side of the 
water-borne section B 1 . The ship’s trim would obviously remain unaltered, since the 
moments produced by the alteration of the stowage balance each other ; and the only 
alteration in the curve of loads would be that the areas of the foremost and aftermost 
loops would be increased, while the area of the loop between R 4 and R 5 would be dimi- 
nished. These changes are indicated in the curve LL, Plate XVII. fig. 12. Although 
the number of the water-borne sections and their positions remain unchanged, this 
transposition of weight has a remarkable effect upon the form and character of the curve 
of shearing-forces, as will be seen by comparing the curves marked V V in figs. 11 & 12. 
Starting from the point A, we find the shearing-force at R 1 R 1 (fig. 11) to be 175 tons, 
while that at the corresponding station in fig. 12 is 1G0 tons. On account of this in- 
crease in the shearing-force, the foremost section of water-borne division ( a a ') falls some- 
what nearer to the water-borne or balanced section R 2 R 2 in fig. 12 than it does in fig. 11, 
and the shearing-force at R 2 is only 5 tons instead of 20 tons. The next section of water- 
borne division (bb 1 in fig. 12) also falls closer to R 2 than it did before; in fact the small 
loop of the curve V V between a a ' and b V in fig. 11 almost disappears in fig. 12. After 
crossing the axis at b the curve V V has continually increasing negative values up to the 
balanced section R 3 R 3 , where the shearing-force is 150 tons instead of 135 tons as in 
fig. 11 ; and this causes the next section of water-borne division ( c d) to lie nearer the 
balanced section R 4 R 4 than it did before. Up to this point, therefore, the curves V V 
for the two cases have very similar characteristics, although they differ in some respects ; 
mdccclxxi. 3 o 
