WEIGHT AND SUPPORT IN SHIPS. 
427 
points and lie partly outside it. The maximum correction at the station g would 
therefore be less than that indicated by the space between V V and V' V'. At the 
station g the ordinate of V V represents a shearing-force of 165 tons, that of V' V ; repre- 
sents a force of 100 tons, and the difference between the ordinates represents 65 tons. 
This last amount undoubtedly exceeds the real error in the curve V V for the reasons set 
forth ; and although it would be necessary to construct the curve V V from A up to e in 
order to determine what its actual ordinate at e would be, we shall be within the mark in 
assuming that in this very exceptional case the error involved by using the fair curve V V 
falls below one third of the actual amount of the shearing-force thus obtained. Propor- 
tionately this correction is very considerable, but in no ordinary ship would such an 
extreme example of concentration be met with, and the error would in nearly all cases be 
much less. It may be added that in practice the exact valuation of the shearing-force 
is not required, and a sufficiently good approximation can be obtained by the graphical 
method. Where weights are very concentrated that method will be most in error, and 
the preceding illustration exemplifies the necessity for great care in its application in such 
cases in order to ensure thoroughly trustworthy results. In all, or nearly all, ships there 
is an ample reserve of strength to resist vertical shearing-forces of the most severe cha- 
racter, and on this account comparatively little interest attaches to the determination of 
the maximum values of the shearing-forces experienced by ships afloat in still water. 
Even in the case of the ‘ Minotaur,’ which is certainly one that may be expected to give 
a limiting value, the shearing-force for still water nowhere exceeds one twenty-second 
part of the total weight ; and in the ‘ Bellerophon ’ the maximum value does not exceed 
one thirty-third part, having been reduced so much by means of the better distribution 
of the weight and buoyancy at the extremities. Without going in detail through the 
investigation of the shearing-forces experienced by the typical ships previously chosen, 
it will suffice therefore to indicate a few general properties of these curves of shearing, 
and to illustrate them by reference to the different ships. 
First, as to the determination of the sections of maximum shearing-strain in a ship. 
The reasoning on which the method of constructing the curves is based obviously leads 
to the conclusion that these sections must coincide with the balanced or water-borne 
sections at which the weight exactly equals the buoyancy. It may be summed up in 
the statements that in proceeding from one end of a ship towards the other the resultant 
vertical forces, or loads, between the end and the water-borne section all act in the same 
direction, and that their sum represents the shearing-force at that section ; while between 
any two water-borne sections, such as E 1 and E 2 in fig. 9, the same law holds respecting 
the resultant vertical forces ; and since their sum reaches a maximum at the bounding 
water-borne sections, the shearing-force, which equals their sum minus a constant quan- 
tity, is also, in most cases, a maximum at those sections*. The number of water-borne 
sections varies, of course, with the distribution of the weight and buoyancy. In the 
* Minimum values of the shearing-force sometimes occur at balanced sections, as I shall show almost imme- 
diately. 
