WEIGHT AND SUPPORT IN SHIPS. 
425 
readily understood, the results that would be arrived at by comparing the curves of 
weight and buoyancy previously constructed for this ship ; and I shall show immediately 
how to pass from it to similar representations of shearing-strains. In Plate XVII. figs. 
8, 9, 10, and 11 the same method has been applied to the cases of the ‘ Minotaur,’ ‘ Belle- 
rophon,’ and ‘ Audacious’ (to the last ship both laden and light), the curves of loads being 
marked L L in each diagram. In order that the hydrostatical conditions of equilibrium 
may be fulfilled, the joint area of the loops of the curve LL lying above the line AB 
must, of course, equal the joint area of the loops lying below AB; and the moments 
of the areas above and of those below A B, about any line perpendicular to it, must be 
equal. The points R 1 , R 2 , &c., where the curves of loads cross the axis A B, obviously 
correspond to what have been previously termed water-borne or balanced sections, where 
the weight equals the buoyancy. 
Next, as to the construction of the curves of shearing-forces. From what has been 
previously said, it will appear that the shearing-force at any transverse section equals the 
resultant upward or downward force, measuring the excess or defect of buoyancy on 
either of the two parts into which the ship is divided by the transverse section. Hence 
it follows that, to construct a curve of shearing-forces, we have only to integrate the 
curve of loads (or to obtain the algebraical sums of the areas of the loops of that curve) 
up to certain stations, and to use the results of these integrations as measures, on a 
certain scale, of the lengths of ordinates to be set upwards or downwards at the stations 
according as the areas above or those below the axis are in excess. In performing the 
integrations we may start from either end. As an example I will take the case of the 
4 Bellerophon’ in fig. 9 for that purpose, remarking the fact that in Plate XVI. fig. 7 and 
Plate XVII. figs. 8 and 9 the curves V V represent the result of these operations for the 
4 Victoria and Albert,’ ‘ Minotaur,’ and 4 Bellerophon ’ respectively, and that the similarly 
marked curves in figs. 10 and 11 represent the shearing-forces experienced by the 
4 Audacious’ when fully laden and when she has only her engines and boilers on board 
respectively. 
Turning to fig. 9, it is necessary to state that A has been chosen as the starting-point 
for the integration of the curve of loads L L, and that the stations up to which the in- 
tegrations have been carried, in order to determine the ordinates of the curve of shearing- 
forces V V, are those (drawn midway between the dotted ordinates of the curve of loads) 
corresponding to the imaginary planes of division, 20 feet apart, with which we started. 
The ordinate at any section, say, R 3 , R 3 , is determined as follows. The area of the loops 
of L L lying below A B and between A and R 3 R 3 is found, as is also the area of the loop 
lying above A B between the same limits ; and the difference between the areas, in this 
case in favour of the downward forces, is set off on a certain scale of tons per inch (marked 
on the diagram) on the ordinate R 3 R 3 . Through points thus determined the curve V V 
is then drawn. Had the point B been taken as the starting place, or origin, of the inte- 
grations, we should obviously have obtained an equal value for the ordinate R 3 R 3 , only 
its direction would have been opposite to that we have found; and generally we may 
