426 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OF 
say that, by starting from B instead of A, the same curves would be obtained, only the 
loops which now lie above the axis A B would lie below it, and vice versa. This would 
not be of the least consequence, however, since any ordinate of the curve Y V simply 
shows the amount of the shearing-force at that station ; and the question of direction 
is immaterial, as the same effect is produced whether the part before the station moves 
upward or downward relatively to that abaft it. 
There are one or two features of interest in the curve V V, Plate XVII. fig. 9, to which 
brief reference may be made before passing on. Its ordinates have continually increasing 
negative values between A and the foremost water-borne section E 1 , while beyond that 
section they gradually decrease (on account of the fact that the curve of loads has 
crossed the axis A B, and has part of its area above as well as part below that line) 
until at the station a a! they pass through a zero value, the area of the part of the curve 
of loads below the axis being there equal to the area of the part above the axis. The 
section a a' therefore divides the ship in such a manner as to render each of the parts 
before and abaft it separately water-borne, and I shall in my future remarks term such 
sections “ sections of water-borne division” *. At the sections b and c c' there are two other 
zero values of the shearing-force; each of these is also a section of water-borne division, 
and in passing through them the shearing-force changes sign. At the extremities there 
is, of course, no shearing-force. The water-borne section B 1 has been shown to be a 
station of maximum shearing, and all the other points where the curve of loads crosses 
the axis (R 2 , R 3 , E 4 ) are also positions where the curve Y V has maximum ordinates. 
If the curves of weight and buoyancy previously laid down in Plate XVI. fig. 3 were 
minutely accurate, the curves of loads and of shearing-forces in Plate XVII. fig. 9 would 
also be accurate ; but as this is not the case, it becomes necessary to examine how great 
an error is introduced into the curve V V by the errors existing in the curves of weight 
and buoyancy, and consequently in the curve of loads. We should naturally look for the 
maximum error in that part of a ship where weights which are really concentrated have 
been spread out over a considerable space in the construction of the curve of weights ; 
and the ‘ Bellcrophon,' in wake of the armoured bulk-heads, affords, as we have seen, a 
very exceptional and extreme illustration of the kind. This has been made use of in 
order to determine what may he fairly assumed to represent the limiting value of the 
error introduced into the curves of shearing-force. For this purpose the corrected curve 
of weights W' W' in fig. 3 has been employed instead of W W in estimating the shearing- 
forces between the stations e and f, and the result has been graphically represented by 
V V' between the corresponding stations e and yin fig. 9. It has been assumed here 
that the curve V V gives the correct shearing-force at e ; but this is not strictly true, and, 
from the difference between the moments about the station e of the areas included by 
TV W and W' TV ' between the ordinates e and f in fig. 3, it appears that the curve V V 
indicates too small a shearing-force at e. The connective curve V' V ought therefore to 
lie somewhat further out from the axis A B, and should cross the curve V V at some 
* “ Sections of water-borne division ” must not be confused with “ water-borne sections.” 
