436 
ME. E. J. EEED ON THE UNEQUAL DISTEIBUTION OF 
Fig. 13. 
Let. LL in diagram fig. 13 represent the curve of loads of a ship that tends to hog 
simply, and let M M' be the section of water-borne division. Then the area ALL must 
equal the area M' M R, since the weight and buoyancy of each of the parts into which 
M M' divides the ship must be balanced. Suppose W =weight in tons represented by 
each of the areas ALE, M' M 11. We may, as far as bending is concerned, consider 
the weight W to be acting through G, the centre of gravity of the area A L E, at a 
known distance a from the section M M 7 , and the buoyancy W to be acting through G', 
the centre of gravity of M' M 11, at a known distance b from that section. Then we 
shall have, obviously, 
hlogging-moment at MM I =W(«-J), 
Next, take any section mm' on the side of MAT further from A, and let L) tons be the 
buoyancy represented by the area M' m 1 m M. Then if G" be the centre of gravity of the 
area M' m' m M, the force D may be considered to act through G" at a known distance 
y from mm'. Hence if x= distance Aim, we shall have 
Hogging-moment at mm!=W(a-\-x) — W(J-)-A’) — ITy 
= W{a-b)-~Dy 
= Hogging-moment at M.M' — I) y. 
That is to say, the bending-moment at mm! is less than that at A! AT. We shall obtain 
similar results if we suppose the section mm! to be situated on the side of MM' nearer 
to A ; for in that case, to obtain the moment of the buoyancy of the area R m m! about 
mm!, we must add the moment of MAT mm' about that station to the moment of the 
whole area R A1 AT about it. Hence, as m m! is now — x distant from M AT, we shall have 
Hogging-moment = W(a—x) — W(b — x) — Dy 
=W(a-b)-Dy, 
as before. Hence it follows that for this distribution of weight and buoyancy the section 
of water-borne division is also the section of maximum bending-moment. For the more 
complex case, where there is an excess of weight amidships as well as at the extremities, 
it can be shown, by a method similar to the foregoing, that the central section of water- 
borne division is a section of minimum bending-moment, and that in the fore and after 
bodies there will be two sections of maximum bending-moment if there are two sections 
