Ogt lvte 
defined for ly| > pC, UP. 
It is assumed that the shipis ''slender'', which means that 
there is a small parameter, ¢, characterizing the smallness of 
beam /length and draft/length ratios. As e« + 0, the ship shrinks 
down to a line, the part of the x axis between the origin and x=L, 
L being the ship length at the waterline. But ''slenderness"' means 
more than this. It implies also that the size and shape of hull cross- 
sections change gradually in the longitudinal direction. In particular, 
we shall require that 
HEAL EE SE OrrGnxt au ds ay 
Ox 
even in the bow near field. 
The ''bow near field'' is defined as the region in which 
2 Zl] ee 
Sis Bhall?snA meh vi ncow ener walls) 
It is assumed that, in the bow near field, the flow variables are 
changed in order of magnitude when they are differentiated, according 
to the following symbolic rules 
3 -1/2 3 pes 
So 5 a hea = O 
Ox te Or dy Oz eS 
These effects could be brought about formally through the introduction 
of new variables, x= Xell2 ,.y=Yeo) z= Ze, after whichiwe 
would require that differentiation with respect to X, Y, and Z have 
no effect on orders of magnitude. However, the rules will simply be 
carried along implicitly, the introduction of such new variables being 
quite unnecessary. 
Note that there is one exception to the above procedure : We 
have already required that b(x,z) =O(€) and db(x,z)/dx =O(e€). This 
is simply a condition on hull geometry. It has nothing to do with the 
nature (or existence) of a flow around the ship. 
1488 
