Vortex Theory for Bodtes Moving tn Water 
= y + G = dF"! a dF'! 
a dig ek hee ito atk fool oe bee 
is the deficiency of Yr due to the deficiency noe defined in 
(7. 30)e:. 
For the sake of simplicity, the true system 6@q of hydro- 
dynamic forces acting on the body is very often replaced by the esti- 
mate 
i = Baling the Bpeorhunghes (7.38). 
The system es - Fo is called the quasi-steady system of 
forces : 
are -“S% 7 Bhs (#82). 
The error involved in the substitution of Gea for Mas! is 
Ra a ee Seal 
Like A 5 ’, represents an inertial effect, but due to the free 
vortex sheet only. 
Let us assume, for example, that a jump of Vx (0) and Q E 
occur in the infinitely small interval (t. - 0, tN and that these two 
velocities remain constant for t > ty. It follows from the third 
equation (7.26). that 
! . = 
bu (Py : to ; O+) 0 for every &— . (7.41). 
Hence the free vortex sheet is not immediately altered. But, 
one has : 
1245 
