464. F. W. Boggs and N. Tokita 
We can solve Eq. (5.1) for e;/id, giving us 
1 
Fo SooiGiuri bs yhicaniion doth ME sinlandtih GR AG) wort 
a,H ey id = (F-G) - iH’ 
© a5 = i 
al 
VEE TAG ® 
ga EKO for large C (5.3) 
F-G 1 1 
GL oe eee ties hy vag Gees ten 
The family of curves given in Fig. 2 can be transformed graphically by a succession of 
projective transformations to give the family of curves given in Fig. 3. This is the appro- 
priate form to use for Eq. (5.3). It should be noted that there is one member of this family 
corresponding to C equals 0, which is a boundary for all members of the family. The value 
of C for which the family of curves passes through the origin corresponds to a minimum 
value of C compatible with complete stability for a rigid flat plate. The study of this en- 
velope is in fact a convenient way of visualizing the stability problem for a rigid wall as 
well as for a nonrigid one and leads to essentially the same results in the former case as 
the procedure employed by Schlichting. 
Let us now proceed to a consideration of the general effect that e, will have on the 
stability of the flow. e, will be represented by a family of curves of the two variables 
25 BS) 5 | 
ae U 
~ 
~ 4 
~ 
~ 
~ 
~ 
= > 
Lig FNS iy 
: ? Wat ak A 
29 COMPLIANCE OF 0°: 
PLATE SURFACE ‘A 
CSA 
0: 
-5 “ee 
-15 
ZA 
Fig. 3. Family of contours in the compliance, obtained by 
transformation from Fig. 2 
