1185 
St 
since, for 1- c/n Ry positive of order unity, 
loya, = 0 (Log €) 
(53) 
Oo 
o 
ze” SES nt 
R 
= 
We thus see that for large € and B a, then up to the time of maximum velocity the assumptions 
that nt'/8 a and ct'/R, are small are both justified, especially tne former since nt’ is itself 
small up to this time. 
Corresponding to the approximation (50) for (16) we have a similar approximation for 
equation (20) given by 
R ~ BY ot? Ba 
= r+ 
minVEtapl vey s0 + Los (54) 
2 pp ct enR, 
whence 
mIntV) =) ga nts i ies + c 
2 a € enk, enk, 
-Pvc 22 2 
=e nee {0 (Z) + 0 (ge) } (55) 
Now at the time of maximum velocity we have from (51) ana (52) 
AV a ee 
Sa te 0 (z) 
‘ ' 
c (Alea oem y ee oanat 
en, enk, 
1 ct" 
0 (2) x 0 ge) 
Loy € 1 1 
: + 0 (2) + 0 (5) 
nv ' 1 
Sp viet ~ @tre~ @ (56) 
‘ 
which is correct to small fractional errors of order 7 ’ z , Fa . 
) 
Thus under the conditions @ a larje andi - wR positive of order unity, when € is large 
the maximum velocity communicated to the plate is given approximately by the same expression (27) 
as for € not large. 
BD Validity of solution when plate leaves the wat 
The solution has been obtained on the assumption implicit in the boundary condition (5) 
that the plate is in contact with the water. If the plate leaves the water at any point P then 
the solution will be valid at P up to this time provided no effect has by then reached P of earlier 
separation of plate and water at other points P' of the plate. Since the effect of such earlier 
Separation will travel from P' to P with velocity C the solution will be valid provided the 
separation of plate and water travels over the plate with velocity greater than C. 
NOW seese 
