14 
and ¢ is said to vanish at infinity, the solution is indeter- 
minate by an infinitesimal amount. Consequently the total 
momentum or flow may be indeterminate to a finite amount. 
On the other hand, the total kinetic energy of the fluid 
motion, involving a summation of the square of the velocity, 
is only indeterminate to an infinitesimal extent. 
In conclusion, it appears that the problem is indeter- 
minate unless the infinite boundary of fluid can be defined 
as the limit of some particular form, and further in that 
case the conditions satisfied at the boundary must also be 
considered. At the best the question of what happens in an 
infinite fluid after an infinite time leads to unreal difficulties; 
the above discussion may serve to show in what way these 
arise when we attempt to force to this extent ordinary solu- 
tions which give consistent results when treated in a 
legitimate manner. 
93 
