164 PROFESSOR O. REYNOLDS ON INCOMPRESSIBLE VISCOUS FLUIDS. 
is of constant value, there is dynamical similarity under geometrically similar circum- 
stances. 
The equation (79) shows that, 
ap dp 
5 dp . 
Vv —_— + =I , iy 
when OP ap de greater than K, 
wv must be finite, and such that the last term in the numerator limits the rate of 
transformation, and thus prevents further increase of wv’. 
The last term in the numerator of equation (79) is of the order and degree 
p Lia*/y? as compared with Lite* 
Z 
a (,H’) the first term in the numerator. 
It is thus easy to see how the limit comes in. It is also seen from equation (79) 
that, above the critical value, the law of resistance is very complex and difficult of 
5 i 
the order and degree of a 
interpretation, except in so far as showing that the resistance varies as a power of the 
velocity higher than the first. 
