940 
MR. 0. REYNOLDS ON THE MOTION OF WATER AND OF 
motion in a way that had not been accomplished and which, considering the general 
intractability of the equations, was not promising. 
The practical method was to test the relation between U, -, and c; this, owing to 
the simple and definite form of the law, seemed to offer, at all events in the first 
place, a far more promising field of research. 
The law of motion in a straight smooth tube offered the simplest possible circum¬ 
stances and the most crucial test. 
The existing experimental knowledge of the resistance of water in tubes, although 
very extensive, was in one important respect incomplete. The previous experiments 
might be divided into two classes : (1) those made under circumstances in which the 
law of resistance was as the square of the velocity, and (2) those made under circum¬ 
stances in which the resistance varied as the velocity. There had not apparently been 
any attempt made to determine the exact circumstances under which the change of law 
took place. 
Again, although it had been definitely pointed out that eddies would explain 
resistance as the square of the velocity, it did not appear that any definite experi¬ 
mental evidence of the existence of eddies in parallel tubes had been obtained, and 
much less was there any evidence as to whether the birth of eddies was simultaneous 
with the change in the law of resistance. 
These open points may be best expressed in the form of queries to which the 
answers anticipated were in the affirmative. 
(1.) What was the exact relation between the diameters of the pipes and the 
velocities of the water at which the law of resistance changed ? 
Was it at a certain value of 
cU ? 
(2.) Did this change depend on the temperature, i.e., the viscosity of water? Was 
it at a certain value of 
(3.) Were there eddies in parallel tubes ? 
(4.) Did steady motion hold up to a critical value and then eddies come in ? 
(5.) Did the eddies come in at a certain value of 
((5.) Did the eddies first make their appearance as small and then increase gradually 
with the velocity, or did they come in suddenly ? 
The bearing of the last query may not be obvious; but, as will appear in the 
sequel, its importance was such that, in spite of satisfactory answers to all the other 
queries, a negative answer to this, in respect of one particular class of motions, led me 
to the reconsideration of the supposed cause of instability. 
