936 
MR. 0. REYNOLDS ON THE MOTION OF WATER, AND OF 
moving through a tube, present themselves mostly in one or other of two simple forms. 
The resistance is generally proportional to the square of the velocity, and when this is 
not the case it takes a simpler form and is proportional to the velocity. 
Again, the internal motion of water assumes one or other of two broadly distinguish 
able forms—either the elements of the fluid follow one another along lines of motion 
which lead in the most direct manner to their destination, or they eddy about in sinuous 
paths the most indirect possible. 
The transparency or the uniform opacity of most fluids renders it impossible to see 
the internal motion, so that, broadly distinct as are the two classes (direct and sinuous) 
of motion, their existence would not have been perceived were it not that the surface 
of water, where otherwise undisturbed, indicates the nature of the motion beneath. 
A clear surface of moving water has two appearances, the one like that of plate glass, 
in which objects are reflected without distortion, the other like that of sheet glass, in 
which the reflected objects appear crumpled up and grimacing. These two characters 
of surface correspond to the two characters of motion. This may be shown by 
adding a few streaks of highly coloured water to the clear moving water. Then 
although the coloured streaks may at first be irregular, they will, if there are no 
eddies, soon be drawn out into even colour bands ; whereas if there are eddies they 
will be curled and whirled about in the manner so familiar with smoke. 
3. Connexion bet ween the leading features of fluid motion .—These leading features 
of fluid motion are well known and are supposed to be more or less connected, but it 
does not appear that hitherto any very determined efforts have been made to trace a 
definite connexion between them, or to trace the characteristics of the circumstances 
under which they are generally presented. Certain circumstances have been definitely 
associated with the particular laws of force. Resistance, as the square of the velocity, 
is associated with motion in tubes of more than capillary dimensions, and with the 
motion of bodies through the water at more than insensibly small velocities, while 
resistance as the velocity is associated with capillary tubes and small velocities. 
The equations of hydrodynamics, although they are applicable to direct motion, i.e., 
without eddies, and show that then the resistance is as the velocity, have hitherto 
thrown no light on the circumstances on which such motion depends. And although 
of late years these equations have been applied to the theory of the eddy, they have 
not been in the least applied to the motion of water which is a mass of eddies, i.e., in 
sinuous motion, nor have they yielded a clue to the cause of resistance varying as the 
square of the velocity. Thus, while as applied to waves and the motion of water in 
capillary tubes the theoretical results agree with the experimental, the theory of 
hydrodynamics has so far failed to afford the slightest hint why it should explain 
these phenomena, and signally fail to explain the law of resistance encountered by 
large bodies moving at sensibly high velocities through water, or that of water in 
sensibly large pipes. 
This accidental fitness of the theory to explain certain phenomena while entirely 
