326 G. H. KNIBBS. 
turbulent agitation, and discussed the manner in which the problem 
of flow might be attacked.* Gauckler also, in 1867, used a 
monomial expression, and recognised that the law of flow for very 
small slopes required a separate formula.1 Reynolds has therefore 
been anticipated five or six times. 
8. General conception of the turbulent régime.—Tf, the rectilinear 
régime being established, say in a glass pipe, its stability be over- 
come by increase of pressure, or temperature, or by unsteadiness, 
a condition supervenes of which the first indication is a waviness 
of the stream lines, as shewn by the motion of coloured threads 
of liquid in Reynolds’ experiments. This is followed by the 
development of vortices in great numbers, so that when the 
turbulent or vortex condition is well established, the liquid may 
be said to constitute a tangle of vortices, the tangle having & 
motion of translation along the pipe. In the rectilinear régime, 
the evidence shews very conclusively that there can be no velocity 
at the boundary,’ the rugosity of which does not in such a case 
affect the flow, since there is no slipping of the water past it, such 
as might be supposed to call into action some species of friction— 
nor is there any disturbance therefrom across the pipe to interfere 
with the continuity of the motion of translation parallel to its axis. 
In rectilinear flow, if we consider the particles of water distributed 
at any instant of time, across a right section of the pipe, then ab 
any later instant the same particles will lie on the surface of @ 
paraboloid, the axis of which is that of the pipe, and whose base 
is the right section considered. , 
In the turbulent régime it is extremely probable if not certain, 
that the water actually in contact with the boundary also has n0 
velocity. Again considering the particles at any moment in 4 
right section, these will move in all directions owing to the 
agitations, but they will on the whole be subjected toa motion of 
translation parallel to the axis of the pipe. If then we imagine 
1 Etudes théoriques et pratiques sur photo caige et les mouvement des 
eaux.—Comptes rendus, t. 64, pp. 818 — 822, 
2 See Journ. Roy. Soc. N.S.W., Vol. stan, * 6, ‘pp. 89 - 93. 
