46 
MR. A. MALLOCK ON EXPERIMENTS ON FLUID VISCOSITY. 
of the instability being marked by the appearance of small dimples and elevations 
which, when the high velocities were reached, covered the whole surface. 
The experiments of series (3), where the width of the annulus was about half-an- 
inch, give a nearer approach to the true value of the coefficient of viscosity than 
series (1), where the annulus had a width of an inch. In some former experiments 
of mine, described in £ Proc. Roy. Soc.,’ December, 1888, where the annulus was 
little more than §• inch wide, the approximation to the true value was very close."' 
The effect of temperature in altering the critical velocity was not as marked as I 
had expected it to be. 
From Professor Osborne Reynolds’ experiments I had supposed that the critical 
velocity would be proportional directly to the viscosity, but Diagrams 6 and 7 show 
that in this form of exj)eriment, at any rate, this is not the case. At a temperature 
of 50° C. the viscosity of water is only about a third of what it is at 0° C., but, at the 
former temperature, instability begins at a speed only 11 or 12 per cent, less than at 
the latter. 
If we deduce the coefficient of fluid friction from the experiments at the higher 
speeds of series (1) and (3) it will be found that the formula which best represents 
the curves is F = av~' n , and that coefficient of friction is ‘058 lb. per square foot of 
area at 10 feet per second instead of - 23 lb. (Froude) and '22 lb. (Unwin). And 
both Mr. Froude and Professor Unwin found the frictional resistance increase as the 
l'8 th power of the velocity for smooth metal surfaces such as those used in my 
experiments. 
It would seem from this that, even when the water in the annulus is in the com¬ 
pletely eddying condition, the character of the motion cannot be the same as that in 
the neighbourhood of Mr. Froude’s plane or Professor Unwin’s disc. 
The case is quite different, however, in the experiments of series (2). Here the 
motion seems essentially unstable at all speeds, and from such experiments no value 
of the coefficient of viscosity can be deduced, but the coefficient of friction which they 
* Since tlie above was written it lias been pointed out to me, by Sir Gr. Stokes, that the formula 
whicli I used for computing the coefficient of viscosity, from these experiments and also from those of 
the present series, was incorrect. 
The values of /i have, therefore, been recomputed for all the experiments (including those of 1888) 
from the formula 
F r? - rP 
/( “ A;V 2r e 
where r e and r; are the radii of the external and internal cylinders respectively, F the tangential force 
acting on the surface of the internal cylinder, A; the area of the surface of the internal cylinder in 
contact with the water, and V f the velocity of the surface of the external cylinder. 
The results of the 1888 experiments are indicated by the spots p, q, r, near the curve c, on diagram 
(10), but they are too close an appi'oximation to the true value of /< to allow of a separate curve being 
drawn through them. 
