JUNE 4, 1914] 
NATURE 365 
expansion takes place in four or five steps, corre- 
sponding to the drills available. It had at first been 
intended to use a smooth curve, but preliminary trials 
showed that this was unnecessary, and the expansion 
by steps has the advantage of bringing before the 
mind the dragging action of the jets upon the thin 
layers of fluid between them and the walls. The 
three pressures concerned are indicated on mano- 
meter tubes as shown, and the two differences of 
level representing head and suction can be taken off 
Fic. 1. 
with compasses and referred to a millimetre scale. 
In starting an observation the water is drawn up in 
the discharge vessel, so far as may be required, with 
the aid of an air-pump. The rubber cork at the top 
of the discharge vessel necessary for this purpose is 
not shown. 
As the head falls during the flow of the water, the 
ratio of head to suction increases. For most of the 
observations I contented myself with recording the 
head for which the ratio of head to suction was exactly 
2:1, as indicated by _ propor- ; 
tional compasses. Thus on 
January 23, when the tempera- 
ture of the water was 9° C., 
the 2:1 ratio occurred on four 
trials “atifxag,; 130, 123,,' 526, 
mean 125 mm. head. The tem- 
perature was then raised with 
precaution by pouring in warm 
water with passages backwards 
and forwards. The occurrence 
of the 2:1 ratio was now much 
retarded, the mean head being 
only 35 mm., corresponding to a 
mean temperature of 37° C. The ratio of head to 
suction is thus dependent upon the head or velocity, 
but when the velocity is altered the original ratio 
may be recovered if at the same time we make a 
suitable alteration of viscosity. 
And the required alteration of viscosity is about 
what might have been expected. From Landolt’s 
tables I find that for 9° C. the viscosity of water is 
0:01368, while for 37° C. it is 0.00704. The ratio of 
viscosities is accordingly 1-943. The ratio of heads is 
125:35- The ratio of velocities is the square-root 
NGie2327, VOL. 93) 
| 
| for a time. 
ee Mudd: 
of this, or 1-890, in sufficiently good agreement with 
the ratio of viscosities. 
In some other trials the ratio of velocities exceeded 
a little the ratio of viscosities. It is not pretended 
that the method would be an accurate one for the 
comparison of viscosities. The change in the ratio 
of head to suction is rather slow, and the measure- 
ment is usually somewhat prejudiced by unsteadiness 
in the suction manometer. Possibly better results 
would be obtained in more elaborate observations by 
several persons, the head and_ suc- 
tion being recorded separately and 
referred to a time scale so as to 
facilitate interpolation. But as they 
stand the results suffice for my 
purpose, showing directly and con- 
clusively the influence of viscosity 
as compensating a change in _ the 
velocity. 
In conclusion, I must touch briefly 
upon a part of the subject where theory 
is still at fault, and I will limit myself 
to the simplest case of all—the 
uniform shearing motion of a viscous 
fluid between two parallel walls, 
one of which is at _ rest, while 
the other moves. tangentially with 
uniform velocity. It is easy to prove 
that a uniform shearing motion of the 
fluid satisfies the dynamical equations, 
but the question remains: Is this motion 
stable? Does a small departure from 
the simple motion tend of itself to die 
out? In the case where the viscosity is 
relatively great, observation suggests an 
affirmative answer; and O. Reynolds, 
whose illness and comparatively early 
death were so great a _ loss to 
science, was able to deduce the 
same conclusion from theory. Reynolds’s method 
has been improved, more especially by Prof. 
Orr of Dublin. The simple motion is thoroughly 
stable if the viscosity exceed a certain specified value 
relative to the velocity of the moving plane and the 
distance between the planes; while if the viscosity 
is less than this, it is possible to propose a kind of 
departure from the original motion which will increase 
It is on this side of the question that 
there is a deficiency. When the viscosity is very 
ZI 
Us 
Fic. 2. 
small, observation appears to show that the simple 
_ motion is unstable, and we ought to be able to derive 
this result from theory. But even if we omit viscosity 
altogether, it does not appear possible to prove in- 
stability a priori, at least so long as we regard the 
walls as mathematically plane. We must confess that 
at the present we are unable to give a satisfactory 
account of skin-friction, in order to overcome which 
millions of horse-power are expended in our ships. 
Even in the older subjects there are plenty of problems 
left ! 
