448 
NATUKE 
[SEPTEMBER 7, 1899 
earth, the ultimate particles would appear to us between the 
size of cricket-balls and foot-balls. I venture to put the same 
fact in another way, that may perhaps strike you more forcibly. 
This tumbler contains half a pint of water. I now close the top. 
Suppose that, by means ofa fine hole, I allow one and a half 
billion particles to fow out per second—that is to say, an exodus 
equal to about one thousand times the population of the world in 
each second,—the time required to empty the glass would be 
between (for of course we can only give certain limits) seven 
million and forty-seven million years. 
In the next place, we have the particles interfering with each 
other’s movements by what we call ‘‘ viscosity.” 
Of course, the general idea of what is meant by a ‘‘ viscous” 
fluid is familiar to everybody, as that quality which treacle and 
tar possess in a markéd degree, glycerine toa less extent, water 
to a less extent than glycerine, and alcohol and spirits least of 
all. In liquids, the property of viscosity resembles a certain 
positive ‘* stickiness ” of the particles to themselves and to other 
bodies ; and would be well represented in our model by coating 
over the various balls with some viscous material, or by the 
clinging together, which might take place by the individuals of 
a crowd, as contrasted with the absence of this in the case of no 
viscosity as represented by the evolutions of a body of soldiers. 
It may be accounted for, to a certain extent, by supposing the 
particles to possess an irregular shape, or to constantly move 
across each other’s paths, causing groups of particles to be 
whirled round together. 
Whatever the real nature of viscosity is, it results in producing 
in water the eddying motion which would be perfectly impos- 
sible if viscosity were absent, and which makes the problem 
of the motion of an imperfect liquid so difficult and perplexing. 
Now, all scientific advance in discovering the laws of nature 
has been made by first simplifying the problem and reducing it 
to certain ideal conditions, and this is what mathematicians 
have done in studying the motion of a liquid. 
We have already seen what almost countless millions of 
particles must exist in a very small space, and it does require a 
much greater stretch of the imagination to consider their number 
altogether without limit. If we then assume that a liquid has 
no viscosity, and that it is incompressible, and that the number 
of particles is infinite, we arrive at a state of things which would 
be represented in the case of the model or the diagram on the 
wall, when the little globes were perfectly smooth, perfectly 
round and perfectly hard, all of them in contact with each 
other, and with an unlimited number occupying the smallest 
part of one of the coloured or clear bands. This agrees with 
the mathematical conception of a perfect liquid, although the 
mathematician has in his mind the idea of something of the nature 
of a jelly consisting of such small particles, rather than of the 
separate particles themselves. The solution of the problem of 
the grouping of the little particles, upon which so much de- 
pends, and which may have at first seemed so simple a matter, 
really represents, though as yet applied to only a few simple 
cases, one of the most remarkable instances of the power of 
higher mathematics, and one of the greatest achievements of 
mathematical genius. 
You will be as glad as I am that it is not my business to-night 
to explain the mathematical processes by which the behaviour of 
a perfect liquid has been to a certain extent investigated. You 
will also understand why such models as we could actually 
make, or any analogy with the things with which we are 
familiar, would not help us very much in obtaining a mental 
picture of the behaviour of a perfect liquid. If, for instance, we 
try to make use of the idea of drilled soldiers, and move the 
lines with that object in view, we see that instead of the or- 
dinary methods of drill, the middle rank soon gains on the 
others, and enters again the parallel portion of the channel in a 
very different relative position to the opposite lines, although 
the stream-lines would all have the same actual velocity when 
once again in the parallel portion. Since, then, we cannot 
use models or any simple analogy with familiar things, or follow— 
at any rate this evening—the mathematical methods of dealing 
with the problem, what way of understanding the subject is left 
to us? 
If we take two sheets of glass, and bring them nearly close 
together, leaving only a space the thickness of a thin card or 
piece of paper, and then by suitable means cause liquid to flow 
under pressure between them, the very property of viscosity, 
which, as before noted, is the cause of the eddying motion in 
large bodies of water, in the present case greatly limits the 
NO. 1558, VOL. 60] 
freedom of motion of the fluid between the two sheets of glass, 
and thus prevents, not only eddying or whirling motion, but also 
counteracts the effect of inertia. Every particle is then com- 
pelled by the pressure behind and around it to move onwards 
without whirling motion, following the path which corresponds 
exactly with the stream-lines in a perfect liquid. 
If we now, by a suitable means, allow distinguishing bands of 
coloured liquid to take part in the general flow, we are able to 
imitate exactly the conditions we are seeking to understand. 
(Prof. Ilele-Shaw here gave demonstrations of the stream-lines 
in liquids flowing under the conditions of a gradually enlarging 
and contracting channel. He proved that the condition of flow 
corresponded closely with that shown in Fig. 5 and xof with 
that given in Fig. 4. The method of the experiments has 
already been described in NaTuRE (vol. lviii. p. 34), though by 
using glycerine instead of water much more perfect results were 
obtained than in those then described. ] 
But at this stage you may reasonably inquire how it is that 
we are able to state, with so much certainty, that the artificial 
conditions of flow with a viscous liquid are really giving us the 
stream-line motion of a perfect one ; and this brings me to the 
results which mathematicians have obtained. 
The view now shown represents a body of circular cross- 
section, past which a fluid of infinite extent is moving, and the 
lines are plotted from mathematical investigation and represents 
the flow of particles. This particular case gives us the means 
Ric. 8. 
of most elaborate comparison ; although we cannot employ a 
fluid of infinite extent, we can prepare the border of the channe} 
to correspond with any one of the particular stream-lines, and 
measure the exact positions of the lines inside. 
By means of a second lantern, the real flow of a viscous 
liquid for this cdse is shown upon the second screen, and you 
will see that it agrees with the calculated flow round a similar 
obstacle of a perfect liquid. The diagram shown on the wall is 
the actual figure employed for comparison, and upon which the 
experimental case was projected. By this means, it was proved 
that the two were in absolute agreement. If we start the im- 
pulses, as before, in a row, we at once see how the middle 
particles lag behind the outer ones, as indicated by the width of 
the bands, showing that it is not necessarily the side stream- 
lines that move more slowly. It may be more interesting to you 
to see, in addition to the foregoing case—in which for conveni- 
ence, and as quite sufficient for measurement only, a semi-cylinder 
was employed—the case of a complete cylinder (Fig. 8). In 
this case two different colours are used in alternate bands, and 
these bands are sent in, not steadily, but impulsively, in order to 
illustrate what I have just pointed out. You will see how the 
greater width of the colour bands before and behind the 
cylinder indicates an increase of pressure in those regions. This 
in a ship-shape form accounts for the standing bow and stern 
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