SEPTEMBER 7, 1899] 
IEAM Fee 
~ 
447 
As long as all the particles move in the straight portion of 
the channel, their behaviour is easy enough to understand. But 
as the channel widens out, it is clear that this model does not 
give us the proper distribution. In the model the wider por- 
tions are not filled up, as they would be with the natural fluid ; 
for it must be clearly understood that the stream-lines do not 
flow on as the balls along these wires, passing through a mass 
of dead water, but redistribute themselves so that every particle 
of water takes part in the flow. Perhaps you may think that if 
these wires were removed, and the wooden balls allowed to find 
their own positions, they would group themselves as with an 
actual liquid. This is not the case; and, for reasons that you 
will see presently, no model of this kind would give us the real 
conditions of actual flow. By means of a model, however, 
we may be able to understand why it is so absolutely essential 
we should realise the correct nature of the grouping which 
occurs. 
First look at the two diagrams (Figs. 4 and 5), which you 
will see represent channels of similar form to the experimental 
one. The same number of particles enter and leave in each 
under apparently the same conditions, so that the idea may 
naturally arise in your minds, that if the particles ultimately 
flow with the same speed whatever their grouping in the larger 
portion of the channel, it cannot much matter in what particular 
kind of formation they actually pass through that wider portion. 
To understand that is really very important. 
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You will see 
that we have two lines of particles which we may consider 
stream-lines, those on the left coloured white, and those on the 
right coloured red. The first and last are now exactly 18 inches 
apart, there being eighteen balls of 1 inch diameter in the row. 
If I move the red ones upward, I cause them to enter a wider 
portion of the channel, where they will have to arrange them- 
model (Fig. 6) specially made for the purpose. 
selves so as to be three abreast (Fig. 7). It is quite clear to 
you, that as I do this their speed in the wider portion of the 
channel is only one-third of that in the narrow portion, as you 
will see from the relative positions of the marked particles. 
Now, directly the first particle entered the wider channel, it 
commenced to move at a reduced speed, with the result that the 
particles immediately behind it must have run up against it, 
exactly in the same way that you have often heard the trucks in 
a goods train run in succession upon the ones in front, when 
the speed of the engine is reduced; and you will doubtless 
have noticed that it was not necessary for the engine actually 
to stop in order that this might take place. Moreover, the 
force of the impact depended largely upon the suddenness with 
which the speed of those in front was reduced. Applying this 
illustration to the model, you will see that the impact of these 
particles in the wider portion would necessarily involve a 
greater pressure in that part. Turning next to the white balls, 
I imitate, by means of the left-hand portion, the flow which 
will occur in a channel six times as large as the original one, 
and you now see (Fig. 7) that as the particles have placed them- 
selves six abreast, and the first and last row are 3 inches apart 
NO. 1558, VOL. 60] 
instead of 18 inches, the speed in the wider portion of the 
channel must have been one-sixth of that in the narrow portion, 
Evidently, therefore, the velocity of the particles has been 
reduced more rapidly than in the previous case, and the 
pressure must consequently be correspondingly greater. 
We may now take it as perfectly clear and evident, that the 
pressure is greater in the wider portion and less in the narrower 
portion of the channel. Turning now to the two diagrams, we 
see that the pressure is in each case greater in every row of 
particles as in the wider portions of the channel, but that 
instead of being suddenly increased, as in the model, it is 
gradually increased. The width of the coloured bands, that is, 
rows of particles, or width apart of stream-lines, is a measure 
of the increased pressure. Thus you will now regard the width 
of the bands, or what is the same thing, the distance apart of 
the stream-lines, as a direct indication of pressure, and the 
narrowness or closeness of the stream-lines as a direct indication 
of velocity. 
Next notice the great difference between the two diagrams. 
In one diagram (Fig. 4) the change of width is uniform across 
the entire section. In diagram (Fig. 5), however, this is not 
the case. In the narrowest portion of the channel in each dia- 
gram there are seven colour bands of little balls each contain- 
ing three abreast, but we find that in one diagram (Fig. 4) they 
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Let us consider a | the other diagram (Fig. 5) 
are equally spaced in the wider part six abreast throughout. In 
the outer row is spaced eight abreast, 
| the second row rather more than six, and the inner rows rather 
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Fic. 6. Fic. 7 
more than four abreast, and the middle row less than four 
abreast, making in all forty-two in a row, as in the previous 
case. One diagram (Fig. 5) therefore will represent an entirely 
different condition to the state represented by the other diagram 
(Fig. 4), the pressure in the wide part of the latter varying from 
4 maximum at the outside to a minimum in the middle, while the 
corresponding velocity is greatest in the middle and least at the 
outside or borders. 
Now, when we know the pressure at every point of a liquid, 
and also the direction in which the particles are moving, 
together with their velocity at every point, we really know all 
about its motion, and you will see how important the question 
of grouping is, and that, in fact, it really constitutes the whole 
point of my lecture to-night. How then shall we ascertain 
which of the two groupings (Fig. 4 or 5) is correct, or whether 
possibly some grouping totally different from either does not 
represent the real conditions cf flow ? 
Now, the model does not help us very far, because there 
seems to be no means of making the grouping follow any regular 
law which might agree with fluid motion. In whatever way 
we improve such a model, we can scarcely hope to imitate by 
merely mechanical means the motion of an actual liquid, for 
reasons which I will now try to explain. 
In the first place, apart from the particles having no dis- 
tinguishing characteristics, either when the liquid is opaque or 
transparent, they are so small and their number is so great as to 
be almost beyond our powers of comprehension, Let me try, 
by means of a simple illustration, to give some idea of their 
number, as arrived at by perfectly well recognised methods of 
physical computation. Lord Kelvin has used the illustration 
that, supposing a drop of water were magnified to the size of the 
