450 
NATURE 
[SEPTEMBER 7, 1899 
filings, or those to which a very small magnetic needle would 
form a tangent.” 
You are all familiar with the way in which iron filings set 
themselves when shaken over the north and south poles of a 
magnet. The magnetic lines are then nearly, but not quite, 
circular curves between the two poles. Now, the mathematics 
of the subject tells us that if the poles could be regarded as 
points, the lines of force between them would be perfect 
circles. 
You are now looking at the colour bands, the edges—or 
indeed any portion—of which represent lines obtained by 
admitting coloured liquid from a series of small holes round a 
central small orifice, which admits clear liquid, and allows them 
to escape through another small orifice (called respectively in 
hydromechanics a source and szz/), and I leave it to you to 
judge how far these curves deviate from the ideal form. 
My assistant is now allowing the colour to flow, first steadily, 
and then in a series of impulses, and the latter gives us the con- 
ception of waves or impulses of magnetic force, though of 
course the magnetic transmission force would be instantaneous. 
Regarded as a liquid, it is here again clear how absolutely the 
truth of our views concerning the slower movement in the 
wider portion is verified by this experiment. 
A last experiment shows the streams admitted, not from a 
source, but from a row of orifices in what corresponds to the 
slowest moving portion of the flow. The result is that the 
colour bands are much narrower, and although the circular 
forms of the curves are, as in the previous experiment, pre- 
served, the lines are so fine at the point of exit, which, as 
before, corresponds to the South Pole, as to really approximate 
to ideal stream-lines. 
The same method enables us to trace the lines of force 
through solid conductors, for, as long as we confine ourselves to 
two dimensions of space we may have flat conductors of any 
shape whatever. But it does something more, for by making 
the film rather deeper in some places than others, more particles 
arrange themselves there, and the lines of flow will naturally 
tend in the direction of the deeper portion. This will give the 
stream-lines identically the same shape as the magnetic or elec- 
trical curves which encounter in their paths a body of less 
resistance, for instance, a para-magnetic body. 
If, on the other hand, at these points the film is made rather 
thinner, less particles will be able to dispose of themselves in 
the shallow portion of the film, and hence the lines of flow will 
be pushed away from this portion, giving us exactly the same 
forms as magnetic lines of force in a magnetic field in proximity 
to a diamagnetic body. 
Here, again, mathematical methods have enabled lines of 
actual flow to be predicted, and you may compare the actual 
flow for the case of a cylindrical para-magnetic body, which was 
worked out some years ago. 
You will doubtless not be inclined to question the practical 
value of stream-lines in the subject which we have just been 
considering, because, unlike the flow of an actual liquid, 
magnetic lines of force can never be themselves seen, and 
because there is no doubt as to the correspondence of the 
directions to the lines of a perfect liquid. It was the conception 
of these lines in the mind of Faraday, and more particularly their 
being cut by a moving wire, that euabled him to realise the 
nature of the subject more clearly than any other man at the 
time, and to do much towards the rapid development of electrical 
science and its practical applications. 
When we come to consider the relation of the study of the 
motion of a perfect liquid with hydromechanics and naval 
architecture, it must be admitted that the matter is a difficult 
one. Probably one of the most perplexing things in engineer- 
ing science is the absence of all apparent connection between 
higher treatises on hydrodynamics and the vast array of works 
on practical hydraulics. The natural connection between the 
treatises of mathematicians and experimental researches of 
engineers would appear to be obvious, but very little, if any, 
such connection exists in reality, and while at every step elec- 
trical applications owe much to the theories which are common 
to electricity and hydromechanics, we look in vain for such 
applications in connection with the actual flow of water. 
Now the reason for this appears to be the immense difference 
between the flow of an actual liquid and that of a perfect one 
owing to the property of viscosity. A comparison of the 
perous experinignis which you have seen to some extent in- 
dicates this. 
NO. 1558, VOL. 60] 
In the first place, let us consider for a moment some of the 
things which would happen if water were a perfect liquid. In 
such a case, a ship would experience a very different amount of 
resistance, because, although waves would be raised, owing to 
the reasons which we have already seen, the chief causes of 
resistance, viz. skin friction and eddying motion, would be 
entirely absent, and of course a submarine boat at a certain 
depth would experience no resistance at all, since the pressures 
fore and aft would be equal. On the other hand, there would 
be no waves raised by the action of the wind, and there would 
be no tidal flow, but to make up for this rivers would flow with 
incredible velocity, since there would be no retarding forces 
owing to the frictionof the banks. But the rivers themselves 
would soon cease to flow because there would be no rainfall 
such as exists at present, since it is due to viscosity that the rain 
is distributed, instead of falling upon the earth in a solid mass 
when condensed. In a word, it may be said that the absence 
of viscosity in water would result in changes which it is 
impossible to realise. 
We may now briefly try to consider the difference between 
practical hydraulics and the mathematical treatment of a perfect 
liquid. 
the flow of water appears to have been made by a Roman 
engineer about 1800 years ago, an effort being made to find the 
law for the flow of water from an orifice. For more than 1500 
years, however, even the simple principle of flow according to 
which the velocity of efflux varies as the square of the head, or 
what is the same thing, the height of surface above the orifice 
varies as the square of the velocity, remained unknown. 
Torricelli, who discovered this, did so as the result of observing 
that a jet of water rose nearly to the height of the surface of the 
body of water from which it issued, and concluded therefore that 
it obeyed the then recently discovered law of all falling bodies. 
Though it was obvious that this law did not exactly hold, it 
was a long time before it was realised that it was the friction or 
viscosity of liquids that caused so marked a deviation from the 
simple theory. Since then problems in practical hydraulics, 
whether in connection with the flow in rivers or pipes, or the 
resistance of ships, have largely consisted in the determination 
of the amount of deviation from the foregoing simple law. 
About one hundred years ago it was discovered that the re- 
sistance of friction varies nearly in accordance with the simple 
law of Torricelli, and also—although for a totally different 
reason—the resistances due to a sudden contraction or enlarge- 
ment of cross-section of channel or to any sudden obstructions 
appear to follow nearly the same law. Now it is extremely 
convenient for reasons which will be understood by students 
of hydraulics to treat all kinds of resistance as following the 
same law, viz. square of velocity which the variation of head 
or height of surface has shown to do. But this is far from 
being exact, and an enormous amount of labour has conse- 
quently been expended in finding for all conceivable conditions 
in actual work tables of coefficients or empirical expressions 
which are required for calculations of various practical ques- 
tions. Such data are continually being accumulated in con- 
nection with the flow of water in rivers and pipes for hydraulic 
motors and naval architecture. This is the practical side of 
the question. 
On the other hand, eminent mathematicians, since the days 
of Newton and the discovery of the method of the calculus, 
have been pursuing the investigation of the behaviour of a 
perfect liquid. The mathematical methods, which I have 
already alluded to as being so wonderful, have, however, 
scarcely been brought to bear with any apparent result upon 
the behaviour of a viscous fluid. Indeed, the mathematician 
has not been really able to adopt the method ot the practical 
investigator, and deal with useful forms of bodies such as 
those of actual ships, or of liquid moving through ordinary 
channels of varying section, even for the case of a perfect liquid, 
but he has had to take those cases, and they are very few 
indeed, that he has been able to discover which fit in with his 
mathematical powers of treatment. 
This brief summary may possibly serve to indicate the nature 
of the difficulties which I have pointed out, and will show you 
the vast field there yet lies open for research in connection with 
the subject of hydromechanics, and the great reception which 
awaits the discovery of a theoretical method of completely deal- 
ing with viscous liquids, instead of having recourse as at present 
principally to empirical formula based on the simple law already 
alluded to, 
The earliest attempts to investigate in a scientific way | 
