Marcu 7, 1884.] 
VORTEX RINGS. 
A treatise on the motion of vortex rings. An essay to 
which the Adams prize was adjudged in 1882, in 
the University of Cambridge. By J. J. THomson, 
Trinity college, Cambridge. London, 1883. 19 
+124p. 8°. 
Tuose cases of fluid motion in which no rota- 
tional motion is present, are, as is well known, 
readily amenable to analysis. Helmholtz * first 
called attention to the nature of the analysis 
by which rotational motion must be treated. 
This memoir was followed by Sir William Thom- 
son’s suggestive paper on vortex atoms,” and 
finally by his important mathematical memoir 
on vortex motion.? The very great mathemati- 
cal difficulties of the theory have operated to 
prevent almost entirely farther progress in the 
investigation of this otherwise alluring subject. 
To the best of our remembrance this essay is 
the first systematic attempt, since 1869, to 
enlarge our knowledge of the theory of vortex 
rings. How great the difficulties to be van- 
quished are, may be imagined from the ap- 
pearance of the pages of the essay before us, 
which bristle with periodic series and compli- 
cated expansions. 
The scope of the essay may perhaps be best 
apprehended fromits opening paragraphs, which 
we quote : — 
““The theory that the properties of matter may be 
explained by supposing matter to be collections of 
vortex lines in a perfect fiuid filling the universe has 
made the subject of vortex motion at present the 
most interesting and important branch of hydrody- 
namics. This theory, which was first started by Sir 
William Thomson as a consequence of the results 
obtained by Helmholtz in his epoch-making paper, 
Ueber integrale der hydrodynamischen gleichnungen 
welche den wirbelbewegungen entsprechen, has a priori 
yery strong recommendations in its favor; for the 
vortex ring obviously possesses many of the qualities 
essential to a molecule that has to be the basis of a 
dynamical theory of gases. It is indestructible and 
indivisible; the strength of the vortex ring, and the 
yolume of liquid composing it, remain forever un- 
altered; and if any vortex ring be knotted, or if two 
yortex rings be linked together in any way, they will 
retain forever the same kind of be-knottedness or 
linking. These properties seem to furnish us with 
good materials for explaining the permanent proper- 
ties of the molecule. Again: the vortex ring, when 
free from the influence of other vortices, moves 
rapidly forward in a straight line. It can possess, in 
virtue of its motion of translation, kinetic energy; it 
can also vibrate about its circular form, and in this 
Way possess internal energy: and thus it affords us 
promising materials for explaining the phenomena of 
heat and radiation. 
* This theory cannot be said to explain what matter 
is, since it postulates the existence of a fiuid possess- 
ing inertia; but it proposes to explain, by means of the 
1 Crelle’s journ., 1858, and translated by Tait, Phil. mag., 
1867 
2 Phil. mag., 1867. ° Edin. trans., 1869. 
SCIENCE. 
289 
laws of hydrodynamics, all the properties of bodies 
as consequences of the motion of this fluid. It is 
thus, evidently, of a very much more fundamental 
character than any theory hitherto started: it does 
not, for example, like the ordinary kinetic theory of 
gases, assume that the atoms attract each other with 
a force which varies as that power of the distance 
which is most convenient; nor can it hope to explain 
any property of bodies by giving the same property 
to the atom. Since this theory is the only one that 
attempts to give any account of the mechanism of 
the intermolecular-forces, it enables us to form much 
the clearest mental representation of what goes on 
when one atom influences another. Though the 
theory is not sufficiently developed for us to say 
whether or not it succeeds in explaining all the prop- 
erties of bodies, yet, since it gives to vortex motion 
the greater part of the interest it possesses, I shall 
not scruple to examine the consequences, according 
to this theory, of any results I may obtain. 
‘““The present essay is divided into four parts: 
the first part, which is a necessary preliminary to the 
others, treats of some general propositions in vortex 
motion, and considers at some length the theory of 
the single vortex ring; the second part treats of the 
mutual action of two vortex rings which never ap- 
proach closer than a large multiple of the diameter 
of either; it also treats of the effect of a solid body 
immersed in the fluid on a vortex ring passing near it; 
the third part treats of knotted and linked vortices; 
and the fourth part contains a sketch of a vortex 
theory of chemical combination, and the application 
of the results obtained in the preceding parts to the 
vortex-ring theory of gases. 
‘It will be seen that the work is almost entirely 
kinematical: we start with the fact that the vortex 
ring always consists of the same particles of fluid 
(the proof of which, however, requires dynamical 
considerations), and we find that the rest of the work 
is kinematical. This is further evidence that the 
vortex theory of matter is of a much more fun- 
damental character than the ordinary solid particle 
theory; since the mutual action of two vortex rings 
can be found by kinematical principles, whilst the 
‘clash of atoms’ in the ordinary theory introduces 
to forces which themselves demand a theory to 
explain them.”’ 
The great difficulty which inheres in the vor- 
tex theory of chemical combination is to suffi- 
ciently account for what takes place at the 
instant of chemical union by showing that 
vortex atoms can, without supposing other 
forces than those due to their motion, have 
any such attractions as are known to exist, 
and especially to account for the enormous 
quantities of heat liberated in many cases of 
chemical decomposition. 
The author, however, postpones all extended 
application of the vortex theory of atoms to 
the dynamical theory of gases for consideration 
in a future paper, but, among other important 
conclusions, states that the phenomena attend- 
ing the diffusion of gases through a porous 
diaphragm which separates portions of gas at 
different temperatures will probably furnish a 
crucial experimental test between the vortex 
atom theory and the ordinary kinetic theory. 
