SEPTEMBER II, 1902] 
NATURE 
481 
The publication, however, of the epoch-making treatise of 
Maxwell on Electricity and Magnetism entirely changed the 
aspect of the question, and in particular threw a new light on 
MacCullagh’s assumption. FitzGerald, in 1879, pointed out 
that the Potential Energy, which in Maxwell’s theory was 
equivalent to the electrostatic energy, really was a quadratic 
function of three variables, which answered to the components 
of MacCullagh’s molecular rotation, and accordingly led to the 
same differential equations of the motion as MacCullagh had 
deduced. 
Subsequently Larmor, in his remarkable investigation of 
the Dynamical Theory of the Electric and Luminiferous Ether, 
deliberately reconsiders MacCullagh’s position, finds in fact in 
his equations the starting point of his own theory. H2 points 
out the real significance of MacCullagh’s function V; that it 
corresponds to a stress-strain system, but one of a very novel 
type ; one in which the stresses depend entirely on the rotational 
displacements of the molecules, and are otherwise absolutely 
unaffected by the ordinary deformation-strains. He further 
shows that the difficulty under which MacCallagh’s theory 
Jaboured, that it did not provide for the rotatory equilibrium of 
the element, could be removed if we allowed ourselves to assume 
the existence of a hidden torque acting on each element. 
As I understand the advocates of this theory, they maintain 
that an important step has been made, even though in the 
present state of our knowledge we may not be able to account 
for the existence of this hidden torque. They pint out, how- 
ever, that such a torque is at least not inconceivable, whether 
its explanation be sought in concealed kinetic phenomena, as in 
Lord Kelvin’s material gyrostatically constituted medium, or in 
quasi-magnetic forces supposed to reside in the ethereal 
elements. 
Should this theory of a rotationally elastic ether obtain final 
acceptance, it will of course be a matter of conzratulation to 
MacCullagh’s countrymen to find that his labours, in this, 
perhaps the most important field of his researches, have not 
been tnrown away ; that they represent no mere play of elegant 
mathematical analysis, but a real step in the progress of 
physical science. 
A few years after MacCullagh, two other well-known men, 
whose names for half a century were associated with the 
Mathematical School in Dublin, were elected Fellows—Andrew 
Searle Hart, afterwards Sir Andrew Hart, and Charles Graves, 
subsequently Bishop of Limerick. They won their Fellowships 
in two successive years, and both lived to an advanced age. 
Hart had a great reputation as a geometer. His examination 
papers were specially noted for the number of original problems 
they contained. As specimens of his work we may instance the 
following. Extending Feuerbach’s theorem for the nine-point 
circle, Hart showed that the circles which touch three given 
circles can be distributed into sets of four all touched by the 
same circle. He also showed that Poncelet’s beautiful porism 
for coaxal circles in plano held for the surface of an ellipsoid, if 
we replace the rectilineal polygons by geodetic polygons and 
the coaxal circles by lines of curvature. 
Graves became Professor of Mathematics on MacCullagh’s 
resigning the Chair in 1843. He was largely influenced by the 
writings of Chasles, of whose two memoirs on Cones and 
Spherical Conics he published a translation. In this were 
incorporated valuable original additions of his own, amongst 
others the remarkable theorem that if two spherical ellipses are 
confocal the sum of the tangents drawn to the inner from any 
point of the outer exceeds the intercepted arc between the 
points of contact by a constant length, a theorem which of 
course includes the corresponding proposition for confocals in 
plano. Graves was one of the first to apply the method of the 
eparation of Symbols to Differential Equations, and gave an 
elegant demonstration by this method of Jacobi’s celebrated test 
for distinguishing between maxima and. minima in the Calculus 
of Variations. 
On the death of MacCullagh it was determined to strengthen 
the Natural Philosophy department by the establishment of a 
second Professorship in that subject, and Jellett, one of the 
ablest of MacCullagh’s pupils, was appointed to the new Chair. 
His first published work was his ‘* Calculus of Variations,” 
which at the time it was written constituted the only systematic 
English treatise on the subject. It is marked by that peculiar 
acuteness and power of fastening oa essential points, whether 
for criticism or exposition, which was th2 author’s leading 
characteristic. Apart from the excellent account he gives of the 
NO. 1715, VOL. 66] 
researches of Continental mathematicians, I would notice 
especially his most interesting chapters on the conditions of 
integrability and many valuable geometrical theorems on sur- 
faces hence resulting. In discussing his more properly original 
work we may arrange it in three divisions: Ist, his papers on 
Elasticity ; 2nd, that on the properties of Inextensible Surfaces ; 
3rd, those on the application of polarised light to the new sub- 
ject of Chemical Equilibrium. 
In taking up the problem of an elastic medium and the propa- 
gation of waves in such medium, Jellett follows the example of 
MacCullagh, who had made this subject one of special interest 
to the Dublin school. In these memoirs he draws attention toa 
remarkable difference in the mode of regarding the molecular 
constitution of the medium, a difference corresponding to what 
is now known as the distinction between the Rari-constant and 
Multi-constant theories. We may, Jellett points out, regard 
the action between two molecules as only conditioned by the 
relative position of these molecules, or as dependent also on the 
position of the neighbouring molecules. The first is termed by 
Jellett the hypothesis of independent action, and this he shows 
to lie at the basis of Cauchy’s theory, whereas the theory of 
Green, the English elastician, essentially involves the second 
hypothesis which Jellett calls ‘‘ modified action.” He established 
in the same papers the important theorem that if a Work 
function exists the three directions of vibration, corresponding 
to a plane-wave, are rectangular, and wice versa. 
In his memoir on Inextensible Surfaces various interesting 
questions are discussed. He proves that in the case of a syn- 
clastic surface if a closed curve on the surface be held fixed, the 
entire surface will be immovable; that on the other hand on an 
anticlastic surface it is possible to draw a curve which may be 
held fixed without involving the immovability of the surface, the 
conditions being that the curve will be that formed by the 
successive elements of the inflectional tangents. The mathe- 
matical theory of such curves had been already studied, but 
Jellett seems to have been the first to signalise their importance 
in the theory of deformation, and, on account of the property 
referred to, he proposed to call them Curves of Flexure. It is 
interesting to remark that Maxwell was attracted by the same 
subject of Inextensible Surfaces, and in one of his earliest papers 
confirms by an entirely different method several of Jellett’s 
conclusions. 
At the close of Jellett’s paper a remarkable proposition is laid 
down, apparently for the first time, that a closed oval surface 
cannot be inextensibly deformed ; in other words, that if such a 
surface be perfectly inextensible it is also perfectly rigid. I 
think we must admit that the proof of this striking theorem 
offered by Jellett is by no means satisfactory. Subsequent 
attempts by others to establish this proposition can hardly be 
said to be more successful. But the fact that it can be rigorously 
proved true for a sphere or more generally for any ellipsoid seems 
to indicate that we have here to do with a real and important 
theorem, but one which needs, as is so often the case, to have 
the limits of its application more clearly defined. 
Many experimental physicists will know Jellett best by the 
beautiful and delicate instrument he invented, ‘‘ The Double- 
plane Analyser,” an instrument which he devised in order to 
secure the more exact determination of the rotation of the plane 
of polarisation than could be obtained by the polariscopes 
hitherto in use. Jellett was actuated here by the consideration 
that he saw in this phenomenon of the rotation of the plane of 
polarisation a means of attacking the interesting problem of 
chemical equilibrium. Chemical equilibrium he defines thus: 
‘*Two or more substances may be said to be in chemical 
equilibrium, if they can be brought into chemical presence of 
each other (as in a solution) without the formation of any new 
compound or change in the amount of any of the former com- 
pounds which have thus been brought together.” In a mixed 
solution of sundry bases and acids where all the possible salts 
are soluble, what are the proportions in which the acids are 
distributed amongst the bases? Such was Jellett’s question, 
and in answering it he arrives by a remarkable train of quasi- 
mathematical reasoning at certain laws governing this distribu- 
tion, and proceeds to establish the truth of these laws by 
observation with his new polariscope. 
He also discusses in the same papers two alternative theories 
which we can hold of chemical combination, the ‘ statical”’ and 
the ‘‘dynamical,” and shows from the consideration of the 
number of equations which subsist that the ‘‘ dynamical theory ” 
is alone admissible. 
