746 
MR. J. LARMOR ON A OTNAMICAL THEORY OF 
ciuiplc. If the iiiediiiin had ac([iured its rotational elasticity by means of a distribution 
of rotatin^f simple gyrostats, such a kinetic cou 2 :)le would be afforded by it so long as 
rotational motion of the element is going on,"" and Stokes’ criticism would not apply 
in this case. If again we imagine an ordinary elastic medium full of elementary 
magnets witli orientations distributed according to some law or even at random, and 
in internal equilibrium eitlier in its own magnetic field or in the field of some external 
magnetic system, then on rotational distortion a coujjle will be required to hold each 
element in equilibrium ; so that the conjugate tangential tractions on the surface of 
tlie element cannot be equal and o^^i^osite in this case either. The couple de 2 )ends 
here on the absolute rotation of the element of volume, not on its angular velocity as 
in the previous illustration. The j^otential energy of such a medium as this will 
contain rotational terms of MacCullagh’s type, and its condition of internal 
equilibrium will be correctly deduced from an energy-function containing such terms 
by the ap^fiication of the Lagrangian analysis. The origin of the elasticity purely 
rotational of MacCullagh’s medium is we may say unknown ; the first exam 2 )le here 
given shows that it cannot be simjily gyrostatic, though Lord Kelvin has invented a 
complex gyrostatic structure that would produce it ;t and either examjile shows that 
we are not warranted in denying the ^oossibility of such a medium because the 
equilibration of an element of it requires an extraneous couple. The exjDlanation of 
gravitation is still outstanding, and necessitates some structure or property quite 
different from, and lorobably more fundamental than, simple rotational elasticity of the 
retlier and simj)le molar elasticity of material aggregations in it; and this propeity 
may very well be also operative in the manner here required. 
38. It becomes indeed clear when attention is draAvn to the matter, that there is 
something not self-contained and therefore not fundamental, in the notion of even a 
gyrostatic medium and the resistance to absolute motion of rotation which it involves. 
For we want some fixed frame of reference outside the medium itself, with respect to 
which the absolute rotation may be S 2 )ecified ; and we also encounter the question 
w'hy it is that rotatory motion reveals absolute directions in this manner. Another 
asjiect of the question ajjpears when we consider the statical model with its rotational 
])roperty produced by small magnets interspersed throughout it, the medium being 
in internal equilibrium in a magnetic field when unstrained ; the unbalanced tractions 
on the element of volume are here siqiplemented by a coiqjle due, as to sense, to 
magtjetic action at a distance, and it is the energy of this action at a distance which 
constitutes the rotational part of the energy of the model. We may if we ^ilease 
iuqiiiose some analogous action at a distance to exist in the case of the actual letlier, 
the ultimate exjolanation of which will be involved in the explanation of gravitation. 
Now in this magnetic analogue to our medium the equations of equilibrium and motion 
are clearly quite correctly determined by the analytical method of Lagrange. So 
* Cf. ‘ Pi’oc. Loud. Math. Soc.,’ 18U0. 
t Lord KiiLviN (SirW. Tuomson), ‘CoinjatesRcudus,’ Ecpt. 16,1889; ‘ Collectedpaiiers,’ Vol. 111.,p. 467. 
