THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
231 
then after a certain interval of time the parts of the fluid will have returned to the 
original conflguration with respecr to the shell, so that the fluid will have been 
rotated bodily in space just like a solid, although its motion at each instant has been 
difierentially irrotational. In fact when the change of position of the element of 
volume is finite we can no longer analyze it definitely into rotations and pure strains, 
in such wise that the order of their application shall be indifferent; thus we obtain 
no longer in that way an analytical specification of the sethereal elastic rotation, and 
a more precise formulation must be made. The rough material model of § 3 indicates 
the necessary modification : in that model a differential pure strain of the element 
of volume does not tend to rotate the sub-element which is elastically effective ; 
thus the efficient elastic rotation is the vector sum of the series of differential 
rotations which the element of the tether has experienced in its previous history. 
This is therefore the more precise definition of the total rotation, proportional to 
(/ h), from which the electrostatic forcive is derived as in Part II., § 18 : it makes 
the rotation equal to the curl of the linear displacement when these quantities are 
both small so that their squares and products can be neglected, but not after the 
long-continued cumulative effect of a permanent magnetic field has come in. In 
that case, however, the small irrotational velocity, say for the moment [p, q, r), 
which constitutes the magnetic field, will contribute to (f, g, h) onlv by shifting by 
convection the element of the medium along with its rotation, while the rotation so 
transferred will be continually re-adjusting itself by elastic action into the new 
equilibrium configuration : the relation between elastic rotation and magnetic force 
will then be of the type dfidt = dyjdy - d/Bjdz - {p)dldx -f qdjdy + rdjdz)f, where 
{p, q, r) is equal to (a, /3, y) multiplied by a very small scalar factor. Unless the 
velocity (y), q, r) is uniform, djdt (^dfjdx -f- dgjdy -p dlijdz) will not be exactly null ; 
so that the movement of the aether by the steady magnetic field will lead to a 
development of electric charge, extremely slow and gradual, throughout the volume 
concerned. On the other hand the combination of permanent electric and magnetic 
fields which is the origin of such a creation of electricity must be confined to a 
limited region, beyond which the aether is in equilibrium ; therefore the electrifica¬ 
tion thus developed consists of compensating amounts of positive and negative 
signs. These diffuse charges, of the second order of small quantities, will sub¬ 
sequently by their mutual attractions drift together again and neutralize each other, 
by moving as strain-forms across the aether without sensibly interfering with the 
motion of the medium itself (§ 6). Thus a steady magnetic field of unlimited 
duiation would not theoretically get interlocked with a concomitant electrostatic 
field, but would relieve itself by very slowly developing a very minute diffuse electri¬ 
fication which will simultaneously gradually fade away by its own natural actions, 
so that no sensible effect would ever be accumulated. The rotational aether scheme 
therefore would not break down in this limiting case, the consequence of long- 
continued cumulation being obviated by a process which is at each instant so 
