230 
MR. J. LARMOR A DYNAMICAL THEORY OF 
The reasoning given in Part IL, § 13, was insufficient, because the correlation between 
the two systems was not there pushed to their individual molecules. 
Consideration of a Limitation of the Rotational Scheme. 
17. In the preceding sections the equations of the aethereal field have been 
expressed (as they were in Part IL) without reference to the dynamical hypothesis 
of a rotational aether which suggested their present form. Reverting now to that 
hypothesis, let us examine whether a limitation of the kind that was unavoidable in 
the material model of § 3, may not also be involved in the general scheme of a 
rotational aether. In the first place, it is natural to take the elastic rotation in the 
medium as very small, so that its translatory velocity which is connected therewith 
is also very small, though the velocities of the strain-centres which flit across it, and 
represent the matter, may have any vadues; this is in agreement with the conclusion 
derived from optical experiments that the aether is practically stagnant. But there 
is one conceivable class of cases in which the changes of position of the elements of 
the medium go on accumulating, that namely of a steady magnetic field kept up sa}" 
by a current of electrons constrained to flow permanently round a circuit. On 
account of the smallness of the velocity of the aether, the corrections to the 
djuiamical equations which arise from the velocity of convection of the elastic strain 
may always bo left out of account, being utterly insignificant in ordinary electro¬ 
dynamics, and actually beyond the limits of experiment in optics : yet in a magnetic 
field continuing steady for an unlimited time the elements of volume of the fether 
will ultimately have wandered far from their original positions, and a difficulty 
presents itself."^ To cover such a case, the definition of the elastic rotation of the 
medium must be made more precise. For the motion of a perfect fluid, which is 
diflerontially irrotational at each instant, will yet result after a time in finite 
rotations of its elements of volume; for example it is known that if a rigid 
ellipsoidal shell be filled with perfect fluid, and be set rotating about a fixed axis, 
* I am indebted to Lord Rayleigh for drawing my attention to this point, as one requiring further 
consideration. 
[A steady magnetic field involves a cyclical motion of the tether; thus in a very great time 
even a very small velocity will produce large changes of po.sition. It is true that any motion of 
electrons whatever will produce change of strain, and therefore movement in the cether, but that move¬ 
ment will be very slight, and will not be cumulative except in the one case of permanent cyclical motion 
which represents absolutely permanent magnets. If there were no other way out of the difficulty 
described in the text, it might be turned by simj^ly asserting that absolutely permanent magnets do 
not exist. 
The nature of the constraints which may be necessary to prevent the nucleus of an electron from 
ever becoming sub-divided is a different question, and wholly outside the scope of the present theory, 
which simply takes these nuclei to exist as it finds them without inquiring in detail into their 
structure.] 
