Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

388 MR LARMOR, ON THE DYNAMICS OF A SYSTEM OF ELECTRONS OR IONS:
W (~)+ G) + HÎ2)a
Thus To (e+ T (2+y z2) + 2e 1(F f+ G + h) d
+ e Y + 1 f h d.
x y z x y z
ao 3o /o o7o /o yo
As the aether is stagnant, so that the position of the element of volume 8r is
fixed, these new terms will not modify the formula for the aethereal force (P', Q', R')
unless the impressed magnetic field varies with the time: but they will modify the
electric forces acting on the ions by the addition of the term
(7oY-/oZ, aoz - o, /3oX - ao).
THE SYSTEM REFERRED TO A ROTATING FRAME.
It is part of the Action principle, of which the validity is at the foundation of
this analysis, that its formal expression is not affected by constitutive relations involving
the time explicitly, provided they do not involve the velocities of the actual motion.
Let then the system be referred to axes of coordinates rotating with angular velocity
(oex, Wy, wez) measured with reference to their instantaneous positions, these quantities being
either constant or assigned functions of the time. For the velocity, instead of (x, y, z)
there must now be substituted, in the formula for T- W,
(x - ywz + ZOy, Y - zox + Xzo, z - Xwy + yOx),
and for (J, g, h) there must be substituted
(f- goz + hwy, g - hwx -+fOz, h -fcwy + gox),
while (x, y, z) remain unchanged. Referred to these moving axes the kinetic energy,
which was, so far as it involves the ion e1 (d1, 2Y, z), given by
To + T = m, (2 + yl2 + z,2) + el (FF,X, + Gl, + HiZ) +...,
where (F1, G1, H1) is the value of the vector potential at the point (x1, y,, zl), has
now additional terms which on neglecting the square of the angular velocity are
- n,1 n /, il + el xi y, z, + e (3'li l + 9y1'G1 + iSl'H1),
X1 yi Z1 F1 G, Hl
CIOx Cy CWZ X o Oy oz
wherein 'F, - e2- +, r,2 jr12j
- E e2(WOyZ 2- Wy) + _h2 - dr.
r12 rJ 2
The exact dynamical equations referred to moving axes may now be directly
obtained by application of the Action principle.