place until it is proved to be in definite contradiction, not removable by suitable modification, with another portion of it.
Application to moving Material Media: approximation up to first order
106. We now recall the equations of the free aether, with a view to changing from axes (x, y, z) at rest in the aether to axes (x', y', z') moving with translatory velocity v parallel to the axis of x; so as thereby to be in a position to examine how phenomena are altered when the observer and his apparatus are in uniform motion through the stationary aether. These equations are
${\begin{array}{ccc}4\pi {\frac {df}{dt}}={\frac {dc}{dy}}{\frac {db}{dz}}&&(4\pi c^{2})^{1}{\frac {da}{dt}}={\frac {dh}{dy}}{\frac {dg}{dz}}\\\\4\pi {\frac {dg}{dt}}={\frac {da}{dz}}{\frac {dc}{dx}}&&(4\pi c^{2})^{1}{\frac {db}{dt}}={\frac {df}{dz}}{\frac {dh}{dx}}\\\\4\pi {\frac {dh}{dt}}={\frac {db}{dx}}{\frac {da}{dy}}&&(4\pi c^{2})^{1}{\frac {dh}{dt}}={\frac {dg}{dx}}{\frac {df}{dy}}.\end{array}}$
When they are referred to the axes (x', y', z') in uniform motion, so that $(x',\ y',\ z')=(xvt,\ y,\ z),\ t'=t$, then $d/dx,\ d/dy,\ d/dz$ become $d/dx',\ d/dy',\ d/dz'$, but d/dt becomes $d/dt'vd/dx'$: thus
${\begin{array}{ccc}4\pi {\frac {df}{dt'}}={\frac {dc'}{dy'}}{\frac {db'}{dz'}}&&(4\pi c^{2})^{1}{\frac {da}{dt'}}={\frac {dh'}{dy'}}{\frac {dg'}{dz'}}\\\\4\pi {\frac {dg}{dt'}}={\frac {da'}{dz'}}{\frac {dc'}{dx'}}&&(4\pi c^{2})^{1}{\frac {db}{dt'}}={\frac {df'}{dz'}}{\frac {dh'}{dx'}}\\\\4\pi {\frac {dh}{dt'}}={\frac {db'}{dx'}}{\frac {da'}{dy'}}&&(4\pi c^{2})^{1}{\frac {dh}{dt'}}={\frac {dg'}{dx'}}{\frac {df'}{dy'}}.\end{array}}$
where

$(a',\ b',\ c')=(a,\ b+4\pi vh,\ c4\pi vg)$
$(f',\ g',\ h')=\left(f,\ g{\frac {v}{4\pi c^{2}}}c,\ h+{\frac {v}{4\pi c^{2}}}b\right).$

We can complete the elimination of (f, g, h) and (a, b, c) so