Page:Aether and Matter, 1900.djvu/209

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CHAPTER XI
MOVING MATERIAL SYSTEM: Approximation carried to the second order

110. The results above obtained have been derived from the correlation developed in § 106, up to the first order of the small quantity v/c, between the equations for aethereal vectors here represented by (f', g', h') and (a', b', c') referred to the axes (x', y', z') at rest in the aether and a time t", and those for related aethereal vectors represented by (f, g, h) and (a, b, c) referred to axes (x', y', z') in uniform translatory motion and a time t'. But we can proceed further, and by aid of a more complete transformation institute a correspondence which will be correct to the second order. Writing as before t" for , the exact equations for (f, g, h) and (a, b, c) referred to the moving axes (x', y', z') and time t' are, as above shown, equivalent to

Now write

for

for or