The specific definition of retarded coordinates is a matter of convenience.
Often the retardation is based on
hypothetical rays moving straight down
with velocity .The definition of these coordinates has utility
even in problems in which the earth velocity varies laterally,
say *v*(*x*,*z*), even though there
may be no rays going exactly straight down.
In principle, any coordinate system may be used to describe any circumstance,
but the utility of the retarded coordinate system generally declines
as the family of rays defining it departs more and more from the actual rays.

Despite the simple case at hand
it is worthwhile to be somewhat formal and precise.
Define the retarded coordinate
system (*t*' ,*x*' ,*z*' ) in terms of ordinary
Cartesian coordinates (*t*,*x*,*z*) by the set of equations

(27) | ||

(28) | ||

(29) |

10/31/1997