  Acoustic rays can be described by null geodesics of a pseudo-Riemannian
manifold. This allows for the immediate generalization of paraxial ray systems
via geodesic deviation. The technique has appeared in the literature for the
past decade and has been used by the author in the development of dynamic ray
trace codes. The techniques involved are powerful but abstract and frequently
unfamiliar in the field of acoustics. This brief paper derives the complete
paraxial system for the case of acoustics in the presence of an inhomogeneous
isotopic time independent media described by a sound speed profile c(x,y,z).
The derivation is performed for three distinct conformal representations of the
acoustic metric.
