\documentstyle{preprint}
\begin{document}
\title{SPIRAL DENSITY WAVE THEORY, COROTATION RESONANCE,\\
~\\
AND THE VELOCITY FIELD OF NGC~4321}
\author{Blaise Canzian\/\thanks{Current address: Universities Space Research
Association, U.S.\ Naval Observatory, P.O.\ Box 1149, Flagstaff, AZ 86002 (email:
blaise@nofs.navy.mil)} 
and Ronald J.\ Allen\/\thanks{Email: rjallen@stsci.edu}\\
\\
Space Telescope Science Institute\/\thanks{Operated by the Association of 
Universities for Research in Astronomy, Inc., under contract with the National
Aeronautics and Space Administration.}\\
\\
3700 San Martin Drive\\
\\
Baltimore, MD  21218}

\pub{The Astrophysical Journal}
\recacc{}{29 October 1996}

\maketitle

\begin{abstract}
We extend the exposition of a new kinematic method (exploiting geometric 
phase) for determining the corotation resonance radius of a grand design
spiral.  We present an explicit formulation in terms of first-order
linear spiral density wave theory for fitting to the velocity field of a
grand design spiral galaxy.  We test the new formulation on the velocity
field of the ionized gas in the grand design spiral NGC~4321 in the
Virgo cluster using Fabry-Perot H$\alpha$ data.  The kinematic method as
currently implemented is specifically useful for determining an upper
bound for the corotation resonance radius.  We illustrate the kinematic
evidence for the corotation in the disk of NGC~4321.
\end{abstract}
\end{document}