```vm - Calculate Virial Mass

EXAMPLES:

vm 1,1,1 ci: vl:6,14	Calculate a virial theorem mass within area 1 using
cone interpolation and velocity limits of 6 to 14
km/s.

ro "/usr/you/vm.out"; do 25 {da cr:;da pl:;vm vl:6,14 dist:470}
Define 25 areas of the current plot, outline those
areas and do the virial mass calculation.  Put the
vm output in "/usr/you/vm.out" for later plotting
with mongo or processing with S, etc.

DESCRIPTION:

Vm calculates the virial mass of an isolated cloud.  It does so by
setting up a grid of spacing sp (arcmin) within the given area and at
each grid point getting an interpolated spectrum from the current
stacks file.  These spectra contribute individually to an intensity
weighted rms velocity and pair wise to the intensity weighted harmonic
method and cautions see appendix II of "Dust and Gas Emission in
Barnard 5" by Langer, Wilson, Goldsmith, and Beichman (ApJ 337:355-381,
1989 Feb. 1).

Vm prints a line of six numbers for each invocation (without v:).  It
prints a header the first time it is invoked in each command line (line
typed from the terminal).  The columns are:  1) the virial mass if the
cloud is at 100 pc and the extra energy terms represented by 'F' are
ignored.  2) The integrated intensity over velocity and area.  3) The
average line intensity integrated over velocity and averaged over
area.  4) The area of in steradians of the 'area' over which the
calculations were done.  5) The Weighted Harmonic mean radius.  6)  The
rms velocity dispersion.

By setting the cloud distance to a known value, you can have the
results scaled to that distance (F could be included by dividing that
distance by F).  By setting scale to the ratio of total mass to
integrated (over velocity and solid angle) line intensity, the second
column can be printed as the mass estimated from the total integrated
line over the area so that a direct comparison can be made.

Stack number limits, center freq limits, and filter width may be given
to pick the the desired data from a stacks file containing extraneous
stacks.

The verbose option gives a line by line report of progress and reports
the number of grid points at which data was available (a possible check