  We present maps and spectra of the HCN(1-0) and HCO$^+$(1-0) lines in the
extreme outer Galaxy, at galactocentric radii between 14 and 22 kpc, with the
13.7 meter Delingha telescope. The 9 molecular clouds were selected from a
CO/$^{13}$CO survey of the outer quadrants. The goal is to better understand
the structure of molecular clouds in these poorly studied subsolar metallicity
regions and the relation with star formation. The lines are all narrow, less
than 2km/s at half power, enabling detection of the HCN hyperfine structure in
the stronger sources and allowing us to observationally test hyperfine
collision rates. The hyperfine line ratios show that the HCN emission is
optically thin with column densities estimated at N(HCN)~$3x10^{12}$\scm. The
HCO$^+$ emission is approximately twice as strong as the HCN (taken as the sum
of all components), in contrast with the inner Galaxy and nearby galaxies where
they are similarly strong. For an abundance ratio $\chi_{HCN}/\chi_{HCO^+} =
3$, this requires a relatively low density solution for the dense gas, with
n(H2) $\sim 10^3 - 10^4$\ccm. The $^{12}$CO/$^{13}$CO line ratios are similar
to solar neighborhood values, roughly 7.5, despite the low $^{13}$CO abundance
expected at such large radii. The HCO$^+$/CO and HCO$^+$/$^{13}$CO integrated
intensity ratios are also standard at about 1/35 and 1/5 respectively. HCN is
weak compared to the CO emission, with HCN/CO $\sim 1/70$ even after summing
all hyperfine components. At the parsec scales observed here, the correlation
between star formation, as traced by 24~$\mu$m emission as is standard in
extragalactic work, and dense gas via the HCN or HCO$^+$ emission, is poor,
perhaps due to the lack of dynamic range. We find that the lowest dense gas
fractions are in the sources at high galactic latitude (b>2, h>300pc above the
plane), possibly due to lower pressure.
