\chapter{Results}
\addcontentsline{lof}{chapter}{\thechapter \hspace{1.5mm} Results}
\addcontentsline{lot}{chapter}{\thechapter \hspace{1.5mm} Results}
\section{Element Distribution Within Each Planetary Nebula}
%\begingroup
%\fontsize{14}{16.8}\selectfont
%\textbf{Chapter 3}\\
%\endgroup
%\begingroup
%\fontsize{13}{15.6}\selectfont
%\\
%\textbf{Results}\\
%\\
%\endgroup
%\textbf{3.1 Element Distribution Within Each Planetary Nebula}
%\\\\
The nebular properties were also calculated using ELSA. To summarize the process, ELSA used the corrected line strengths and a 5-level atom scheme to calculate the abundances while propagating uncertainties of each ionic state. These uncertainties account for the errors from the line strengths as well as the temperature, density and logarithmic extinction. Then, for elements with unseen ionization states, ionization correction factors (ICFs) were calculated by ELSA and then applied to the sum of the observed ionic states to determine elemental abundances. These ICFs are calculated using the prescriptions outlined in Paper~I and \citet{kwi01}. For carbon and nitrogen, Paper~I showed that the direct sum of the observed ionic states was more accurate than an ICF derived total abundance so the total abundances for carbon and nitrogen are the result of summing the observed ionic states.
Table~\ref{ionabun1} lists the ionic abundances for every observed element. The ionic species and wavelength (in \AA ngstroms) of the specific emission line used to derive the ionic abundance are provided in the first column. Each column to the right of column 1 contains the ionic abundances for each region identified in the column head. Additionally, an ICF value is listed below the observed ions for each element (except for carbon and nitrogen, since those ICFs were not used to determine the total abundance). Each region follows in the remaining columns with its associated ionic abundances and ICFs. Finally, at the end of each object column are the inferred values for the [O III] temperature and the C III] or [S II] density of the nebula.
\begin{landscape}
\begin{deluxetable}{cccccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
\tablecaption{Ionic Abundances\tablenotemark{a}, Temperatures and Densities\label{ionabun1}}
\tablehead{\multicolumn{8}{c}{Ionic Abundances\tablenotemark{a}, Temperatures and Densities}
}
\startdata
Ion & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 & IC2165 5 & IC2165 6\\ 
\tableline
He$^{+}$(5876) & 5.67$\pm$1.62(-2) & 5.12$\pm$1.50(-2) & 3.87$\pm$1.60(-2) & 3.95$\pm$1.30(-2) & 2.97$\pm$1.12(-2) & 6.86$\pm$1.07(-2) & 1.00$\pm$0.28(-1)\\
He$^{+2}$(4686) & 5.65$\pm$0.27(-2) & 5.47$\pm$0.33(-2) & 7.52$\pm$0.43(-2) & 6.42$\pm$0.39(-2) & 7.33$\pm$0.36(-2) & 3.58$\pm$0.28(-2) & \nodata\\
icf(He) & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
O$^{+}$(3727) & 7.44$\pm$4.06(-6) & 7.91$\pm$3.45(-6) & 9.00$\pm$2.89(-6) & 5.80$\pm$3.51(-6) & 2.11$\pm$1.72(-6)  & 1.24$\pm$0.33(-5) & 1.48$\pm$0.77(-4)\\
O$^{+}$(7325) & 2.31$\pm$2.24(-5) & 8.55$\pm$4.08(-6) & 3.66$\pm$2.16(-6) & 9.65$\pm$8.20(-6) & 5.91$\pm$7.13(-6) & 2.02$\pm$0.79(-5) & 6.68$\pm$5.23(-5)\\
O$^{+}$(adopt) & 1.14$\pm$0.41(-5) & 8.06$\pm$2.76(-6) & 7.94$\pm$2.54(-6) & 6.90$\pm$3.60(-6) & 3.74$\pm$4.18(-6) & 1.44$\pm$0.33(-5) & 1.29$\pm$0.69(-4)\\ 
O$^{+2}$(5007) & 1.60$\pm$0.21(-4) & 1.71$\pm$0.37(-4) & 1.08$\pm$0.18(-4) & 1.31$\pm$0.32(-4) & 1.11$\pm$0.30(-4) & 2.13$\pm$0.41(-4) & 7.61$\pm$5.41(-4)\\
O$^{+2}$(4959) & 1.55$\pm$0.20(-4) & 1.64$\pm$0.35(-4) & 1.08$\pm$0.18(-4) & 1.32$\pm$0.32(-4) & 1.08$\pm$0.29(-4) & 2.15$\pm$0.42(-4) & 6.60$\pm$4.69(-4)\\
O$^{+2}$(4363) & 1.56$\pm$0.21(-4) & 1.71$\pm$0.37(-4) & 1.08$\pm$0.18(-4) & 1.31$\pm$0.32(-4) & 1.11$\pm$0.30(-4) & 2.13$\pm$0.41(-4) & 7.61$\pm$5.41(-4)\\
O$^{+2}$(adopt) & 1.59$\pm$0.20(-4) & 1.70$\pm$0.37(-4) & 1.08$\pm$0.18(-4) & 1.32$\pm$0.32(-4) & 1.10$\pm$0.30(-4) & 2.13$\pm$0.41(-4) & 7.39$\pm$5.25(-4)\\
icf(O) & 2.00$\pm$0.29 & 2.07$\pm$0.31 & 2.94$\pm$0.80 & 2.63$\pm$0.54 & 3.47$\pm$0.92 & 1.52$\pm$0.09 & 1.00\\
Ar$^{+2}$(7135) & 3.93$\pm$0.67(-7) & 4.59$\pm$1.01(-7) & 2.65$\pm$0.86(-7) & 3.20$\pm$0.75(-7) & 2.61$\pm$0.79(-7) & 5.04$\pm$1.00(-7) & 1.30$\pm$0.72(-6)\\
Ar$^{+2}$(7751) & 6.94$\pm$3.54(-7) & 8.61$\pm$5.81(-7) & 3.40$\pm$4.71(-7) & 5.37$\pm$5.92(-7) & 6.76$\pm$3.36(-7) & 8.87$\pm$3.35(-7) & 1.70$\pm$1.58(-6)\\
Ar$^{+2}$(adopt) & 4.88$\pm$1.52(-7) & 5.91$\pm$2.63(-7) & 2.84$\pm$1.53(-7) & 3.86$\pm$2.39(-7) & 4.27$\pm$1.90(-7) & 6.25$\pm$1.60(-7) & 1.41$\pm$0.84(-6)\\ 
icf(Ar) & 2.07$\pm$0.28 & 2.11$\pm$0.32 & 3.02$\pm$0.81 & 2.68$\pm$0.54 & 3.50$\pm$0.92 & 1.59$\pm$0.09 & 1.18$\pm$0.05\\
C$^{+}$(2325) & 1.00$\pm$0.16(-6) & 7.56$\pm$1.81(-7) & 8.29$\pm$2.71(-7) & 5.24$\pm$2.48(-7) & 4.09$\pm$1.56(-7) & 1.17$\pm$0.26(-6) & 1.08$\pm$0.40(-5)\\
C$^{+2}$(1909) & 2.14$\pm$0.58(-5) & 1.91$\pm$0.84(-4) & 1.77$\pm$0.61(-4) & 1.66$\pm$0.83(-4) & 1.29$\pm$0.71(-4) & 2.63$\pm$1.07(-4) & 5.69$\pm$9.45(-5)\\
C$^{+2}$(1907) & 2.14$\pm$0.58(-5) & 1.90$\pm$0.84(-4) & 1.76$\pm$0.61(-4) & 1.66$\pm$0.83(-4) & 1.29$\pm$0.71(-4) & 2.63$\pm$1.06(-4) & 5.69$\pm$9.44(-5)\\
C$^{+2}$(adopt) & 2.14$\pm$0.58(-5) & 1.90$\pm$0.84(-4) & 1.76$\pm$0.61(-4) & 1.66$\pm$0.83(-4) & 1.29$\pm$0.71(-4) & 2.63$\pm$1.07(-4) & 5.69$\pm$9.44(-4)\\
C$^{+3}$(1549) & 2.00$\pm$0.65(-5) & 1.19$\pm$0.63(-4) & 2.05$\pm$0.83(-4) & 2.17$\pm$1.30(-4) & 1.62$\pm$1.07(-4) & 1.60$\pm$0.78(-4) & 3.21$\pm$6.54(-3)\\
N$^{+}$(6584) & 3.80$\pm$0.28(-5) & 1.91$\pm$0.19(-6) & 1.66$\pm$0.15(-6) & 1.95$\pm$0.22(-6) & 9.01$\pm$1.28(-7) & 4.84$\pm$0.40(-6) & 3.60$\pm$1.25(-5)\\
N$^{+}$(6548) & 3.46$\pm$0.33(-5) & 1.65$\pm$0.28(-6) & 1.26$\pm$0.28(-6) & 1.85$\pm$0.32(-6) & 1.12$\pm$0.28(-6) & 4.75$\pm$0.49(-6) & 3.14$\pm$1.10(-5)\\
N$^{+}$(adopt) & 3.72$\pm$0.28(-5) & 1.85$\pm$0.19(-6) & 1.58$\pm$0.14(-6) & 1.93$\pm$0.22(-6) & 9.67$\pm$1.48(-7) & 4.82$\pm$0.40(-6) & 3.49$\pm$1.21(-5)\\
N$^{+3}$(1485) & 6.80$\pm$2.28(-5) & 4.07$\pm$2.26(-5) & 7.08$\pm$3.00(-5) & 7.38$\pm$4.61(-5) & 5.92$\pm$4.08(-5) & 4.99$\pm$2.56(-5) & 2.09$\pm$4.54(-4)\\
N$^{+4}$(1240) & 4.62$\pm$1.84(-5) & 1.04$\pm$0.75(-5) & 4.81$\pm$2.40(-5) & 7.30$\pm$5.36(-5) & 4.45$\pm$3.60(-5) & 1.18$\pm$0.82(-5) & \nodata\\ 
Ne$^{+2}$(3869) & 2.57$\pm$0.41(-5) & 2.59$\pm$0.65(-6) & 1.77$\pm$0.37(-5) & 1.97$\pm$0.59(-5) & 1.66$\pm$0.54(-5) & 3.75$\pm$0.85(-5) & 1.64$\pm$1.40(-4)\\
Ne$^{+3}$(1602) & 6.59$\pm$2.27(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ne$^{+4}$(1575) & 1.04$\pm$0.37(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
icf(Ne) & 2.09$\pm$0.35 & 2.16$\pm$0.34 & 3.19$\pm$0.88  & 2.74$\pm$0.57 & 3.53$\pm$0.95 & 1.61$\pm$0.10 & 1.20$\pm$0.07\\
Ion & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 & IC2165 5 & IC2165 6\\ 
\tableline
S$^{+}$(6716) & 1.04$\pm$0.62(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(6731) & 1.01$\pm$0.63(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(adopt) & 1.02$\pm$0.62(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+2}$(9069) & \nodata & 7.33$\pm$2.33(-7) & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+2}$(9532) & 8.13$\pm$0.86(-7) & \nodata & 6.25$\pm$0.94(-7) & 7.8$\pm$1.58(-7) & 6.14$\pm$1.41(-7) & 1.18$\pm$0.18(-6) & 1.85$\pm$0.85(-6)\\
icf(S) & 1.97$\pm$0.34 & 1.98$\pm$0.35 & 1.84$\pm$0.26 & 2.26$\pm$0.66 & 4.42$\pm$2.94 & 1.66$\pm$0.14 & 1.22$\pm$0.05\\
%\\
%Ion & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 & IC2165 5 & IC2165 6\\ 
\tableline
\[[O III] T$_{e}$(K) & 13600$\pm$600 & 13900$\pm$1000 & 14300$\pm$800 & 13700$\pm$1100 & 14000$\pm$1300 & 13300$\pm$900 & 9300$\pm$1900\\
\[[S II] N$_{e}$($cm^{-3}$) & 1500$\pm$3800 & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
C III] N$_{e}$($cm^{-3}$) & 7700$\pm$1200 & 6600$\pm$1800 & 14200$\pm$2300 & 5400$\pm$1800 & 6800$\pm$1600 & 4500$\pm$1200 & 10800$\pm$3400\\
\tableline
%\tablebreak
Ion & IC3568 Full & IC3568 1 & IC3568 2 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 \\ 
\tableline
He$^{+}$(5876) & 9.39$\pm$1.36(-2) & 9.79$\pm$2.38(-2) & 8.80$\pm$2.59(-2) & 1.00$\pm$0.74(-1) & 5.13$\pm$0.77(-2) & 7.05$\pm$2.32(-2) & 1.02$\pm$0.08(-1)\\
He$^{+2}$(4686) & 1.49$\pm$1.05(-3) & 2.21$\pm$1.70(-3) & 1.09$\pm$1.17(-3) & \nodata & 7.49$\pm$0.27(-2) & 5.08$\pm$0.22(-2) & \nodata \\
icf(He) & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
O$^{0}$(6300) & \nodata & \nodata & \nodata & \nodata & 1.63$\pm$0.32(-5) & 3.08$\pm$0.77(-5) & 5.04$\pm$3.96(-6)\\
O$^{0}$(6363) & \nodata & \nodata & \nodata & \nodata & 1.32$\pm$0.31(-5) & 2.40$\pm$0.92(-5) & \nodata\\
O$^{0}$(adopt) & \nodata & \nodata & \nodata & \nodata & 1.56$\pm$0.31(-5) & 2.94$\pm$0.74(-5) & \nodata\\
O$^{+}$(3727) & 7.16$\pm$4.15(-6) & 1.05$\pm$0.55(-5) & 4.55$\pm$2.06(-6) & \nodata & 1.93$\pm$0.71(-5) & 4.59$\pm$3.46(-5) & 1.25$\pm$1.49(-6)\\
O$^{+}$(7325) & \nodata & \nodata & \nodata & \nodata & 3.63$\pm$1.36(-5) & 8.94$\pm$5.86(-5) & \nodata\\
O$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 2.25$\pm$0.63(-5) & 5.29$\pm$2.32(-5) & \nodata\\
O$^{+2}$(5007) & 4.02$\pm$1.27(-4) & 3.01$\pm$0.68(-4) & 4.24$\pm$1.76(-4) & 7.67$\pm$7.14 (-4) & 1.53$\pm$0.19(-4) & 1.74$\pm$0.18(-4) & 6.33$\pm$4.15(-5)\\
O$^{+2}$(4959) & 3.58$\pm$1.13(-4) & 2.69$\pm$0.61(-4) & 3.77$\pm$1.57(-4) & 6.56$\pm$6.10 (-4) & 1.49$\pm$0.18(-4) & 1.73$\pm$0.18(-4) & 5.62$\pm$3.69(-5)\\
O$^{+2}$(4363) & 4.02$\pm$1.27(-4) & 3.01$\pm$0.68(-4) & 4.24$\pm$1.76(-4) & 7.67$\pm$7.14 (-4) & 1.50$\pm$0.18(-4) & 1.75$\pm$0.19(-4) & 6.33$\pm$4.15(-5) \\
O$^{+2}$(adopt) & 3.92$\pm$1.24(-4) & 2.94$\pm$0.66(-4) & 4.13$\pm$1.72(-4) & 7.42$\pm$6.91 (-4) & 1.52$\pm$0.18(-4) & 1.74$\pm$0.18(-4) & 6.17$\pm$4.05(-5) \\
icf(O) & 1.02$\pm$0.01 & 1.02$\pm$0.02 & 1.01$\pm$0.01 & 1.00 & 2.46$\pm$0.22 & 1.72$\pm$0.24 & 1.00 \\
Ar$^{+2}$(7135) & 6.79$\pm$2.09(-7) & 5.61$\pm$2.45(-7) & 6.47$\pm$2.79(-7) & 1.29$\pm$1.23(-6) & 7.79$\pm$0.78(-7) & 9.13$\pm$0.87(-7) & 3.50$\pm$1.84(-7)\\
Ar$^{+2}$(7751) & \nodata & \nodata & \nodata & \nodata & 9.24$\pm$1.28(-7) & 7.81$\pm$2.20(-7) & 7.08$\pm$3.82(-7)\\
Ar$^{+2}$(adopt) & \nodata & \nodata & \nodata & \nodata & 8.13$\pm$0.82(-7) & 8.89$\pm$0.87(-7) & 4.71$\pm$2.45(-7)\\
Ar$^{+3}$(4740) & \nodata & \nodata & \nodata & \nodata & 7.05$\pm$1.01(-7) & 1.09$\pm$0.14(-6) & 3.99$\pm$2.92(-7)\\
Ar$^{+4}$(7005) & \nodata & \nodata & \nodata & \nodata & 3.30$\pm$0.66(-7) & 1.49$\pm$1.30(-7) & 5.44$\pm$3.48(-7)\\
Ion & IC3568 Full & IC3568 1 & IC3568 2 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 \\ 
\tableline
icf(Ar) & 1.87 & 1.87 & 1.87 & 1.87 & 2.60$\pm$0.24 & 1.99$\pm$0.32 & 1.02$\pm$0.03 \\
C$^{+}$(2325) & 2.02$\pm$0.85(-7) & 2.6$\pm$3.76(-7) & 1.40$\pm$2.65(-7) & \nodata & 2.04$\pm$0.27(-6) & 2.01$\pm$0.31(-6) & 9.33$\pm$3.44(-7) \\
C$^{+2}$(1909) & 3.49$\pm$2.50(-4) & 1.51$\pm$0.77(-4) & 4.41$\pm$4.19(-4) & 2.00$\pm$4.38 (-3) & 1.60$\pm$0.40(-4) & 1.17$\pm$0.25(-4) & 8.72$\pm$11.30(-5) \\
C$^{+2}$(1907) & 3.49$\pm$2.50(-4) & 1.51$\pm$0.77(-4) & 4.40$\pm$4.19(-4) & 1.99$\pm$4.38 (-3) & 1.60$\pm$0.40(-4) & 1.17$\pm$0.25(-4) & 8.71$\pm$11.30(-5) \\
C$^{+2}$(adopt) & 3.49$\pm$2.50(-4) & 1.51$\pm$0.77(-4) & 4.40$\pm$4.19(-4) & 1.99$\pm$4.38 (-3) & 1.60$\pm$0.40(-4) & 1.17$\pm$0.25(-4) & 8.72$\pm$11.30(-5) \\
C$^{+3}$(1549) & 1.17$\pm$1.04(-4) & 5.17$\pm$3.22(-5) & 1.34$\pm$1.58(-4) & 7.26$\pm$19.60 (-3) & 5.75$\pm$1.72(-4) & 3.47$\pm$0.87(-5) & 5.99$\pm$9.43(-5) \\
N$^{+}$(6584) & \nodata & \nodata & \nodata & \nodata & 6.52$\pm$0.87(-5) & 1.23$\pm$0.24(-4) & 6.60$\pm$3.15(-6) \\
N$^{+}$(6548) & \nodata & \nodata & \nodata & \nodata & 6.22$\pm$0.83(-5) & 1.17$\pm$0.23(-4) & 6.44$\pm$3.07(-6)\\
N$^{+}$(5755) & \nodata & \nodata & \nodata & \nodata & 6.52$\pm$0.87(-5) & 1.23$\pm$0.24(-4) & 6.6$\pm$3.15(-6) \\
N$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 6.45$\pm$0.86(-5) & 1.22$\pm$0.23(-4) & 6.56$\pm$3.13(-6) \\
N$^{+2}$(1751) & \nodata & \nodata & \nodata & \nodata & 1.32$\pm$0.36(-4) & 9.19$\pm$2.67(-5) & 6.96$\pm$9.87(-5) \\
N$^{+3}$(1485) & \nodata & \nodata & \nodata & \nodata & 2.06$\pm$0.64(-4) & 1.12$\pm$0.29(-4) & 1.56$\pm$2.54(-4) \\
N$^{+4}$(1240) & \nodata & \nodata & \nodata & \nodata & 5.95$\pm$2.17(-5) & 1.59$\pm$0.51(-5) & 5.67$\pm$10.80(-5) \\
%Ion & IC3568 Full & IC3568 1 & IC3568 2 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 \\ 
%\tableline
Ne$^{+2}$(3869) & 7.89$\pm$2.95(-5) & 5.65$\pm$1.48(-5) & 8.85$\pm$4.35(-5) & 1.25$\pm$1.43(-4) & 2.54$\pm$0.36(-5) & 3.26$\pm$0.40(-5) & 6.12$\pm$4.75(-6) \\
Ne$^{+3}$(1602) & \nodata & \nodata & \nodata & \nodata & 4.71$\pm$1.55(-5) & 2.85$\pm$1.51(-5) & 2.83$\pm$4.36(-5) \\
Ne$^{+4}$(1575) & \nodata & \nodata & \nodata & \nodata & 1.07$\pm$0.32(-5) & \nodata & 1.23$\pm$1.18(-5) \\ 
icf(Ne) & 1.03$\pm$0.02 & 1.06$\pm$0.03 & 1.02$\pm$0.02 & 1.00 & 2.77$\pm$0.33 & 2.17$\pm$0.61 & 1.02$\pm$0.03 \\
S$^{+}$(6716) & \nodata & \nodata & \nodata & \nodata & 2.11$\pm$0.76(-7) & 2.89$\pm$2.06(-7) & \nodata \\ 
S$^{+}$(6731) & \nodata & \nodata & \nodata & \nodata & 2.07$\pm$0.74(-7) & 2.80$\pm$2.07(-7) & \nodata \\ 
S$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 2.08$\pm$0.75(-7) & 2.84$\pm$2.12(-7) & \nodata \\ 
S$^{+2}$(9069) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 3.25$\pm$2.04(-7) \\
S$^{+2}$(9532) & \nodata & \nodata & \nodata & \nodata & 7.69$\pm$0.73(-7) & 7.70$\pm$0.88(-7) & \nodata \\ 
icf(S) & \nodata & \nodata & \nodata & \nodata & 1.56$\pm$0.12 & 1.28$\pm$0.11 & 2.05$\pm$1.06 \\
\tableline 
\[[O III] T$_{e}$(K) & 10100$\pm$900 & 11000$\pm$800 & 9800$\pm$1200 & 8800$\pm$2300 & 14400$\pm$600 & 14400$\pm$500 & 15700$\pm$3800\\
\[[S II] N$_{e}$($cm^{-3}$) & \nodata & \nodata & \nodata & \nodata & 1700$\pm$1700 & 1500$\pm$3700 & \nodata \\ 
C III] N$_{e}$($cm^{-3}$) & 5300$\pm$3100 & 7000$\pm$6500 & 2600$\pm$3200 & 6800$\pm$10400 & 7100$\pm$500 & 100$\pm$1300 & 12600$\pm$2200\\ 
\tableline
%\tablebreak
Ion & NGC2440 3 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 & NGC3242 5\\
\tableline
He$^{+}$(5876) & 4.39$\pm$0.87(-2) & 6.25$\pm$0.45(-2) & 0.106$\pm$0.026 & 8.10$\pm$1.56(-2) & 5.99$\pm$2.27(-2) & 6.61$\pm$2.55(-2) & 5.15$\pm$1.60(-2)\\
He$^{+2}$(4686) & 8.03$\pm$0.35(-2) & 4.40$\pm$0.07(-2) & 1.73$\pm$0.36(-2) & 3.82$\pm$0.28(-2) & 5.16$\pm$0.23(-2) & 3.40$\pm$0.37(-2) & 4.43$\pm$0.30(-2)\\
Ion & NGC2440 3 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 & NGC3242 5\\
\tableline
icf(He)  & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
O$^{0}$(6300) & 1.14$\pm$0.29(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
%Ion & NGC2440 3 & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full\\
%\tableline
O$^{0}$(6363) & 1.12$\pm$0.34(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
O$^{0}$(adopt) & 1.14$\pm$0.29(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
O$^{+}$(3727) & 1.77$\pm$1.21(-5) & 2.23$\pm$0.90(-6) & \nodata & \nodata & \nodata & \nodata & \nodata\\
O$^{+}$(7325) & 1.88$\pm$0.44(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
O$^{+}$(adopt) & 1.80$\pm$0.95(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
O$^{+2}$(5007) & 1.44$\pm$0.15(-4) & 2.58$\pm$0.21(-4) & 3.17$\pm$1.21(-4) & 2.67$\pm$0.27(-4) & 2.04$\pm$0.40(-4) & 2.48$\pm$0.53(-4) & 2.67$\pm$0.74(-4)\\
O$^{+2}$(4959) & 1.46$\pm$0.15(-4) & 2.59$\pm$0.21(-4) & 3.18$\pm$1.22(-4) & 2.68$\pm$0.27(-4) & 2.05$\pm$0.40(-4) & 2.48$\pm$0.54(-4) & 2.67$\pm$0.74(-4)\\
O$^{+2}$(4363) & 1.43$\pm$0.16(-4) & 2.58$\pm$0.21(-4) & 3.17$\pm$1.21(-4) & 2.67$\pm$0.27(-4) & 2.04$\pm$0.40(-4) & 2.48$\pm$0.53(-4) & 2.67$\pm$0.74(-4)\\
O$^{+2}$(adopt) & 1.45$\pm$0.15(-4) & 2.59$\pm$0.21(-4) & 3.17$\pm$1.21(-4) & 2.67$\pm$0.27(-4) & 2.04$\pm$0.40(-4) & 2.48$\pm$0.53(-4) & 2.67$\pm$0.74(-4)\\
icf(O) & 2.83$\pm$0.37 & 1.70$\pm$0.05 & 1.16$\pm$0.05 & 1.47$\pm$0.10 & 1.86$\pm$0.33 & 1.52$\pm$0.2 & 1.86$\pm$0.27\\
Ar$^{+2}$(7135)  & 7.54$\pm$0.67(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+2}$(7751) & 7.95$\pm$2.10(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+2}$(adopt) & 7.63$\pm$0.79(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+3}$(4740) & 5.57$\pm$1.67(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+4}$(7005) & 3.10$\pm$0.64(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
icf(Ar) & 2.94$\pm$0.40 & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
C$^{+}$(2325) & 2.64$\pm$0.34(-6) & 3.72$\pm$0.28(-7)  & 3.20$\pm$1.09(-7)  & 3.43$\pm$0.66(-7)  & 3.50$\pm$0.70(-7)  & 4.26$\pm$1.19(-7) & 3.46$\pm$0.72(-7)\\
C$^{+2}$(1909) & 1.63$\pm$0.36(-4) & 2.01$\pm$0.35(-4)  & 2.35$\pm$1.96(-4)  & 1.87$\pm$0.42(-4)  & 1.51$\pm$0.62(-4)  & 1.73$\pm$0.80(-4) & 2.18$\pm$1.30(-4)\\
C$^{+2}$(1907) & 1.63$\pm$0.36(-4) & 2.01$\pm$0.35(-4)  & 2.35$\pm$1.96(-4)  & 1.87$\pm$0.42(-4)  & 1.51$\pm$0.62(-4)  & 1.73$\pm$0.80(-4) & 2.17$\pm$1.30(-4)\\
C$^{+2}$(adopt) & 1.63$\pm$0.36(-4) & 2.01$\pm$0.35(-4)  & 2.35$\pm$1.96(-4)  & 1.87$\pm$0.42(-4)  & 1.51$\pm$0.62(-4)  & 1.73$\pm$0.80(-4) & 2.67$\pm$0.74(-4)\\
C$^{+3}$(1549) & 3.40$\pm$0.87(-4) & 3.12$\pm$0.67(-5)  & 3.08$\pm$3.14(-5)  & 3.36$\pm$0.90(-5)  & 2.54$\pm$1.27(-5)  & 2.09$\pm$1.17(-5) & 2.88$\pm$2.10(-5)\\
N$^{+}$(6584) & 5.12$\pm$1.01(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
N$^{+}$(6548) & 4.93$\pm$0.97(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
N$^{+}$(5755) & 5.12$\pm$1.01(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
N$^{+}$(adopt) & 5.07$\pm$1.00(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
N$^{+2}$(1751) & 1.38$\pm$0.33(-4) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
N$^{+3}$(1485) & 1.68$\pm$0.45(-4) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ion & NGC2440 3 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 & NGC3242 5\\
\tableline
N$^{+4}$(1240) & 3.79$\pm$1.19(-4) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ne$^{+2}$(3869) & 2.23$\pm$0.28(-5) & 5.60$\pm$0.53(-5)  & 6.89$\pm$3.06(-5)  & 5.65$\pm$0.75(-5)  & 4.50$\pm$1.02(-5)  & 5.36$\pm$1.34(-5) & 5.74$\pm$1.85(-5)\\
Ne$^{+3}$(1602) & 4.40$\pm$1.58(-5) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
Ne$^{+4}$(1575) & 1.12$\pm$0.41(-5) & 3.52$\pm$0.45(-5)  & 2.66$\pm$1.61(-5)  & 4.23$\pm$0.99(-5)  & 2.40$\pm$0.75(-5)  & 2.63$\pm$1.20(-5) & 3.46$\pm$1.74(-5)\\
icf(Ne) & 3.18$\pm$0.57 &  1.72$\pm$0.05  & 1.16$\pm$0.05  & 1.47$\pm$0.10  & 1.86$\pm$0.33  & 1.52$\pm$0.20 & 1.86$\pm$0.27\\
S$^{+}$(6716) & 3.21$\pm$2.04(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(6731) & 3.17$\pm$2.03(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(adopt) & 3.18$\pm$2.03(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
S$^{+2}$(9532) & 7.34$\pm$0.70(-7) & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
icf(S) & 1.63$\pm$0.26 & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
\tableline 
\[[O III] T$_{e}$(K)  & 15100$\pm$600 & 11700$\pm$300 & 11400$\pm$1400 & 11900$\pm$400 & 12200$\pm$800  & 12200$\pm$800 & 11700$\pm$1000\\
\[[S II] N$_{e}$($cm^{-3}$) & 4700$\pm$4900 & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata\\
C III] N$_{e}$($cm^{-3}$)  & 7800$\pm$500 & 4500$\pm$300 & 1800$\pm$1700 & 7000$\pm$900 & 3300$\pm$1000 & 3700$\pm$1400 & 4400$\pm$1300\\
\tableline
%\tablebreak
Ion & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 & NGC5315 Full & NGC5315 1 &\\
\tableline
He$^{+}$(5876) & 4.84$\pm$1.68(-2)  & 4.75$\pm$1.31(-2)  & 3.60$\pm$0.96(-2)  & 7.26$\pm$2.62(-2) & 1.19$\pm$0.02(-1) & 7.95$\pm$1.07(-2)\\
He$^{+2}$(4686) & 4.42$\pm$0.39(-2)  & 4.87$\pm$0.40(-2)  & 6.34$\pm$0.22(-2)  & 4.36$\pm$0.44(-2) & \nodata & \nodata\\
icf(He)  & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
O$^{0}$(6300) & \nodata & \nodata & \nodata & \nodata & 2.74$\pm$0.50(-6) & 4.14$\pm$1.31(-6)\\
O$^{0}$(6363) & \nodata & \nodata & \nodata & \nodata & 4.63$\pm$0.95(-6) &  9.43$\pm$4.97(-6)\\
O$^{0}$(adopt) & \nodata & \nodata & \nodata & \nodata & 3.41$\pm$0.64(-6) &  6.39$\pm$2.90(-6)\\
O$^{+}$(3727) & \nodata & \nodata & \nodata & \nodata & 1.03$\pm$0.46(-5) & 2.45$\pm$0.91(-5)\\
O$^{+}$(7325) & \nodata & \nodata & \nodata & \nodata & 1.31$\pm$0.20(-5) & 1.69$\pm$0.44(-5)\\
O$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 1.17$\pm$0.32(-5) & 2.22$\pm$0.71(-5)\\
O$^{+2}$(5007) & 2.54$\pm$0.76(-4)  & 2.45$\pm$0.68(-4)  & 1.96$\pm$0.35(-4)  & 2.55$\pm$0.40(-4) & 4.95$\pm$0.32(-4) & 3.87$\pm$1.42(-4)\\
O$^{+2}$(4959) & 2.55$\pm$0.76(-4)  & 2.46$\pm$0.68(-4)  & 1.96$\pm$0.35(-4)  & 2.55$\pm$0.40(-4) & 4.82$\pm$0.31(-4) & 2.97$\pm$1.09(-4)\\
O$^{+2}$(4363) & 2.54$\pm$0.76(-4)  & 2.45$\pm$0.68(-4)  & 1.96$\pm$0.35(-4)  & 2.55$\pm$0.40(-4) & 4.04$\pm$0.30(-4) & 3.01$\pm$1.13(-4)\\
O$^{+2}$(adopt) & 2.55$\pm$0.76(-4)  & 2.45$\pm$0.68(-4)  & 1.96$\pm$0.35(-4)  & 2.55$\pm$0.40(-4) & 4.92$\pm$0.31(-4) & 3.69$\pm$1.35(-4)\\
icf(O) & 1.91$\pm$0.33 & 2.02$\pm$0.29 & 2.76$\pm$0.47 & 1.60$\pm$0.23 & 1.00 & 1.00\\
Ar$^{+2}$(7135)  & \nodata & \nodata & \nodata & \nodata & 3.70$\pm$0.16(-6) & 2.88$\pm$0.74(-6)\\
Ion & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 & NGC5315 Full & NGC5315 1 &\\
\tableline
Ar$^{+2}$(7751) & \nodata & \nodata & \nodata & \nodata & 3.67$\pm$0.20(-6) & 3.47$\pm$1.10(-6)\\
Ar$^{+2}$(adopt) & \nodata & \nodata & \nodata & \nodata & 3.69$\pm$0.16(-6) & 3.03$\pm$0.80(-6)\\
icf(Ar) & \nodata & \nodata & \nodata & \nodata & 1.02$\pm$0.01 & 1.06$\pm$0.03\\
C$^{+}$(2325) & 4.51$\pm$1.05(-7)  & 3.78$\pm$1.34(-7)  & 3.76$\pm$1.20(-7)  & 3.13$\pm$1.69(-7) & 4.65$\pm$0.36(-7) & 8.45$\pm$4.01(-7)\\
C$^{+2}$(1909) & 1.99$\pm$1.26(-4)  & 2.01$\pm$1.19(-4)  & 1.40$\pm$0.53(-4)  & 1.69$\pm$0.59(-4) & 2.22$\pm$0.34(-4) & 2.35$\pm$2.01(-4)\\
C$^{+2}$(1907) & 1.99$\pm$1.26(-4)  & 2.01$\pm$1.19(-4)  & 1.40$\pm$0.53(-4)  & 1.69$\pm$0.59(-4) & 2.22$\pm$0.34(-4) & 2.34$\pm$2.00(-4)\\
C$^{+2}$(adopt) & 1.99$\pm$1.26(-4)  & 2.01$\pm$1.19(-4)  & 1.40$\pm$0.53(-4)  & 1.69$\pm$0.59(-4) & 2.22$\pm$0.34(-4) & 2.35$\pm$2.01(-4)\\
C$^{+3}$(1549) & 2.49$\pm$1.93(-5)  & 2.06$\pm$1.49(-5)  & 1.88$\pm$0.86(-5)  & 4.57$\pm$1.90(-5) & 2.98$\pm$0.56(-4) & 5.51$\pm$5.71(-4)\\
N$^{+}$(6584) & \nodata & \nodata & \nodata & \nodata & 1.82$\pm$0.25(-5) & 3.14$\pm$0.46(-5)\\
N$^{+}$(6548) & \nodata & \nodata & \nodata & \nodata & 1.85$\pm$0.26(-5) & 3.35$\pm$0.49(-5)\\
N$^{+}$(5755) & \nodata & \nodata & \nodata & \nodata & 1.82$\pm$0.25(-5) & 3.14$\pm$0.46(-5)\\
N$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 1.83$\pm$0.25(-5) & 3.19$\pm$0.47(-5)\\
Ne$^{+2}$(3869) & 5.81$\pm$2.00(-5)  & 5.30$\pm$1.70(-5)  & 4.53$\pm$0.93(-5)  & 5.52$\pm$1.04(-5) & 1.27$\pm$0.10(-4) & 7.04$\pm$3.07(-5)\\
Ne$^{+4}$(1575) & 3.60$\pm$1.59(-5)  & 4.64$\pm$1.92(-5)  & 2.83$\pm$0.86(-5)  & 2.66$\pm$1.20(-5) & \nodata & \nodata\\ 
icf(Ne) &  1.91$\pm$0.33 &  2.02$\pm$0.29 &  2.76$\pm$0.47 &  1.60$\pm$0.23 & 1.02$\pm$0.01 & 1.06$\pm$0.03\\
S$^{+}$(6716) & \nodata & \nodata & \nodata & \nodata & 4.85$\pm$1.81(-7) & 9.74$\pm$2.96(-7)\\ 
S$^{+}$(6731) & \nodata & \nodata & \nodata & \nodata & 4.88$\pm$1.78(-7) & 9.86$\pm$2.92(-7)\\ 
S$^{+}$(adopt) & \nodata & \nodata & \nodata & \nodata & 4.87$\pm$1.79(-7) & 9.82$\pm$2.94(-7)\\ 
S$^{+2}$(9532) & \nodata & \nodata & \nodata & \nodata & 9.76$\pm$0.38(-6) & 7.19$\pm$1.61(-6)\\
icf(S) & \nodata & \nodata & \nodata & \nodata & 2.02$\pm$0.35 & 1.44$\pm$0.14\\
\tableline 
\[[O III] T$_{e}$(K)  &  11900$\pm$1100 &  11800$\pm$1000 &  12300$\pm$700 & 12000$\pm$600  & 8900$\pm$200 & 9600$\pm$1000\\
\[[S II] N$_{e}$($cm^{-3}$) & \nodata & \nodata & \nodata & \nodata & 10800$\pm$4700 & 6500$\pm$2800\\ 
C III] N$_{e}$($cm^{-3}$)  & 4500$\pm$1200 & 9000$\pm$1200 & 4000$\pm$1300 & 1500$\pm$2000  & 63600$\pm$7900 & 74000$\pm$34900\\
\tableline
%\tablebreak
Ion & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full & NGC5882 1 & NGC5882 2 &\\
\tableline
He$^{+}$(5876) & 1.22$\pm$0.13(-1) & 1.21$\pm$0.02(-1) & 1.11$\pm$0.07(-1) & 1.12$\pm$0.07(-1) & 1.14$\pm$0.14(-1) & 1.10$\pm$0.09(-1) \\
He$^{+2}$(4686) & \nodata & \nodata & \nodata & 3.22$\pm$0.77(-3) & 4.78$\pm$1.04(-3) & 3.80$\pm$0.69(-3) \\
icf(He)  & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 & 1.00\\
O$^{0}$(6300) & 1.55$\pm$0.08(-6) & 4.41$\pm$1.25(-6) & 1.51$\pm$0.45(-5) & \nodata & \nodata & \nodata\\
O$^{0}$(6363) & 2.23$\pm$0.17(-6) & 6.97$\pm$2.10(-6) & 2.77$\pm$1.16(-5) & \nodata & \nodata & \nodata\\
Ion & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full & NGC5882 1 & NGC5882 2 &\\
\tableline
O$^{0}$(adopt) & 1.76$\pm$0.10(-6) & 5.28$\pm$1.50(-6) & 1.98$\pm$0.68(-5) & \nodata & \nodata & \nodata\\
O$^{+}$(3727) & 6.29$\pm$0.35(-6) & 2.43$\pm$1.59(-5) & 6.77$\pm$4.72(-5) & 5.13$\pm$2.14(-6) & 8.61$\pm$1.81(-6) & 3.13$\pm$5.00(-6) \\
O$^{+}$(7325) & 7.20$\pm$0.47(-6) & 2.49$\pm$0.90(-5) & 6.71$\pm$1.73(-5) & 1.55$\pm$1.25(-5) & 2.92$\pm$1.22(-5) & 5.38$\pm$5.33(-6) \\
O$^{+}$(adopt) & 6.86$\pm$0.41(-6) & 2.46$\pm$1.22(-5) & 6.75$\pm$3.61(-5) & 7.19$\pm$2.05(-6) & 1.22$\pm$0.34(-5) & 3.77$\pm$2.16(-6)\\
O$^{+2}$(5007) & 5.07$\pm$0.13(-4) & 5.79$\pm$0.82(-4) & 8.36$\pm$5.19(-4) & 7.62$\pm$1.50(-4) & 6.79$\pm$2.33(-4) & 7.38$\pm$1.81(-4) \\
O$^{+2}$(4959) & 5.14$\pm$0.14(-4) & 5.39$\pm$0.76(-4) & 6.90$\pm$4.29(-4) & 6.37$\pm$1.25(-4) & 5.70$\pm$1.95(-4) & 6.27$\pm$1.54(-4) \\
O$^{+2}$(4363) & 4.31$\pm$0.12(-4) & 4.89$\pm$0.77(-4) & 7.12$\pm$4.49(-4) & 6.81$\pm$1.36(-4) & 6.79$\pm$2.33(-4) & 7.38$\pm$1.82(-4) \\
O$^{+2}$(adopt) & 5.09$\pm$0.13(-4) & 5.69$\pm$0.80(-4) & 8.04$\pm$5.00(-4) & 7.35$\pm$1.45(-4) & 6.56$\pm$2.24(-4) & 7.14$\pm$1.75(-4) \\
icf(O) & 1.00 & 1.00 & 1.00 & 1.03$\pm$0.01 & 1.04$\pm$0.01 & 1.03$\pm$0.01 \\
Ar$^{+2}$(7135) & 3.80$\pm$0.06(-6) & 4.01$\pm$0.39(-6) & 4.62$\pm$2.01(-6) & 1.98$\pm$0.29(-6) & 2.02$\pm$0.50(-6) & 1.84$\pm$0.30(-6)\\
Ar$^{+2}$(7751) & 3.61$\pm$0.10(-6) & 4.00$\pm$0.40(-6) & 4.54$\pm$2.54(-6) & 1.98$\pm$0.44(-6) & 1.86$\pm$0.63(-6) & 1.95$\pm$0.40(-6)\\
Ar$^{+2}$(adopt) & 3.76$\pm$0.07(-6) & 4.01$\pm$0.39(-6) & 4.60$\pm$2.03(-6) & 1.98$\pm$0.29(-6) & 1.99$\pm$0.50(-6) & 1.87$\pm$0.31(-6) \\
Ar$^{+3}$(4740) & \nodata & \nodata & \nodata & 7.56$\pm$3.32(-7) & 6.72$\pm$3.39(-7) & 1.19$\pm$0.51(-6) \\
icf(Ar) & 1.01$\pm$0.01 & 1.04$\pm$0.02 & 1.08$\pm$0.06 & 1.04$\pm$0.01 & 1.06$\pm$0.01 & 1.04$\pm$0.01 \\
C$^{+}$(2325) & 3.62$\pm$0.37(-7) & 4.89$\pm$0.61(-7) & 1.51$\pm$0.57(-6) & 6.09$\pm$3.53(-8) & 6.87$\pm$5.03(-8) & 6.87$\pm$3.83(-8) \\
C$^{+2}$(1909) & 1.94$\pm$0.12(-4) & 3.15$\pm$1.07(-4) & 1.71$\pm$2.57(-3) & 2.23$\pm$1.05(-4) & 1.26$\pm$1.05(-4) & 2.52$\pm$1.50(-4) \\
C$^{+2}$(1907) & 1.93$\pm$0.12(-4) & 3.15$\pm$1.07(-4) & 1.71$\pm$2.57(-3) & 2.23$\pm$1.05(-4) & \nodata & \nodata \\
C$^{+2}$(adopt) & 1.94$\pm$0.12(-4) & 3.15$\pm$1.07(-4) & 1.71$\pm$2.57(-3) & 2.23$\pm$1.05(-4) & \nodata & \nodata \\
C$^{+3}$(1549) & 1.64$\pm$0.15(-4) & 5.41$\pm$2.23(-4) & 4.93$\pm$9.13(-3) & 4.91$\pm$3.03(-5) & 4.22$\pm$4.40(-5) & 6.19$\pm$4.49(-5) \\
N$^{+}$(6584) & 1.05$\pm$0.03(-5) & 2.74$\pm$0.67(-5) & 7.33$\pm$1.70(-5) & 2.27$\pm$0.14(-6) & 3.86$\pm$0.29(-6) & 1.09$\pm$0.27(-6) \\
N$^{+}$(6548) & 1.10$\pm$0.03(-5) & 2.74$\pm$0.67(-5) & 7.32$\pm$1.70(-5) & 1.99$\pm$0.23(-6) & 3.42$\pm$0.33(-6) & 7.93$\pm$2.21(-7) \\
N$^{+}$(5755) & 1.05$\pm$0.03(-5) & 2.74$\pm$0.67(-5) & 7.33$\pm$1.70(-5) & \nodata & \nodata & \nodata\\
N$^{+}$(adopt) & 1.07$\pm$0.03(-5) & 2.74$\pm$0.67(-5) & 7.33$\pm$1.70(-5) & 2.21$\pm$0.13(-6) & 3.76$\pm$0.28(-6) & 1.04$\pm$0.25(-6) \\
Ne$^{+2}$(3869) & 1.41$\pm$0.04(-4) & 1.33$\pm$0.22(-4) & 2.16$\pm$1.64(-4) & 1.72$\pm$0.41(-4) & 1.51$\pm$0.62(-4) & 1.87$\pm$0.53(-4) \\
Ne$^{+4}$(1575) & \nodata & \nodata & \nodata  & 4.91$\pm$2.61(-5) & \nodata & \nodata\\ 
icf(Ne) & 1.01$\pm$0.01 & 1.04$\pm$0.03 & 1.08$\pm$0.07 & 1.04$\pm$0.01 & 1.06$\pm$0.01 & 1.04$\pm$0.01 \\
S$^{+}$(6716) & 2.39$\pm$0.21(-7) & 8.87$\pm$4.54(-7) & 2.14$\pm$1.25(-6) & 7.98$\pm$3.84(-8) & 1.28$\pm$0.12(-7) & 6.48$\pm$10.40(-8) \\ 
S$^{+}$(6731) & 2.44$\pm$0.11(-7) & 8.86$\pm$4.50(-7) & 2.16$\pm$1.24(-6) & 8.11$\pm$3.80(-8) & 1.30$\pm$0.13(-7) & 6.51$\pm$10.50(-8) \\ 
S$^{+}$(adopt) & 2.43$\pm$0.10(-7) & 8.86$\pm$4.52(-7) & 2.15$\pm$1.24(-6) & 8.06$\pm$3.84(-8) & 1.29$\pm$0.12(-7) & 6.50$\pm$10.40(-8) \\ 
Ion & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full & NGC5882 1 & NGC5882 2 &\\
\tableline
S$^{+2}$(9069) & \nodata & 1.02$\pm$1.87(-5) & 9.23$\pm$3.34(-6) & \nodata & \nodata & \nodata \\
S$^{+2}$(9532) & 1.03$\pm$0.02(-5) & \nodata & \nodata & 3.13$\pm$0.37(-6) & 3.53$\pm$0.73(-6) & 2.61$\pm$0.35(-6) \\
icf(S) & 2.58$\pm$0.08 & 1.60$\pm$0.27 & 1.38$\pm$0.22 & 3.72$\pm$1.14 & 2.56$\pm$0.47 & 5.34$\pm$6.86\\
\tableline 
\[[O III] T$_{e}$(K)  & 8900$\pm$100 & 8500$\pm$300 & 7500$\pm$1100 & 8500$\pm$400 & 8700$\pm$800 & 8500$\pm$500 \\
\[[S II] N$_{e}$($cm^{-3}$) & \nodata & 17600$\pm$8300 & 7600$\pm$3300 & 1400$\pm$2800 & 900$\pm$300 & 6700$\pm$20500 \\ 
C III] N$_{e}$($cm^{-3}$)  & 62900$\pm$6700 & 61200$\pm$14000 & 45300$\pm$26700 & 27700$\pm$9200 & \nodata & \nodata\\
\tableline
%\tablebreak
Ion & NGC5882 3 & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & & \\ 
\tableline
He$^{+}$(5876) & 1.08$\pm$0.12(-1) & 5.11$\pm$0.75(-2) & 7.05$\pm$2.71(-2) & 4.58$\pm$2.22(-2) & 3.96$\pm$1.50(-2)\\
He$^{+2}$(4686) & \nodata & 4.90$\pm$0.09(-2) & 4.55$\pm$0.21(-2) & 5.90$\pm$0.14(-2) & 5.47$\pm$0.20(-2) \\
icf(He)  & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
O$^{+}$(3727)  & 5.51$\pm$5.21(-6) & 2.80$\pm$0.92(-6) & 5.15$\pm$2.38(-6) & 3.33$\pm$2.02(-6) & 2.07$\pm$1.15(-6) \\
O$^{+}$(7325) & 1.33$\pm$1.47(-5) & \nodata & \nodata & \nodata & \nodata\\
O$^{+}$(adopt) & 6.99$\pm$5.53(-6) & \nodata & \nodata & \nodata & \nodata\\
O$^{+2}$(5007) & 8.95$\pm$7.35(-4) & 2.30$\pm$0.15(-4) & 3.18$\pm$0.51(-4) & 2.40$\pm$0.29(-4) & 2.32$\pm$0.19(-4) \\
O$^{+2}$(4959) & 7.39$\pm$6.07(-4) & 2.09$\pm$0.13(-4) & 2.88$\pm$0.46(-4) & 2.23$\pm$0.27(-4) & 1.98$\pm$0.16(-4) \\
O$^{+2}$(4363) & 8.95$\pm$7.35(-4) & 2.30$\pm$0.15(-4) & 3.18$\pm$0.51(-4) & 2.40$\pm$0.29(-4) & 2.32$\pm$0.19(-4) \\
O$^{+2}$(adopt) & 8.62$\pm$7.07(-4) & 2.25$\pm$0.14(-4) & 3.11$\pm$0.50(-4) & 2.36$\pm$0.28(-4) & 2.25$\pm$0.18(-4) \\
icf(O) & 1.00 & 1.96$\pm$0.14 & 1.65$\pm$0.25 & 2.29$\pm$0.63 & 2.38$\pm$0.53 \\
Ar$^{+2}$(7135) & 2.35$\pm$1.36(-6) & 4.26$\pm$0.54(-7) & 5.38$\pm$0.99(-7) & 5.12$\pm$0.77(-7) & 4.96$\pm$0.53(-7) \\
Ar$^{+2}$(7751) & 2.39$\pm$1.90(-6) & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+2}$(adopt) & 2.35$\pm$1.39(-6) & \nodata & \nodata & \nodata & \nodata\\
Ar$^{+3}$(4740)  & 1.01$\pm$0.97(-6) & 4.40$\pm$0.72(-7) & 3.31$\pm$2.30(-7) & 3.32$\pm$1.20(-7) & 3.67$\pm$1.96(-7) \\
icf(Ar) & 1.01$\pm$0.01 & 1.97$\pm$0.14 & 1.66$\pm$0.25 & 2.30$\pm$0.63 & 2.39$\pm$0.53\\
C$^{+}$(2325) & 3.09$\pm$3.34(-8) & 5.37$\pm$0.43(-7) & 6.77$\pm$1.50(-7) & 5.20$\pm$0.99(-7) & 4.65$\pm$1.24(-7) \\
C$^{+2}$(1909) & 4.40$\pm$8.61(-4) & 2.15$\pm$0.29(-4) & 3.03$\pm$1.03(-4) & 2.23$\pm$0.56(-4) & 2.32$\pm$0.43(-4) \\
C$^{+2}$(1907) & \nodata & 2.15$\pm$0.29(-4) & 3.03$\pm$1.03(-4) & 2.22$\pm$0.56(-4) & 2.32$\pm$0.43(-4) \\
C$^{+2}$(adopt) & \nodata & 2.15$\pm$0.29(-4) & 3.03$\pm$1.03(-4) & 2.23$\pm$0.56(-4) & 2.32$\pm$0.43(-4) \\
C$^{+3}$(1549)  & 2.47$\pm$6.53(-5) & 1.93$\pm$0.31(-4) & 1.85$\pm$0.76(-4) & 1.63$\pm$0.50(-4) & 2.13$\pm$0.46(-4) \\
N$^{+}$(6584) & 2.01$\pm$0.78(-6) & 5.21$\pm$0.72(-7) & 7.00$\pm$2.14(-7) & 5.28$\pm$1.61(-7) & 5.51$\pm$0.86(-7) \\
Ion & NGC5882 3 & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & & \\ 
\tableline
N$^{+}$(6548) & 2.00$\pm$0.82(-6) & \nodata & \nodata & \nodata & \nodata\\
N$^{+}$(adopt)  & 2.01$\pm$0.78(-6) & \nodata & \nodata & \nodata & \nodata\\
N$^{+2}$(1751) & \nodata & 2.54$\pm$0.70(-5) & 7.63$\pm$4.55(-5) & 2.32$\pm$1.64(-5) & 3.42$\pm$1.38(-5) \\
N$^{+3}$(1485) & \nodata & 4.69$\pm$0.81(-5) & 4.21$\pm$1.92(-5) & 4.14$\pm$1.36(-5) & 5.69$\pm$1.38(-5) \\
N$^{+4}$(1240) & \nodata & 4.45$\pm$1.00(-6) & \nodata & \nodata & \nodata  \\
Ne$^{+2}$(3869) & 2.05$\pm$2.03(-4) & 4.53$\pm$0.34(-5) & 6.84$\pm$1.26(-5) & 4.64$\pm$0.66(-5) & 4.32$\pm$0.45(-5) \\
Ne$^{+3}$(1602) & \nodata & 4.78$\pm$1.23(-5) & 5.66$\pm$4.89(-5) & 2.86$\pm$1.91(-5) & 5.38$\pm$2.52(-5) \\
Ne$^{+4}$(1575) & \nodata & 1.38$\pm$2.22(-5) & 1.54$\pm$2.78(-5) & 1.44$\pm$1.69(-5) & 1.69$\pm$1.13(-5) \\ 
icf(Ne) & 1.01$\pm$0.01 & 1.98$\pm$0.14 & 1.67$\pm$0.25 & 2.32$\pm$0.63 & 2.40$\pm$0.53 \\
S$^{+}$(6716)  & 7.41$\pm$4.00(-8) & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(6731)  & 7.53$\pm$4.07(-8) & \nodata & \nodata & \nodata & \nodata\\
S$^{+}$(adopt)  & 7.48$\pm$4.05(-8) & \nodata & \nodata & \nodata & \nodata\\
S$^{+2}$(9069) & \nodata & \nodata & 9.79$\pm$4.44(-7) & \nodata & 9.46$\pm$2.11(-7) \\ 
S$^{+2}$(9532)  & 3.32$\pm$1.62(-6)  & 6.63$\pm$0.69(-7) & \nodata & 1.04$\pm$0.19(-6) & \nodata \\
icf(S) & 3.87$\pm$2.21 & 3.91$\pm$0.92 & 2.90$\pm$0.83 & 3.99$\pm$1.92 &5.80$\pm$3.06\\
\tableline 
\[[O III] T$_{e}$(K)  & 8100$\pm$1700 & 12700$\pm$300 & 12300$\pm$600 & 12600$\pm$500 & 12400$\pm$300 \\
\[[S II] N$_{e}$($cm^{-3}$)  & 1800$\pm$2500 & \nodata & \nodata & \nodata & \nodata\\
C III] N$_{e}$($cm^{-3}$)  & \nodata & 3200$\pm$1200 & 4000$\pm$1000 & 5700$\pm$700 & 4500$\pm$500 \\
\tableline
%\tablebreak
Ion & NGC7662 4 & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & &\\ 
\tableline
He$^{+}$(5876)  & 3.09$\pm$0.96(-2) & 4.03$\pm$1.02(-2) & 5.37$\pm$0.63(-2) & 8.23$\pm$1.91(-2) & 5.32$\pm$2.14(-2) \\
He$^{+2}$(4686) & 6.30$\pm$0.14(-2) & 6.53$\pm$0.15(-2) & 5.20$\pm$0.11(-2) & 3.49$\pm$0.13(-2) & 4.36$\pm$0.28(-2) \\
icf(He) & 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
O$^{+}$(3727) & 2.20$\pm$1.53(-6) & 2.83$\pm$1.67(-6) & 3.31$\pm$1.39(-6) & 2.16$\pm$0.68(-6) & 2.75$\pm$1.40(-6) \\
O$^{+2}$(5007) & 1.73$\pm$0.07(-4) & 1.79$\pm$0.36(-4) & 2.42$\pm$0.23(-4) & 2.59$\pm$0.24(-4) & 2.58$\pm$0.58(-4) \\
O$^{+2}$(4959) & 1.57$\pm$0.07(-4) & 1.69$\pm$0.34(-4) & 2.19$\pm$0.20(-4) & 2.22$\pm$0.21(-4) & 2.53$\pm$0.57(-4) \\
O$^{+2}$(4363) & 1.73$\pm$0.07(-4) & 1.79$\pm$0.36(-4) & 2.42$\pm$0.23(-4) & 2.59$\pm$0.24(-4) & 2.58$\pm$0.58(-4) \\
O$^{+2}$(adopt) & 1.69$\pm$0.07(-4) & 1.77$\pm$0.35(-4) & 2.37$\pm$0.22(-4) & 2.51$\pm$0.24(-4) & 2.57$\pm$0.58(-4) \\
icf(O) & 3.04$\pm$0.63 & 2.62$\pm$0.41 & 1.97$\pm$0.12 & 1.42$\pm$0.10 & 1.82$\pm$0.33 \\
Ar$^{+2}$(7135) & 3.65$\pm$0.47(-7) & 3.90$\pm$0.92(-7) & 3.99$\pm$0.73(-7) & 4.19$\pm$0.54(-7) & 2.82$\pm$2.18(-7) \\
Ion & NGC7662 4 & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & &\\ 
\tableline
Ar$^{+3}$(4740) & 4.80$\pm$0.88(-7) & 6.25$\pm$1.81(-7) & 3.39$\pm$0.84(-7) & 5.35$\pm$1.28(-7) & 3.76$\pm$1.59(-7) \\
icf(Ar)  & 3.05$\pm$0.63 & 2.64$\pm$0.41 & 1.98$\pm$0.12 & 1.43$\pm$0.10 & 1.83$\pm$0.33 \\
C$^{+}$(2325) & 5.67$\pm$0.96(-7) & 5.32$\pm$1.11(-7) & 6.44$\pm$0.96(-7) & 4.53$\pm$0.97(-7) & 5.29$\pm$2.19(-7) \\
C$^{+2}$(1909) & 1.67$\pm$0.17(-4) & 1.78$\pm$0.72(-4) & 2.28$\pm$0.44(-4) & 2.15$\pm$0.44(-4) & 2.63$\pm$1.24(-4) \\
C$^{+2}$(1907) & 1.67$\pm$0.17(-4) & 1.78$\pm$0.72(-4) & 2.28$\pm$0.44(-4) & 2.15$\pm$0.44(-4) & 2.63$\pm$1.23(-4) \\
C$^{+2}$(adopt) & 1.67$\pm$0.17(-4) & 1.78$\pm$0.72(-4) & 2.28$\pm$0.44(-4) & 2.15$\pm$0.44(-4) & 2.63$\pm$1.23(-4) \\
C$^{+3}$(1549) & 1.35$\pm$0.16(-4) & 1.52$\pm$0.75(-4) & 1.89$\pm$0.44(-4) & 2.43$\pm$0.59(-4) & 3.99$\pm$2.28(-4) \\
N$^{+}$(6584) & 5.32$\pm$0.47(-7) & 5.14$\pm$0.96(-7) & 5.95$\pm$1.11(-7) & 5.77$\pm$1.01(-7) & 4.34$\pm$0.58(-7) \\
N$^{+2}$(1751) & 1.69$\pm$0.93(-5) & 2.32$\pm$1.22(-5) & 2.10$\pm$1.03(-5) & 2.27$\pm$1.40(-5) & 2.46$\pm$3.15(-5) \\
N$^{+3}$(1485) & 3.72$\pm$0.52(-5) & 4.63$\pm$2.42(-5) & 4.70$\pm$1.23(-5) & 4.42$\pm$1.19(-5) & 6.57$\pm$4.02(-5) \\
Ne$^{+2}$(3869) & 3.64$\pm$0.20(-5) & 3.70$\pm$0.84(-5) & 4.26$\pm$0.46(-5) & 5.03$\pm$0.56(-5) & 5.52$\pm$1.43(-5) \\
Ne$^{+3}$(1602) & 5.97$\pm$2.58(-5) & 6.22$\pm$3.72(-5) & 3.60$\pm$2.47(-5) & 2.98$\pm$2.16(-5) & 3.80$\pm$2.40(-5) \\
Ne$^{+4}$(1575) & 6.53$\pm$7.55(-6) & 1.27$\pm$0.78(-5) & 1.86$\pm$1.12(-5) & 1.37$\pm$1.43(-5) & 2.34$\pm$4.19(-5) \\
icf(Ne) & 3.08$\pm$0.64 & 2.66$\pm$0.42 & 2.00$\pm$0.12 & 1.44$\pm$0.10 & 1.84$\pm$0.34 \\
S$^{+2}$(9069) & 7.13$\pm$1.12(-7) & \nodata & \nodata & \nodata & \nodata \\ 
%Ion & NGC7662 4 & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & &\\ 
%\tableline
S$^{+2}$(9532)& \nodata & 6.20$\pm$1.21(-7) & 5.92$\pm$0.87(-7) & 5.47$\pm$0.97(-7) & 4.57$\pm$3.71(-7) \\
icf(S) & 5.34$\pm$3.25 & 4.03$\pm$1.80 & 3.61$\pm$1.05 &4.04$\pm$0.95& 4.12$\pm$1.68 \\
\tableline 
\[[O III] T$_{e}$(K) & 13400$\pm$200 & 13200$\pm$900 & 12900$\pm$400 & 12400$\pm$400 & 12800$\pm$900 \\
C III] N$_{e}$($cm^{-3}$) & 1600$\pm$500 & 2400$\pm$500 & 3900$\pm$500 & 2200$\pm$900 & 4700$\pm$1600 \\
\enddata
\tablenotetext{a}{\footnotesize Abundances relative to H$^{+}$; n.nn$\pm$n.nn(-k) == (n.nn$\pm$n.nn) x 10$^{-k}$}
\end{deluxetable}
\end{landscape}

The final abundances for each of the seven elements measured in each region are presented in Table~\ref{tab:abun1}. The abundances relative to hydrogen or oxygen are given in columns 2-7, while the solar values from~\citet{asp09} are provided in column 8. Figures~\ref{fig:abun1}-\ref{fig:abun3} compare the total abundances of each region with the values scaled to the abundance of the full region in each planetary nebula. The bottom two panels of Figure~\ref{fig:abun3} also compare the [O III] temperature and C III] density of each region with each value scaled in the same manner as the abundances. Out of all the regions, only region 2 of NGC 2440 and region 1 of NGC 5315 show abundances that are significantly lower than the respective full regions. For region 2 of NGC 2440, this can likely be attributed to both the lack of co-spatiality between the UV and optical observations as well as NGC 2440's high ionization stratification (see e.g. \citet{lop98} and \citet{ric91}). Spurious abundances would result from combining areas where the distributions of the ionized states for a particular element are different. For region 1 of NGC 5315, a higher electron temperature is measured compared with the temperature of its full region, causing the inferred abundances to be lower. However, the temperature is consistent (given the errors) with the full region, and substituting the full region's temperature value in for the abundance calculations of Region 1 yields abundances consistent with the full region's values.
\begin{landscape}
\begin{deluxetable}{lcccccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
\tablecaption{Total Elemental Abundances\label{tab:abun1}}
\tablehead{
\multicolumn{9}{c}{Total Elemental Abundances}
}
\startdata
Parameter & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 & IC2165 5 & IC2165 6 & Solar\tablenotemark{a}\\ 
\tableline
He/H (10$^{-2}$) 	& 11.30$^{+1.65}_{-1.65}$ & 10.60$^{+1.56}_{-1.56}$ & 11.40$^{+1.67}_{-1.67}$ & 10.40$^{+1.38}_{-1.38}$ & 10.30$^{+1.21}_{-1.21}$ & 10.40$^{+1.13}_{-1.13}$ & 10.00$^{+2.78}_{-2.78}$ & 8.51 \\
C/H (10$^{-4}$) 	& 4.14$^{+0.87}_{-0.87}$ & 3.09$^{+1.05}_{-1.05}$ & 3.81$^{+1.03}_{-1.03}$ & 3.83$^{+1.54}_{-1.54}$ & 2.91$^{+1.28}_{-1.28}$ & 4.23$^{+1.32}_{-1.32}$ & 89.00$^{+114.84}_{-114.84}$ & 2.69 \\
C/O 			& 1.221$^{+0.343}_{-0.343}$ & 0.842$^{+0.348}_{-0.348}$ & 1.117$^{+0.453}_{-0.453}$ & 1.052$^{+0.519}_{-0.519}$ & 0.735$^{+0.409}_{-0.409}$ & 1.223$^{+0.443}_{-0.443}$ & 10.253$^{+14.954}_{-14.954}$ & 0.550 \\
N/H (10$^{-4}$) 	& 1.18$^{+0.29}_{-0.29}$ & 0.53$^{+0.24}_{-0.24}$ & 1.21$^{+0.38}_{-0.38}$ & 1.49$^{+0.71}_{-0.71}$ & 1.05$^{+0.54}_{-0.54}$ & 0.67$^{+0.27}_{-0.27}$ & 2.44$^{+4.54}_{-4.54}$ & 0.68 \\
N/O 			& 0.348$^{+0.108}_{-0.108}$ & 0.144$^{+0.073}_{-0.073}$ & 0.353$^{+0.155}_{-0.155}$ & 0.409$^{+0.227}_{-0.227}$ & 0.264$^{+0.164}_{-0.164}$ & 0.192$^{+0.085}_{-0.085}$ & 0.281$^{+0.557}_{-0.557}$ & 0.138 \\
O/H (10$^{-4}$) 	& 3.39$^{+0.64}_{-0.64}$ & 3.67$^{+0.87}_{-0.87}$ & 3.41$^{+1.03}_{-1.03}$ & 3.64$^{+1.04}_{-1.04}$ & 3.96$^{+1.35}_{-1.35}$ & 3.46$^{+0.63}_{-0.63}$ & 8.68$^{+5.90}_{-5.90}$ & 4.90 \\
Ne/H (10$^{-5}$) 	& 5.36$^{+1.26}_{-1.26}$ & 5.61$^{+1.49}_{-1.49}$ & 5.63$^{+1.84}_{-1.84}$ & 5.41$^{+1.78}_{-1.78}$ & 5.86$^{+2.22}_{-2.22}$ & 6.03$^{+1.31}_{-1.31}$ & 19.50$^{+16.00}_{-16.00}$ & 8.51 \\
Ne/O 			& 0.158$^{+0.048}_{-0.048}$ & 0.153$^{+0.054}_{-0.054}$ & 0.165$^{+0.073}_{-0.073}$ & 0.149$^{+0.065}_{-0.065}$ & 0.148$^{+0.075}_{-0.075}$ & 0.174$^{+0.049}_{-0.049}$ & 0.225$^{+0.239}_{-0.239}$ & 0.174 \\
S/H (10$^{-6}$) 	& 1.80$^{+0.31}_{-0.31}$ & 1.45$^{+0.56}_{-0.56}$ & 1.15$^{+0.25}_{-0.25}$ & 1.76$^{+0.67}_{-0.67}$ & 2.71$^{+1.98}_{-1.98}$ & 1.95$^{+0.38}_{-0.38}$ & 2.26$^{+1.10}_{-1.10}$ & 13.2 \\
S/O 			& 0.005$^{+0.001}_{-0.001}$ & 0.004$^{+0.002}_{-0.002}$ & 0.003$^{+0.001}_{-0.001}$ & 0.005$^{+0.002}_{-0.002}$ & 0.007$^{+0.006}_{-0.006}$ & 0.006$^{+0.002}_{-0.002}$ & 0.003$^{+0.002}_{-0.002}$ & 0.027 \\
Ar/H (10$^{-7}$) 	& 10.10$^{+3.42}_{-3.42}$ & 12.50$^{+5.73}_{-5.73}$ & 8.55$^{+5.08}_{-5.08}$ & 10.30$^{+6.62}_{-6.62}$ & 14.90$^{+7.39}_{-7.39}$ & 9.91$^{+2.48}_{-2.48}$ & 16.60$^{+9.47}_{-9.47}$ & 25.12 \\
Ar/O 			& 0.003$^{+0.001}_{-0.001}$ & 0.003$^{+0.002}_{-0.002}$ & 0.003$^{+0.002}_{-0.002}$ & 0.003$^{+0.002}_{-0.002}$ & 0.004$^{+0.002}_{-0.002}$ & 0.003$^{+0.001}_{-0.001}$ & 0.002$^{+0.002}_{-0.002}$ & 0.005 \\
\tableline
  & IC3568 Full & IC3568 1 & IC3568 2 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 &\\
\tableline
He/H (10$^{-2}$) 	 & 9.53$^{+1.36}_{-1.36}$ & 10.00$^{+2.39}_{-2.39}$ & 8.91$^{+2.59}_{-2.59}$ & 10.00$^{+7.38}_{-7.38}$ & 12.60$^{+0.84}_{-0.84}$ & 12.10$^{+2.33}_{-2.33}$ & 10.20$^{+0.80}_{-0.80}$ & 8.51 \\
C/H (10$^{-4}$) 	& 4.66$^{+2.71}_{-2.71}$ & 2.03$^{+0.83}_{-0.83}$ & 5.74$^{+4.48}_{-4.48}$ & 27.16$^{+47.99}_{-47.99}$ & 2.18$^{+0.44}_{-0.44}$ & 1.52$^{+0.27}_{-0.27}$ & 1.47$^{+1.47}_{-1.47}$ & 2.69 \\
C/O 			 & 1.148$^{+0.756}_{-0.756}$ & 0.652$^{+0.304}_{-0.304}$ & 1.357$^{+1.197}_{-1.197}$ & 3.660$^{+7.310}_{-7.310}$ & 0.506$^{+0.127}_{-0.127}$ & 0.388$^{+0.119}_{-0.119}$ & 2.339$^{+2.787}_{-2.787}$ & 0.550 \\
N/H (10$^{-4}$) 	& \nodata & \nodata & \nodata & \nodata & 4.62$^{+0.77}_{-0.77}$ & 3.42$^{+0.46}_{-0.46}$ & 2.89$^{+2.93}_{-2.93}$ & 0.68 \\
N/O 			& \nodata & \nodata & \nodata & \nodata & 1.074$^{+0.241}_{-0.241}$ & 0.874$^{+0.249}_{-0.249}$ & 4.592$^{+5.527}_{-5.527}$ & 0.138 \\
%Parameter & IC3568 Full & IC3568 1 & IC3568 2 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & Solar\tablenotemark{a}\\
%\tableline
O/H (10$^{-4}$) 	& 4.06$^{+1.26}_{-1.26}$ & 3.11$^{+0.69}_{-0.69}$ & 4.23$^{+1.74}_{-1.74}$ & 7.42$^{+6.91}_{-6.91}$ & 4.30$^{+0.65}_{-0.65}$ & 3.91$^{+0.98}_{-0.98}$ & 0.63$^{+0.41}_{-0.41}$ & 4.90 \\
Ne/H (10$^{-5}$) 	 & 8.15$^{+1.26}_{-1.26}$ & 5.98$^{+1.49}_{-1.49}$ & 9.05$^{+1.84}_{-1.84}$ & 12.50$^{+1.78}_{-1.78}$ & 7.03$^{+1.24}_{-1.24}$ & 7.08$^{+2.25}_{-2.25}$ & 0.62$^{+0.48}_{-0.48}$ & 8.51 \\
Ne/O 			& 0.201$^{+0.070}_{-0.070}$ & 0.192$^{+0.064}_{-0.064}$ & 0.214$^{+0.098}_{-0.098}$ & 0.168$^{+0.159}_{-0.159}$ & 0.163$^{+0.038}_{-0.038}$ & 0.181$^{+0.073}_{-0.073}$ & 0.099$^{+0.100}_{-0.100}$ & 0.174 \\
S/H (10$^{-6}$) 	& \nodata & \nodata & \nodata & \nodata & 1.52$^{+0.16}_{-0.16}$ & 1.35$^{+0.23}_{-0.23}$ & 0.67$^{+0.61}_{-0.61}$ & 13.2 \\
S/O 			& \nodata & \nodata & \nodata & \nodata & 0.004$^{+0.001}_{-0.001}$ & 0.003$^{+0.001}_{-0.001}$ & 0.011$^{+0.012}_{-0.012}$ & 0.027 \\
Ar/H (10$^{-7}$) 	& 12.70$^{+3.91}_{-3.91}$ & 10.50$^{+4.58}_{-4.58}$ & 12.10$^{+5.21}_{-5.21}$ & 24.10$^{+23.00}_{-23.00}$ & 48.00$^{+6.47}_{-6.47}$ & 42.40$^{+8.45}_{-8.45}$ & 14.40$^{+8.11}_{-8.11}$ & 25.12 \\
Ar/O 			& 0.003$^{+0.001}_{-0.001}$ & 0.003$^{+0.002}_{-0.002}$ & 0.003$^{+0.002}_{-0.002}$ & 0.003$^{+0.004}_{-0.004}$ & 0.011$^{+0.002}_{-0.002}$ & 0.011$^{+0.003}_{-0.003}$ & 0.023$^{+0.020}_{-0.020}$ & 0.005 \\
\tableline
 & NGC2440 3 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 & NGC3242 5 & \\
\tableline
He/H (10$^{-2}$) 	& 12.40$^{+0.95}_{-0.95}$ & 10.60$^{+0.50}_{-0.50}$ & 12.30$^{+2.60}_{-2.60}$ & 11.90$^{+1.60}_{-1.60}$ & 11.1$^{+2.3}_{-2.3}$ & 10.0$^{+2.58}_{-2.58}$ & 9.57$^{+1.63}_{-1.63}$ & 8.51 \\
C/H (10$^{-4}$) 	 & 1.97$^{+0.37}_{-0.37}$ & 2.32$^{+0.36}_{-0.36}$ & 2.66$^{+1.98}_{-1.98}$ & 2.21$^{+0.43}_{-0.43}$ & 1.76$^{+0.63}_{-0.63}$ & 1.94$^{+0.80}_{-0.80}$ & 2.47$^{+1.32}_{-1.32}$ & 2.69 \\
C/O 			& 0.427$^{+0.116}_{-0.116}$ & 0.523$^{+0.091}_{-0.091}$ & 0.721$^{+0.602}_{-0.602}$ & 0.562$^{+0.127}_{-0.127}$ & 0.463$^{+0.203}_{-0.203}$ & 0.517$^{+0.248}_{-0.248}$ & 0.498$^{+0.304}_{-0.304}$ & 0.550 \\
Parameter & NGC2440 3 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 & NGC3242 5 & Solar\tablenotemark{a}\\
\tableline
N/H (10$^{-4}$) 	& 3.95$^{+0.58}_{-0.58}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 0.68 \\
N/O 			& 0.856$^{+0.211}_{-0.211}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 0.138 \\
O/H (10$^{-4}$) 	& 4.61$^{+0.91}_{-0.91}$ & 4.44$^{+0.36}_{-0.36}$ & 3.69$^{+1.40}_{-1.40}$ & 3.93$^{+0.45}_{-0.45}$ & 3.80$^{+0.96}_{-0.96}$ & 3.75$^{+0.92}_{-0.92}$ & 4.96$^{+1.46}_{-1.46}$ & 4.90 \\
Ne/H (10$^{-5}$) 	& 7.08$^{+1.60}_{-1.60}$ & 9.62$^{+0.91}_{-0.91}$ & 8.02$^{+3.55}_{-3.55}$ & 8.31$^{+1.20}_{-1.20}$ & 8.37$^{+2.31}_{-2.31}$ & 8.12$^{+2.23}_{-2.23}$ & 10.70$^{+3.60}_{-3.60}$ & 8.51 \\
Ne/O 			& 0.154$^{+0.046}_{-0.046}$ & 0.217$^{+0.004}_{-0.004}$ & 0.217$^{+0.016}_{-0.016}$ & 0.211$^{+0.014}_{-0.014}$ & 0.220$^{+0.012}_{-0.012}$ & 0.216$^{+0.011}_{-0.011}$ & 0.215$^{+0.013}_{-0.013}$ & 0.174 \\
S/H (10$^{-6}$) 	& 1.71$^{+0.19}_{-0.19}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 13.2 \\
S/O 			& 0.004$^{+0.001}_{-0.001}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 0.027 \\
Ar/H (10$^{-7}$) 	& 48.00$^{+9.19}_{-9.19}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 25.12 \\
Ar/O 			& 0.010$^{+0.003}_{-0.003}$ & \nodata & \nodata & \nodata & \nodata & \nodata & \nodata & 0.005 \\
\tableline
 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 & NGC5315 Full & NGC5315 1 & \nodata & \\
\tableline
He/H (10$^{-2}$) 	& 9.26$^{+1.74}_{-1.74}$ & 9.62$^{+1.38}_{-1.38}$ & 9.93$^{+1.00}_{-1.00}$ & 11.6$^{+2.70}_{-2.70}$ & 11.90$^{+0.17}_{-0.17}$ & 7.95$^{+1.07}_{-1.07}$ & \nodata & 8.51 \\
C/H (10$^{-4}$) 	 & 2.24$^{+1.27}_{-1.27}$ & 2.22$^{+1.20}_{-1.20}$ & 1.59$^{+0.53}_{-0.53}$ & 2.15$^{+0.62}_{-0.62}$ & 5.20$^{+0.65}_{-0.65}$ & 7.86$^{+6.05}_{-6.05}$ & \nodata & 2.69 \\
C/O 			& 0.460$^{+0.300}_{-0.300}$ & 0.447$^{+0.273}_{-0.273}$ & 0.294$^{+0.119}_{-0.119}$ & 0.527$^{+0.187}_{-0.187}$ & 1.032$^{+0.146}_{-0.146}$ & 2.010$^{+1.701}_{-1.701}$ & \nodata & 0.550 \\
N/H (10$^{-4}$) 	& \nodata & \nodata & \nodata & \nodata & 7.86$^{+1.01}_{-1.01}$ & 5.63$^{+2.29}_{-2.29}$ & \nodata & 0.68 \\
N/O 			& \nodata & \nodata & \nodata & \nodata & 1.560$^{+0.224}_{-0.224}$ & 1.440$^{+0.773}_{-0.773}$ & \nodata & 0.138 \\
O/H (10$^{-4}$) 	& 4.87$^{+1.56}_{-1.56}$ & 4.97$^{+1.42}_{-1.42}$ & 5.41$^{+1.25}_{-1.25}$ & 4.08$^{+0.85}_{-0.85}$ & 5.04$^{+0.33}_{-0.33}$ & 3.91$^{+1.37}_{-1.37}$ & \nodata & 4.90 \\
Ne/H (10$^{-5}$) 	& 11.1$^{+4.00}_{-4.00}$ & 10.7$^{+3.50}_{-3.50}$ & 12.5$^{+3.20}_{-3.20}$ & 8.83$^{+2.06}_{-2.06}$ & 12.90$^{+1.01}_{-1.01}$ & 7.48$^{+3.15}_{-3.15}$ & \nodata & 8.51 \\
Ne/O 			& 0.228$^{+0.014}_{-0.014}$ & 0.216$^{+0.014}_{-0.014}$ & 0.231$^{+0.010}_{-0.010}$ & 0.216$^{+0.012}_{-0.012}$ & 0.256$^{+0.026}_{-0.026}$ & 0.191$^{+0.105}_{-0.105}$ & \nodata & 0.174 \\
S/H (10$^{-6}$) 	& \nodata & \nodata & \nodata & \nodata  & 20.70$^{+3.23}_{-3.23}$ & 11.80$^{+3.19}_{-3.19}$ & \nodata & 13.2 \\
S/O 			& \nodata & \nodata & \nodata & \nodata  & 0.041$^{+0.007}_{-0.007}$ & 0.030$^{+0.013}_{-0.013}$ & \nodata & 0.027 \\
Ar/H (10$^{-7}$) 	& \nodata & \nodata & \nodata & \nodata  & 37.80$^{+1.70}_{-1.70}$ & 32.00$^{+7.96}_{-7.96}$ & \nodata & 25.12 \\
Ar/O 			& \nodata & \nodata & \nodata & \nodata & 0.008$^{+0.001}_{-0.001}$ & 0.008$^{+0.004}_{-0.004}$ & \nodata & 0.005 \\
\tableline
 & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full & NGC5882 1 & NGC5882 2 & \nodata & \\
\tableline
He/H (10$^{-2}$) 	& 12.20$^{+0.13}_{-0.13}$ & 12.10$^{+0.18}_{-0.18}$ & 11.10$^{+0.66}_{-0.66}$ & 11.50$^{+0.73}_{-0.73}$ & 11.80$^{+1.39}_{-1.39}$ & 11.40$^{+0.93}_{-0.93}$ & \nodata & 8.51 \\
C/H (10$^{-4}$) 	 & 3.58$^{+0.20}_{-0.20}$ & 8.56$^{+2.47}_{-2.47}$ & 66.40$^{+94.85}_{-94.85}$ & 2.72$^{+1.09}_{-1.09}$ & 1.66$^{+1.14}_{-1.14}$ & 3.14$^{+1.57}_{-1.57}$ & \nodata & 2.69 \\
C/O 			& 0.694$^{+0.042}_{-0.042}$ & 1.441$^{+0.464}_{-0.464}$ & 7.615$^{+11.747}_{-11.747}$ & 0.357$^{+0.159}_{-0.159}$ & 0.239$^{+0.182}_{-0.182}$ & 0.423$^{+0.235}_{-0.235}$ & \nodata & 0.550 \\
N/H (10$^{-4}$) 	& 8.01$^{+0.35}_{-0.35}$ & 6.61$^{+1.59}_{-1.59}$ & 9.46$^{+6.22}_{-6.22}$ & 2.34$^{+0.83}_{-0.83}$ & 2.14$^{+0.93}_{-0.93}$ & 2.04$^{+0.77}_{-0.77}$ & \nodata & 0.68 \\
N/O 			& 1.552$^{+0.079}_{-0.079}$ & 1.113$^{+0.311}_{-0.311}$ & 1.085$^{+0.953}_{-0.953}$ & 0.307$^{+0.125}_{-0.125}$ & 0.307$^{+0.169}_{-0.169}$ & 0.275$^{+0.124}_{-0.124}$ & \nodata & 0.138 \\
O/H (10$^{-4}$) 	& 5.16$^{+0.13}_{-0.13}$ & 5.94$^{+0.84}_{-0.84}$ & 8.72$^{+5.08}_{-5.08}$ & 7.63$^{+1.49}_{-1.49}$ & 6.96$^{+2.35}_{-2.35}$ & 7.42$^{+1.83}_{-1.83}$ & \nodata & 4.90 \\
Parameter & NGC5315 2 & NGC5315 3 & NGC5315 4 & NGC5882 Full & NGC5882 1 & NGC5882 2 & \nodata & Solar\tablenotemark{a}\\
\tableline
Ne/H (10$^{-5}$) 	& 14.30$^{+0.42}_{-0.42}$ & 13.90$^{+2.39}_{-2.39}$ & 23.40$^{+16.80}_{-16.80}$ & 17.80$^{+4.21}_{-4.21}$ & 15.90$^{+6.45}_{-6.45}$ & 19.40$^{+5.56}_{-5.56}$ & \nodata & 8.51 \\
Ne/O 			& 0.277$^{+0.011}_{-0.011}$ & 0.234$^{+0.052}_{-0.052}$ & 0.268$^{+0.248}_{-0.248}$ & 0.233$^{+0.072}_{-0.072}$ & 0.228$^{+0.121}_{-0.121}$ & 0.261$^{+0.099}_{-0.099}$ & \nodata & 0.174 \\
S/H (10$^{-6}$) 	& 27.20$^{+1.13}_{-1.13}$ & 17.70$^{+2.76}_{-2.76}$ & 15.70$^{+6.40}_{-6.40}$ & 11.90$^{+4.29}_{-4.29}$ & 9.36$^{+3.43}_{-3.43}$ & 14.30$^{+17.80}_{-17.80}$ & \nodata & 13.2 \\
S/O 			& 0.053$^{+0.003}_{-0.003}$ & 0.030$^{+0.006}_{-0.006}$ & 0.018$^{+0.013}_{-0.013}$ & 0.016$^{+0.006}_{-0.006}$ & 0.013$^{+0.007}_{-0.007}$ & 0.019$^{+0.024}_{-0.024}$ & \nodata & 0.027 \\
Ar/H (10$^{-7}$) 	& 38.10$^{+0.66}_{-0.66}$ & 41.80$^{+4.13}_{-4.13}$ & 49.90$^{+20.20}_{-20.20}$ & 28.50$^{+5.34}_{-5.34}$ & 28.20$^{+7.78}_{-7.78}$ & 31.80$^{+6.74}_{-6.74}$ & \nodata & 25.12 \\
Ar/O 			& 0.007$^{+0.001}_{-0.001}$ & 0.007$^{+0.001}_{-0.001}$ & 0.006$^{+0.004}_{-0.004}$ & 0.004$^{+0.001}_{-0.001}$ & 0.004$^{+0.002}_{-0.002}$ & 0.004$^{+0.001}_{-0.001}$ & \nodata & 0.005 \\
\tableline
%\tablebreak
 & NGC5882 3 & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & \nodata & \nodata & Solar\tablenotemark{a}\\
\tableline
He/H (10$^{-2}$) 	& 10.80$^{+1.18}_{-1.18}$ & 10.00$^{+0.76}_{-0.76}$ & 11.60$^{+2.72}_{-2.72}$ & 10.50$^{+2.23}_{-2.23}$ & 9.43$^{+1.52}_{-1.52}$ & \nodata & \nodata & 8.51 \\
C/H (10$^{-4}$) 	& 4.65$^{+8.63}_{-8.63}$ & 4.08$^{+0.43}_{-0.43}$ & 4.88$^{+1.28}_{-1.28}$ & 3.86$^{+0.75}_{-0.75}$ & 4.45$^{+0.63}_{-0.63}$ & \nodata & \nodata & 2.69 \\
C/O 			& 0.535$^{+1.086}_{-1.086}$ & 0.913$^{+0.129}_{-0.129}$ & 0.938$^{+0.316}_{-0.316}$ & 0.704$^{+0.247}_{-0.247}$ & 0.824$^{+0.224}_{-0.224}$ & \nodata & \nodata & 0.550 \\
N/H (10$^{-4}$) 	& 2.49$^{+1.69}_{-1.69}$ & 0.77$^{+0.11}_{-0.11}$ & 1.19$^{+0.49}_{-0.49}$ & 0.65$^{+0.21}_{-0.21}$ & 0.92$^{+0.20}_{-0.20}$ & \nodata & \nodata & 0.68 \\
N/O 			& 0.287$^{+0.305}_{-0.305}$ & 0.173$^{+0.029}_{-0.029}$ & 0.229$^{+0.107}_{-0.107}$ & 0.119$^{+0.052}_{-0.052}$ & 0.170$^{+0.053}_{-0.053}$ & \nodata & \nodata & 0.138 \\
O/H (10$^{-4}$) 	& 8.69$^{+7.12}_{-7.12}$ & 4.47$^{+0.42}_{-0.42}$ & 5.20$^{+1.10}_{-1.10}$ & 5.48$^{+1.60}_{-1.60}$ & 5.40$^{+1.25}_{-1.25}$ & \nodata & \nodata & 4.90 \\
Ne/H (10$^{-5}$) 	& 20.60$^{+20.40}_{-20.40}$ & 8.99$^{+0.92}_{-0.92}$ & 11.40$^{+2.63}_{-2.63}$ & 10.80$^{+3.24}_{-3.24}$ & 10.40$^{+2.50}_{-2.50}$ & \nodata & \nodata & 8.51 \\
Ne/O 			& 0.237$^{+0.305}_{-0.305}$ & 0.201$^{+0.028}_{-0.028}$ & 0.219$^{+0.069}_{-0.069}$ & 0.197$^{+0.083}_{-0.083}$ & 0.193$^{+0.064}_{-0.064}$ & \nodata & \nodata & 0.174 \\
S/H (10$^{-6}$) 	& 13.10$^{+11.30}_{-11.30}$ & 2.59$^{+0.68}_{-0.68}$ & 2.84$^{+1.55}_{-1.55}$ & 4.17$^{+2.18}_{-2.18}$ & 5.49$^{+3.17}_{-3.17}$ & \nodata & \nodata & 13.2 \\
S/O 			& 0.015$^{+0.018}_{-0.018}$ & 0.006$^{+0.002}_{-0.002}$ & 0.005$^{+0.003}_{-0.003}$ & 0.008$^{+0.005}_{-0.005}$ & 0.010$^{+0.006}_{-0.006}$ & \nodata & \nodata & 0.027 \\
Ar/H (10$^{-7}$) 	& 33.90$^{+22.20}_{-22.20}$ & 17.10$^{+2.16}_{-2.16}$ & 14.40$^{+4.79}_{-4.79}$ & 19.40$^{+6.25}_{-6.25}$ & 20.60$^{+6.65}_{-6.65}$ & \nodata & \nodata & 25.12 \\
Ar/O 			& 0.004$^{+0.004}_{-0.004}$ & 0.004$^{+0.001}_{-0.001}$ & 0.003$^{+0.001}_{-0.001}$ & 0.004$^{+0.002}_{-0.002}$ & 0.004$^{+0.002}_{-0.002}$ & \nodata & \nodata & 0.005 \\
\tableline
 & NGC7662 4  & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \nodata & \nodata & \\
\tableline
He/H (10$^{-2}$) 	& 9.38$^{+0.97}_{-0.97}$ & 10.60$^{+1.05}_{-1.05}$ & 10.60$^{+0.65}_{-0.65}$ & 11.70$^{+1.91}_{-1.91}$ & 9.68$^{+2.16}_{-2.16}$ & \nodata & \nodata & 8.51 \\
C/H (10$^{-4}$) 	& 3.02$^{+0.23}_{-0.23}$ & 3.30$^{+1.04}_{-1.04}$ & 4.17$^{+0.62}_{-0.62}$ & 4.58$^{+0.74}_{-0.74}$ & 6.62$^{+2.59}_{-2.59}$ & \nodata & \nodata & 2.69 \\
C/O 			& 0.579$^{+0.131}_{-0.131}$ & 0.701$^{+0.275}_{-0.275}$ & 0.882$^{+0.159}_{-0.159}$ & 1.272$^{+0.252}_{-0.252}$ & 1.403$^{+0.669}_{-0.669}$ & \nodata & \nodata & 0.550 \\
N/H (10$^{-4}$) 	& 0.55$^{+0.11}_{-0.11}$ & 0.70$^{+0.27}_{-0.27}$ & 0.69$^{+0.16}_{-0.16}$ & 0.68$^{+0.18}_{-0.18}$ & 0.91$^{+0.51}_{-0.51}$ & \nodata & \nodata & 0.68 \\
N/O 			& 0.105$^{+0.030}_{-0.030}$ & 0.149$^{+0.067}_{-0.067}$ & 0.145$^{+0.037}_{-0.037}$ & 0.187$^{+0.055}_{-0.055}$ & 0.192$^{+0.120}_{-0.120}$ & \nodata & \nodata & 0.138 \\
O/H (10$^{-4}$) 	& 5.22$^{+1.11}_{-1.11}$ & 4.71$^{+1.10}_{-1.10}$ & 4.73$^{+0.48}_{-0.48}$ & 3.60$^{+0.41}_{-0.41}$ & 4.72$^{+1.29}_{-1.29}$ & \nodata & \nodata & 4.90 \\
Ne/H (10$^{-5}$) 	& 11.20$^{+2.41}_{-2.41}$ & 9.85$^{+2.52}_{-2.52}$ & 8.49$^{+0.97}_{-0.97}$ & 7.22$^{+0.93}_{-0.93}$ & 10.20$^{+3.03}_{-3.03}$ & \nodata & \nodata & 8.51 \\
Ne/O 			& 0.215$^{+0.065}_{-0.065}$ & 0.209$^{+0.072}_{-0.072}$ & 0.179$^{+0.027}_{-0.027}$ & 0.201$^{+0.034}_{-0.034}$ & 0.216$^{+0.087}_{-0.087}$ & \nodata & \nodata & 0.174 \\
S/H (10$^{-6}$) 	& 3.81$^{+2.40}_{-2.40}$ & 2.50$^{+1.27}_{-1.27}$ & 2.14$^{+0.71}_{-0.71}$ & 2.21$^{+0.68}_{-0.68}$ & 1.88$^{+1.74}_{-1.74}$ & \nodata & \nodata & 13.2 \\
Parameter & NGC7662 4  & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \nodata & \nodata & Solar\tablenotemark{a}\\
\tableline
S/O 			& 0.007$^{+0.005}_{-0.005}$ & 0.005$^{+0.003}_{-0.003}$ & 0.005$^{+0.002}_{-0.002}$ & 0.006$^{+0.002}_{-0.002}$ & 0.004$^{+0.004}_{-0.004}$ & \nodata & \nodata & 0.027 \\
Ar/H (10$^{-7}$) 	& 25.80$^{+6.14}_{-6.14}$ & 26.80$^{+7.00}_{-7.00}$ & 14.60$^{+2.42}_{-2.42}$ & 13.70$^{+2.27}_{-2.27}$ & 12.00$^{+5.49}_{-5.49}$ & \nodata & \nodata & 25.12 \\
Ar/O 			& 0.005$^{+0.002}_{-0.002}$ & 0.006$^{+0.002}_{-0.002}$ & 0.003$^{+0.001}_{-0.001}$ & 0.004$^{+0.001}_{-0.001}$ & 0.003$^{+0.001}_{-0.001}$ & \nodata & \nodata & 0.005 \\
\enddata
\tablenotetext{a}{\citet{asp09}}
\end{deluxetable}
\end{landscape}
\begin{landscape}
\begin{figure}
\caption{Helium, carbon, and nitrogen abundances for each region listed in Table~\ref{tab:abun1} scaled to the full region of each PN. The abundances at nearly all positions in each object are consistent within errors, with outliers discussed in the text.\newline}
\includegraphics[scale=0.47]{Abun1.png}
\label{fig:abun1}
\end{figure}
\end{landscape}
\begin{landscape}
\begin{figure}
\caption{Same as Figure~\ref{fig:abun1} but for oxygen, neon and argon.\newline}
\includegraphics[scale=0.47]{Abun2.png}
\label{fig:abun2}
\end{figure}
\end{landscape}
\begin{landscape}
\begin{figure}
\caption{Top panel: Same as Figure~\ref{fig:abun1} but for sulfur. Middle and bottom panels show the [O III] electron temperature and C III] electron density listed in Table~\ref{ionabun1} for each region in a PN.\newline}
\includegraphics[scale=0.47]{Abun3.png}
\label{fig:abun3}
\end{figure}
\end{landscape}

A literature search over the last twenty years shows that only NGC 2440, NGC 3242, and NGC 5882 from this sample have been investigated previously for abundance variations.~\citet{per98} presented results on the abundances of helium, oxygen, nitrogen, neon, argon, and sulfur for NGC 2440. They made long-slit observations from 3600-9600 \AA~along the major axis using the Boller \& Chivens spectrograph and the 1.52m ESO telescope at La Silla, Chile. The observations were divided into seven regions spanning the slit length and width of 76.1$''$ and 2$''$, respectively. There were no observed spatial variations between the seven regions within their uncertainties for every element. \citet{mon13} addressed the idea of chemical inhomogeneity in NGC 3242. They observed the nebula between 3900-7000~\AA~using 6400 fibers onboard the instrument VIMOS-IFU, covering an area of 54$''$x54$''$. They measured accurate oxygen and helium abundances from the most abundant ionic species in this range. For other elements in the study, i.e., nitrogen, sulfur and chlorine, only less abundant ionic species were observable, resulting in large (as high as 6x) discrepancies in the total abundances measured at different locations in the nebula. \citet{mon13} concluded that helium and oxygen were homogeneous throughout NGC 3242. NGC 5882 was observed by~\citet{gue99} over the wavelength range 3400-10,300 \AA~using the same instrument as the one employed by~\citet{per98}. They compared the outermost halo to the inner two shells as a whole. They found the abundances of helium, oxygen, and neon to be consistent within errors between the halo and shells. 

Table~\ref{tab:abuncomp} compares the full region abundances for each planetary nebula with other values in the literature. Each PN has two comparison values from either authors with quoted uncertainties or average values with standard deviations from multiple authors. The majority of the abundances match within 1$\sigma$ and nearly all are consistent within 2$\sigma$ with the other authors. The largest discrepancy is seen in the nitrogen abundance of NGC 2440 when compared to the value of \citet{kwi03}. This is most likely caused by the fact that the nitrogen abundance of \citet{kwi03} was calculated using the ICF method (ICF value of 9.71) whereas this value is the sum of the observed ionic species, which includes the most populated ionic states.
\begin{landscape}
\begin{deluxetable}{lcccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
%\rotate
\tablecaption{Comparison: Total Elemental Abundances\label{tab:abuncomp}}
\tablehead{
\multicolumn{7}{c}{Comparison: Total Elemental Abundances}
}
\startdata
 & \multicolumn{3}{c}{IC 2165 Full} & \multicolumn{3}{c}{IC 3568 Full}\\
\tableline
Element & This Work & \citet{kwi03} & BH\tablenotemark{a} & This Work & \citet{hen04} & \citet{kwi98} \\
\tableline
He/H (10$^{-2}$) 	& 11.30$^{+1.65}_{-1.65}$ & 9.00$^{+3.00}_{-3.00}$ & 10.83$^{+0.66}_{-0.66}$ & 9.53$^{+1.36}_{-1.36}$ & 12.00$^{+4.00}_{-4.00}$ & 11.00$^{+1.65}_{-1.65}$ \\
C/H (10$^{-4}$) 	& 4.14$^{+0.87}_{-0.87}$ & \nodata & 6.54$^{+1.76}_{-1.76}$ & 4.66$^{+2.71}_{-2.71}$ & \nodata & 0.97$^{+0.49}_{-0.49}$ \\
N/H (10$^{-4}$) 	& 1.18$^{+0.29}_{-0.29}$ & 1.33$^{+0.19}_{-0.19}$ & 1.20$^{+0.32}_{-0.32}$ & \nodata & \nodata & \nodata\\
O/H (10$^{-4}$) 	& 3.39$^{+0.64}_{-0.64}$ & 3.11$^{+0.44}_{-0.44}$ & 2.28$^{+0.31}_{-0.31}$ & 4.06$^{+1.26}_{-1.26}$ & 3.77$^{+0.53}_{-0.53}$ & 3.14$^{+0.47}_{-0.47}$ \\
Ne/H (10$^{-5}$) 	& 5.36$^{+1.26}_{-1.26}$ & 6.90$^{+0.93}_{-0.93}$ & 5.66$^{+2.23}_{-2.23}$ & 8.15$^{+1.26}_{-1.26}$ & 7.16$^{+1.13}_{-1.13}$ & 4.08$^{+0.61}_{-0.61}$ \\
S/H (10$^{-6}$) 	& 1.80$^{+0.31}_{-0.31}$ & 2.70$^{+0.31}_{-0.31}$ & 3.62$^{+1.29}_{-1.29}$ & \nodata & \nodata & \nodata\\
Ar/H (10$^{-7}$) 	& 10.10$^{+3.42}_{-3.42}$ & 16.00$^{+2.18}_{-2.18}$ & 13.23$^{+4.57}_{-4.57}$ & 12.70$^{+3.91}_{-3.91}$ & 10.56$^{+3.39}_{-3.39}$ & \nodata\\
\tableline
 & \multicolumn{3}{c}{NGC 2440 Full} & \multicolumn{3}{c}{NGC 3242 Full}\\
\tableline
Element & This Work & \citet{kwi03} & \citet{hyu98} & This Work & \citet{hen00} & \citet{mil02}\\
\tableline
He/H (10$^{-2}$) 	& 12.60$^{+0.84}_{-0.84}$ & 10.00$^{+3.00}_{-3.00}$ & 12.00$^{+1.20}_{-1.20}$ & 10.60$^{+0.45}_{-0.45}$ & 8.00$^{+1.00}_{-1.00}$ & 11.00$^{+3.30}_{-3.30}$\\
C/H (10$^{-4}$) 	& 2.18$^{+0.44}_{-0.44}$ & \nodata & 4.00$^{+2.00}_{-2.00}$ & 2.35$^{+0.36}_{-0.36}$ & 4.12$^{+1.66}_{-1.66}$ & \nodata\\
N/H (10$^{-4}$) 	& 4.62$^{+0.77}_{-0.77}$ & 10.67$^{+1.51}_{-1.51}$ & 9.50$^{+2.38}_{-2.38}$ & \nodata & \nodata & \nodata\\
O/H (10$^{-4}$) 	& 4.30$^{+0.65}_{-0.65}$ & 5.19$^{+0.73}_{-0.73}$ & 4.40$^{+0.70}_{-0.70}$ & 4.44$^{+0.36}_{-0.36}$ & 3.38$^{+0.51}_{-0.51}$ & 4.37$^{+1.31}_{-1.31}$\\
Ne/H (10$^{-5}$) 	& 7.03$^{+1.24}_{-1.24}$ & 10.70$^{+1.56}_{-1.56}$ & 9.00$^{+1.35}_{-1.35}$ & 9.62$^{+0.91}_{-0.91}$ & 8.10$^{+1.35}_{-1.35}$ & 9.00$^{+2.70}_{-2.70}$\\
S/H (10$^{-6}$) 	& 1.52$^{+0.16}_{-0.16}$ & 2.80$^{+0.52}_{-0.52}$ & 2.00$^{+0.60}_{-0.60}$ & \nodata & \nodata & \nodata\\
Ar/H (10$^{-7}$) 	& 48.00$^{+6.47}_{-6.47}$ & 40.60$^{+5.71}_{-5.71}$ & 21.00$^{+4.20}_{-4.20}$ & \nodata & \nodata & \nodata\\
\tableline
& \multicolumn{3}{c}{NGC 5315 Full} & \multicolumn{3}{c}{NGC 5882 Full}\\
\tableline
Element & This Work & \citet{pei04} & TKSDT\tablenotemark{b} & This Work & \citet{kwi03} & \citet{gue99} \\
\tableline
He/H (10$^{-2}$) 	& 11.90$^{+0.17}_{-0.17}$ & 11.75$^{+0.11}_{-0.11}$ & 10.71$^{+1.20}_{-1.20}$ & 11.50$^{+0.73}_{-0.73}$ & 12.00$^{+4.00}_{-4.00}$ & 11.10$^{+0.70}_{-0.70}$\\
C/H (10$^{-4}$) 	& 5.20$^{+0.65}_{-0.65}$ & 7.08$^{+1.47}_{-1.47}$ & 5.96$^{+5.40}_{-5.40}$ & 2.72$^{+1.09}_{-1.09}$ & \nodata & \nodata\\
N/H (10$^{-4}$) 	& 7.86$^{+1.01}_{-1.01}$ & 6.92$^{+2.39}_{-2.39}$ & 3.61$^{+1.75}_{-1.75}$ & 2.34$^{+0.83}_{-0.83}$ & 1.80$^{+0.27}_{-0.27}$ & 1.40$^{+0.40}_{-0.40}$\\
O/H (10$^{-4}$) 	& 5.04$^{+0.33}_{-0.33}$ & 7.41$^{+0.51}_{-0.51}$ & 6.02$^{+1.55}_{-1.55}$ & 7.63$^{+1.49}_{-1.49}$ & 5.48$^{+0.77}_{-0.77}$ & 4.93$^{+0.45}_{-0.45}$\\
Ne/H (10$^{-5}$) 	& 12.90$^{+1.01}_{-1.01}$ & 20.41$^{+4.70}_{-4.70}$ & 16.66$^{+4.95}_{-4.95}$ & 17.80$^{+4.21}_{-4.21}$ & 14.80$^{+2.19}_{-2.19}$ & 8.40$^{+1.20}_{-1.20}$\\
S/H (10$^{-6}$) 	& 20.70$^{+3.23}_{-3.23}$ & 32.35$^{+8.94}_{-8.94}$ & 17.87$^{+3.31}_{-3.31}$ & 11.90$^{+4.29}_{-4.29}$ & 7.20$^{+1.10}_{-1.10}$ & 7.00$^{+0.70}_{-0.70}$\\
Ar/H (10$^{-7}$) 	& 37.80$^{+1.70}_{-1.70}$ & 56.21$^{+10.35}_{-10.35}$ & 49.58$^{+14.20}_{-14.21}$& 28.50$^{+5.34}_{-5.34}$ & 27.90$^{+3.84}_{-3.84}$ & 31.50$^{+1.08}_{-1.08}$\\
\tableline
\tablebreak
& \multicolumn{3}{c}{NGC 7662 Full} & & &\\
\tableline
Element & This Work & \citet{kwi03} & LHBA\tablenotemark{c} \\
\tableline
He/H (10$^{-2}$) 	& 10.00$^{+0.76}_{-0.76}$ & 10.00$^{+3.00}_{-3.00}$ & 10.05$^{+1.15}_{-1.15}$\\
C/H (10$^{-4}$) 	& 4.08$^{+0.43}_{-0.43}$ & \nodata & 6.27$^{+2.48}_{-2.48}$\\
N/H (10$^{-4}$) 	& 0.77$^{+0.11}_{-0.11}$ & 0.74$^{+0.13}_{-0.13}$ & 1.00$^{+0.42}_{-0.42}$\\
O/H (10$^{-4}$) 	& 4.47$^{+0.42}_{-0.42}$ & 4.19$^{+0.59}_{-0.59}$ & 4.59$^{+1.70}_{-1.70}$\\
Ne/H (10$^{-5}$) 	& 8.99$^{+0.92}_{-0.92}$ & 7.10$^{+0.84}_{-0.84}$ & 7.58$^{+1.80}_{-1.80}$\\
S/H (10$^{-6}$) 	& 2.59$^{+0.68}_{-0.68}$ & 4.30$^{+0.42}_{-0.42}$ & 5.71$^{+1.52}_{-1.52}$\\
Ar/H (10$^{-7}$) 	& 17.10$^{+2.16}_{-2.16}$ & 24.60$^{+3.35}_{-3.35}$ & 14.80$^{+4.46}_{-4.46}$\\
\enddata
\tablenotetext{a}{Values and uncertainties are averages and standard deviations, respectively, from \citet{boh13} and \citet{hyu94}.}
\tablenotetext{b}{Values and uncertainties are averages and standard deviations, respectively, from \citet{tsa03}, \citet{kin94}, \citet{sam92}, \citet{def91}, and \citet{tor81}.}
\tablenotetext{c}{Values and uncertainties are averages and standard deviations, respectively, from \citet{liu04}, \citet{hyu97}, \citet{bar86}, and \citet{all83}.}
\end{deluxetable}
\end{landscape} 

Looking at the temperatures of each region, only region 6 of IC 2165 is significantly lower than its full region temperature. This region probes the middle shell of IC 2165, as opposed to the other regions that probe the innermost shell. Therefore, this may indeed be cooler gas since it is farther from the central star and may be optically thick such that the effect of heating by radiation hardening doesn't occur. Lastly, most of the density variations appear to coincide with brighter areas of each PN for the higher densities, and dimmer areas for the lower densities. This is consistent with the assumption that the brightness is proportional to the density squared and may be the result of clumps of ejected material that form prior/during the formation of the planetary nebula. The only regions with densities that are unusual are Regions 2, 1 and 7 of IC 2165, IC 3568 and NGC 3242, respectively. A plausible explanation is that there is a small knot of enhanced density in each region that is emitting the observed light, though a literature search turns up no corroboration.

To summarize, first, dereddened emission line intensities for various regions across each planetary nebula were presented. Next, these emission lines were used to calculate nebular properties of temperature and density as well as ionic abundances. Last, total abundances for He, C, N, O, Ne, S and Ar were calculated from the ionic abundances for each region. \textit{The major result is that each of the seven planetary nebulae appears to exhibit a chemically homogeneous distribution of these elements.}
\section{Central Star Properties}
%\\\\
%\textbf{3.2 Central Star Properties}
%\\\\
In order to constrain the central star's temperature and luminosity of each planetary nebula, Cloudy version 13.03~(\citet{fer13}) was used to generate photoionization models of each PN. For a given set of input parameters, Cloudy simultaneously solves energy and ionization equilibrium equations at specific radial points in the PN model. Three iterations for each model were carried  out to ensure that each model had converged to a solution. The assumed spectral energy distribution (SED) of the central star was taken to be either the Rauch H-Ni or the Rauch pg1159 atmospheric simulations~(\citet{rau03}), depending on the known atmospheric properties of the central stars. Rauch H-Ni includes line blanketing for lines from hydrogen to nickel, whereas for Rauch pg1159, the line blanketing effects only include lines of helium, carbon, nitrogen, and oxygen. NGC 5315 was the only PN for which the Rauch pg1159 SED was employed, since its central star was observed to be hydrogen deficient by~\citet{men82}. Assumptions for each model were a spherically symmetric and static geometry without shock heating of the gas. The initial stellar parameters were chosen to be the average of the most reliable values found in the literature (\citet{sha85}, \citet{sha89}, \citet{zha93}, \citet{cor03}, and \citet{fre08}) but were left variable in the modeling. Fixed angular radii for the models were measured from archival HST WFPC2 images and the values are as follows; IC 2165 r=2.67$''$, IC 3568 r=3.54$''$, NGC 2440 r=6.51$''$, NGC 3242 r=9.30$''$, NGC 5315 r=1.50$''$, NGC 5882 r=3.21$''$, and NGC 7662 r=10.71$''$. These fixed angular radii ensured that a change in the outer radius of each model resulted in a change in the assumed distance to the nebula. Lastly, the nebular properties initially were set to the values discussed in \S2 (densities in Table~\ref{emisstab1} and total abundances in Table~\ref{tab:abun1}) but also left variable.

The calculations for converting the internal model gas properties into model emission line strengths were made with the self-written C++ program PANIC (PlAnetary Nebula Intensity Calculator). To summarize the process, radial emissivity values from each Cloudy model are read into PANIC, which then calculates the model line intensities based on the geometry and other properties of the modeled gas. Specifically, PANIC calculates the volume of gas intersected by each region for each radial distance from the model, multiplies this volume by the appropriate emissivity, and adds up each contribution to determine the maximum emission strength for a particular line. Finally, this maximum emission strength is scaled by the filling factor (the ratio of the volume of gas to the total, physical volume) to get the total emission line strength. To weight the emission lines equally, only one\footnotemark~emission line per ion was used in the comparison to the models and only for lines having a S/N $>$ 3. A total rms value was calculated for each model from the expression $\sqrt{\frac{1}{N}\sum_{1}^{N}{(1-\frac{model}{observed})^2}}$, where \textit{N} is the total number of lines and diagnostics, \textit{model} is the value of each line or diagnostic predicted by the model, and \textit{observed} is the observed value. A similar rms value for the observations was calculated by using the line uncertainty in place of the \textit{model} parameter in the above expression. This observed rms value was later used in the calculation of the uncertainties in the parameters from each model. The model that yielded the lowest rms value was chosen to be the best model. Degeneracies between models with similar rms values were broken by employing five common diagnostics\footnotemark.
\footnotetext[2]{Additional lines from some ions were used in diagnostic line ratios only.}
\footnotetext[3]{([O III] $\lambda$5007+$\lambda$4959+$\lambda$3727)/H$\beta$, ([O II] $\lambda$3727)/([O III] $\lambda$5007), (He II $\lambda$4686)/(He I $\lambda$5876), [O III] ($\lambda$4363/$\lambda$5007), and C III] ($\lambda$1909/$\lambda$1907)}

To test the validity of the described rms method for assessing the best model, the method of~\citet{mor09} was used for NGC 3242. In their method, a quality factor, \textit{Q}, is calculated by the expression $\frac{log(\frac{model}{observed})}{log(1+RelativeError)}$ where \textit{RelativeError} is $\frac{uncertainty}{observed}$. Minimizing this \textit{Q} value instead of the rms resulted in a small difference in the best fit stellar temperature and luminosity of only 200 K and 0.011 dex, respectively.

Also, to test the sensitivity of the best stellar parameters on the choice of density profiles, a total of three density profiles were used. The first had a constant density throughout the entire gas region (constant density profile). The brightest portions of each nebula are primarily from one shell, so a constant density profile is a sensible first choice. However, the sharp cutoff of the gas at the boundaries is unphysical in nature. Therefore, the second profile replaces the constant density with a Gaussian shaped density profile (Gaussian density profile), allowing for a smoother transition to low density areas. The Gaussian density profile, however, does not take into account the less luminous, exterior shells of gas seen in most of the objects. To represent these outer shells in the third profile, a radially decreasing power-law is appended to the Gaussian density profile (Gaussian with a power-law density profile). Figures~\ref{densfig1}~\&~\ref{densfig2} shows the different profiles for each planetary nebula's Full Region.
\begin{figure}
\caption{The three different density profiles used for the full regions of IC 2165, IC 3568, NGC 2440 and NGC 3242 are shown here. The solid red lines are the constant density profiles. The blue dash lines are the Gaussian density profile. The combination of the blue dash lines and green dot-dash lines are the Gaussian with a power-law density profiles.\newline}
\includegraphics[scale=0.29]{4PNeDenShape.png}
\label{densfig1}
\end{figure}
\begin{figure}
\caption{The same as Figure~\ref{densfig1} but for NGC 5315, NGC 5882, and NGC 7662.\newline}
\includegraphics[scale=0.29]{3PNeDenShape.png}
\label{densfig2}
\end{figure}

Since each model assumes a specific value for each stellar and nebular parameter, locating the global minimum (in parameter space) or best value for each stellar parameter is critical. Two methods were used to find these minima. The first method employed a suite of constant density models spanning a wide range of stellar and nebular parameters, using resources from the OU Supercomputing Center for Education and Research at the University of Oklahoma. The benefit to this method is that local minima can be easily identified and avoided. The downside is the sheer number of models required to adequately probe each parameter. The second method determined the rms after each model run and kept parameters that reduced the rms value. This way drastically reduces the number of models required to be run but can be susceptible to stopping in local minima. Both methods were used for NGC 3242 with negligible differences in the final stellar parameters found. Also, it was observed by inspecting the rms values from the large suite of models that local minima were not a major concern for the stellar parameters. Therefore, only the second method was used for the other six planetary nebulae. 

Descibing the first method in detail, a primary grid of 81,000 models was produced by varying the stellar temperature and luminosity, the inner and outer radii, and the filling factor of the gas while holding the abundances of He, C, Ne, and O constant. The range of the stellar temperature and luminosity was between 50,000-100,000K ($\bigtriangleup$T = 1000K) and (log[L/L$_{\astrosun}$])=3.0-5.0 ($\bigtriangleup$dex = 0.1), respectively. These ranges cover all published values of these stellar parameters. The filling factor was varied between 0.01 and 0.5, a range which encompasses typical values of planetary nebulae, in steps of 0.01. The inner/outer radius were varied from 0.039pc/0.0415pc to 0.041pc/0.0437pc with a step size of 10$^{-3}$pc/10$^{-4}$pc, covering values that are reasonable for the assumed distance. The nebular composition was chosen to be the full region's values from Table~\ref{tab:abun1}, since all regions had elemental abundances within error of the full region's values. Grains were chosen to be the \textit{planetary nebula} set internal to Cloudy with a fixed scaling factor of 1.0.  The density was chosen to be the full region's value of 4500~cm$^{-3}$ except for Regions 1, 2, 7, and 9.

Next, the set of observed emission lines strengths for NGC 3242 were used to reduce the primary grid to a smaller group of models which were the most successful at reproducing the observations, as determined by the previously discussed rms analysis. Finally, the abundances were varied within the observed errors to produce a secondary grid of over 10 million models to further reduce the model rms. Ultimately, the best values were found by starting with the best model from the grid, and manually adjusting each input parameter and keeping the values that lowered the model rms. An estimation of the error for each parameter was carried out by starting with the best model and varying each parameter one at a time (the stellar temperature and luminosity were varied together) until the model rms was larger than the sum of the best fit model rms and observed rms\footnotemark, e.g. model rms $>$ 0.21 for Region Full. This estimation process was used only for the constant density models, due to constraints imposed by computational time requirements.
\footnotetext[4]{Admittedly, each parameter is not fully independent. However, varying the stellar parameters together takes into account more of the covariance.}

For the second method, the nebular and stellar parameters described above were used as starting values and other parameters such as the grain properties and filling factor were set to typical PN values. The density was then adjusted until the carbon density diagnostic, C III] ($\lambda$1909/$\lambda$1907), was within roughly 1\% of the observed value. Next, the radius and overall thickness of the gas was adjusted until the line strength of H$\beta$ was within 10\% of the observed value. Finally, all other parameters (abundances, stellar properties, etc.) were adjusted as needed to get the rms down around 0.3, ensuring an average error for all lines and diagnostics near 10\%. From there, the best parameters set so far were entered into a script that varied each parameter one at a time, calculated the rms after each model run by calling PANIC, compared the new rms to the previous values, and retained the sets that resulted in a smaller rms. It continuously looped through all parameters until it failed to produce a lower rms value. To minimize convergence times, the step size for each parameter began at relatively large values (e.g. $\bigtriangleup$T=500K, log[L/L$_{\astrosun}$] $\bigtriangleup$dex=0.1, abundance $\bigtriangleup$dex=0.1), but then was reduced to smaller values (e.g. $\bigtriangleup$T=100K, log[L/L$_{\astrosun}$] $\bigtriangleup$dex=0.01, abundance $\bigtriangleup$dex=0.01) to yield the smallest rms and subsequent best parameters.

The Gaussian and Gaussian with a power-law density profiles initially assumed the best fit constant density parameters as the initial values with the inner and outer radii held fixed. Since there is less gas contained within a Gaussian profile of equal height and width relative to a constant profile, the density peak of the Gaussian profile was increased by trial and error to compensate for the decrease in the H$\beta$ line strength. However, for NGC 5315, the increase was found to be too large to keep the carbon density diagnostic within reasonable error, so the inner and outer radii were increased while keeping the peak of the Gaussian distribution at the center of the best constant density model. The slope of the power-law was chosen such that the Gaussian side of the profile was around 2000 cm$^{-3}$ and decreased to about 10 cm$^{-3}$ at the location of the outermost known shell/halo of each planetary nebula. The error estimation process was the same as what was described above in the first method.

Table~\ref{modline1} contains the ratios of the model-predicted strengths to their observed counterparts of important emission lines for each nebular region. The wavelength of each emission line is in the first column followed by the identification of the ion that produces it in the second column. The remaining columns contain the individual region's model$/$observed ratio. The majority of modeled lines for each full region fall within the respective errors shown in Table~\ref{emisstab1}. Region Full of NGC 3242 has the most lines that are outside the errors listed in Tables~\ref{emisstab1}. This is probably due to the modeling assumptions becoming less valid compared to the smaller regions and the smaller uncertainties in the line strengths. Table~\ref{nmodline1} provides the same type of comparison as Table~\ref{modline1} but for the other two density profiles and only for the full regions. IC 2165 and NGC 2440 have the largest increase in the number of lines falling outside of the observed errors for the two non-constant density profiles compared to the constant density profile. This suggests that the PN are better represented by the constant density profile.
\begin{landscape}
\begin{deluxetable}{clccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
%\rotate
\tablecaption{Constant Density Model Emission Lines Compared to Observations\label{modline1}}
\tablehead{
\multicolumn{7}{c}{Constant Density Model Emission Lines Compared to Observations}
}
\startdata
Wave & & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 \\ 
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 & N IV] 	& 1.00 & 1.00 & 1.00 & 1.00 & 1.01 \\     
1907 & C III]		& 1.01 & 0.96 & 1.05 & 1.03 & 1.06 \\    
1909\tablenotemark{b} & C III]  	& 1.00 & 0.97 & 1.04 & 1.03 & 1.06 \\        
3869 & [Ne III]  	& 1.00 & 1.00 & 1.00 & 1.00 & 1.01 \\  
4363\tablenotemark{b} & [O III]  	& 1.01 & 0.87 & 1.11 & 1.04 & 1.10 \\       
4686 & He II  	& 1.00 & 1.09\tablenotemark{a} & 0.81\tablenotemark{a} & 0.97 & 0.85\tablenotemark{a} \\
4861 & H$\beta$  	& 0.98 & 1.00 & 0.95\tablenotemark{a} & 0.94\tablenotemark{a} & 0.84\tablenotemark{a} \\  
4959\tablenotemark{b} & [O III]  	& 1.03\tablenotemark{a} & 0.99 & 1.04\tablenotemark{a} & 1.01 & 1.11 \\       
5007 & [O III]  	& 1.01 & 0.95\tablenotemark{a} & 1.04\tablenotemark{a} & 1.03\tablenotemark{a} & 1.08\tablenotemark{a} \\   
5876 & He I  		& 1.00 & 1.06 & 0.95 & 0.98 & 0.93 \\
7136 & [Ar III]  	& 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\  
9532 & [S III]  	& 1.00 & 1.00 & 1.00 & 1.00 & 1.00 \\
\tableline
 & & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  	& 1.00 & 0.97 & \nodata & \nodata & \nodata \\   
1549 & C IV 		& \nodata & \nodata & 1.00 & 1.00 & 1.02 \\ 
1907 &  C III]  	& 0.92 & 0.91 & 1.00 & 1.02 & 0.99 \\   
1909\tablenotemark{b} &  C III]  	& 0.92 & 0.91 & 1.01 & 1.01 & 1.03 \\ 
%\tableline   
% & & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
%\cline{3-7}           
% & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline  
3869 &  [Ne III]  	& 0.99 & 0.99 & 1.00 & 1.00 & 1.01 \\ 
4363\tablenotemark{b} &  [O III]  	& 0.81\tablenotemark{a} & 0.96 & 0.99 & 1.01 & 0.97 \\              
4686 &  He II  	& 1.00 & 1.10 & \nodata & \nodata & \nodata \\   
4861 &  H$\beta$  	& 1.10\tablenotemark{a} & 1.21\tablenotemark{a} & 0.94\tablenotemark{a} & 0.87\tablenotemark{a} & 0.96 \\ 
4959\tablenotemark{b} &  [O III]  	& 0.87\tablenotemark{a} & 0.99 & 1.12\tablenotemark{a} & 1.18\tablenotemark{a} & 1.13\tablenotemark{a} \\              
5007 &  [O III]  	& 0.89\tablenotemark{a} & 0.87\tablenotemark{a} & 1.00 & 1.07\tablenotemark{a} & 1.01 \\  
5876 &  He I  	& 1.03 & 1.01 & 1.00 & 0.99 & 1.00 \\
7136 &  [Ar III]  	& 1.01 & 1.00 & 1.00 & 1.01 & 1.00 \\ 
9532 &  [S III]  	& 0.99 & 1.00 & \nodata & \nodata & \nodata \\
\tableline
\tablebreak
Wave & & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  	& \nodata & 0.98 & 0.97 & 0.79\tablenotemark{a} & 0.85\tablenotemark{a} \\ 
1907 &  C III]  	& 1.00 & 0.99 & 0.95 & 0.99 & 0.92 \\   
1909\tablenotemark{b} &  C III]  	& 1.00 & 0.97 & 1.01 & 0.96 & 0.91 \\               
3727 & [O II] 	& \nodata & 0.98 & 0.93\tablenotemark{a} & 1.11 & 0.93 \\  
3869 &  [Ne III]  	& 1.00 & 1.00 & 0.98 & 1.01 & 0.98 \\ 
4363\tablenotemark{b} &  [O III]  	& 0.98 & 1.00 & 0.70\tablenotemark{a} & 1.05 & 0.97 \\              
4686 &  He II  	& \nodata & 1.03 & 1.14\tablenotemark{a} & 0.89\tablenotemark{a} & 1.06\tablenotemark{a} \\ 
%Wave & & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
%\cline{3-7}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline
4861 &  H$\beta$  	& 1.02 & 0.98 & 0.84\tablenotemark{a} & 1.01 & 1.14\tablenotemark{a} \\ 
4959\tablenotemark{b} &  [O III]  	& 1.13\tablenotemark{a} & 1.01 & 0.84\tablenotemark{a} & 1.05 & 1.02 \\              
5007 &  [O III]  	& 0.98 & 0.99 & 0.84\tablenotemark{a} & 0.94\tablenotemark{a} & 1.04\tablenotemark{a} \\  
5876 &  He I  	& 1.00 & 1.01 & 1.09 & \nodata & 1.05 \\  
6584 & [N II] 	& \nodata & 1.02\tablenotemark{a} & 0.97\tablenotemark{a} & 1.14\tablenotemark{a} & 1.05\tablenotemark{a} \\  
7136 &  [Ar III]  	& 1.00 & 1.00 & 1.00 & 1.01 & 1.01 \\ 
9532 &  [S III]  	& \nodata & 1.00 & 0.99 & 1.00 & 1.00 \\
\tableline
%\tablebreak
 & & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
 \tableline
1485 & N IV] & 0.999 & 1.003 & 1.001 & 1.009 & 1.001 \\
1907 & C III] & 1.047\tablenotemark{a} & 1.013 & 1.007 & 1.014 & 1.006 \\
1909\tablenotemark{b} & C III] & 1.048\tablenotemark{a} & 1.009 & 1.007 & 1.020 & 1.003 \\
3727 & [O II] & 0.954 & \nodata & \nodata & \nodata & \nodata\\
3869 & [Ne III] & 1.038\tablenotemark{a} & 1.011 & 1.003 & 1.001 & 1.005 \\
%3969\tablenotemark{c} & [Ne III] & 1.057\tablenotemark{a} & 1.018 & 1.054 & 1.110 & 0.982 \\
%4101\tablenotemark{c} & H$\delta$ & 0.886\tablenotemark{a} & 0.721\tablenotemark{a} & 0.880\tablenotemark{a} & 0.968 & 0.861 \\
%4340\tablenotemark{c} & H$\gamma$ & 0.939\tablenotemark{a} & 0.910 & 0.999 & 1.032 & 0.955 \\
4363\tablenotemark{b} & [O III] & 1.078\tablenotemark{a} & 0.986 & 0.969 & 0.934 & 0.952 \\
4686 & He II & 0.941\tablenotemark{a} & 1.001 & 0.904\tablenotemark{a} & 0.898\tablenotemark{a} & 0.985 \\
4861 & H$\beta$ & 0.914\tablenotemark{a} & 0.931\tablenotemark{a} & 0.961\tablenotemark{a} & 0.944\tablenotemark{a} & 0.977 \\
4959\tablenotemark{b} & [O III] & 1.068\tablenotemark{a} & 1.015 & 1.006 & 0.996 & 0.989 \\
5007 & [O III] & 1.081\tablenotemark{a} & 1.028 & 1.019\tablenotemark{a} & 1.008 & 1.001 \\
5876 & He I & 0.963 & 0.996 & 0.947 & 0.975 & 1.000 \\
%6563\tablenotemark{c} & H$\alpha$ & 0.918\tablenotemark{a} & 0.943\tablenotemark{a} & 0.967\tablenotemark{a} & 0.949\tablenotemark{a} & 0.974\tablenotemark{a} \\
%6678\tablenotemark{b}\tablenotemark{c} & He I & 1.114 & \nodata & \nodata & \nodata & \nodata \\
7136 & [Ar III] & 1.003 & \nodata & \nodata & \nodata & \nodata \\
Wave & & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\cline{3-7}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
9532 & [S III] & 1.013 & \nodata & \nodata & \nodata & \nodata \\
\tableline
 & & NGC3242 5 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 \\
\cline{3-7}
  & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
 \tableline
1485 & N IV] & 1.007 & 1.003 & 1.003 & 1.002 & 1.004 \\
1907 & C III] & 1.023 & 1.011 & 1.022 & 1.000 & 0.991 \\
1909\tablenotemark{b} & C III] & 1.025 & 1.010 & 1.027 & 0.998 & 0.995 \\
3869 & [Ne III] & 1.011 & 1.002 & 1.007 & 0.998 & 0.998 \\
%3969\tablenotemark{b} & [Ne III] & 1.036 & 1.006 & 1.106 & 1.029 & 1.124 \\
%4101\tablenotemark{b} & H$\delta$ & 0.969 & 0.992 & 1.008 & 0.961 & 1.053 \\
%4340\tablenotemark{b} & H$\gamma$ & 0.952 & 0.976 & 1.008 & 0.953 & 1.006 \\
4363\tablenotemark{b} & [O III] & 1.067 & 1.010 & 1.097 & 0.933 & 0.987 \\
4686 & He II & 1.001 & 0.992 & 0.985 & 0.727\tablenotemark{a} & 0.957 \\
4861 & H$\beta$ & 0.886\tablenotemark{a} & 0.954\tablenotemark{a} & 0.969 & 0.960\tablenotemark{a} & 0.979 \\
4959\tablenotemark{b} & [O III] & 1.070\tablenotemark{a} & 1.017 & 1.068\tablenotemark{a} & 0.994 & 1.020 \\
5007 & [O III] & 1.084\tablenotemark{a} & 1.030\tablenotemark{a} & 1.081\tablenotemark{a} & 1.006 & 1.032\tablenotemark{a} \\
5876 & He I & 0.992 & 0.996 & 0.981 & 0.889 & 0.989 \\
%6563\tablenotemark{b} & H$\alpha$ & 0.889\tablenotemark{a} & 0.946\tablenotemark{a} & 0.976\tablenotemark{a} & 0.966\tablenotemark{a} & 0.987\tablenotemark{a}  
\tableline
 & & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\cline{3-7}
 & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1549 & C IV 		& 0.99 & 0.99 & 0.99 & 1.04 & 0.99 \\
1907 &  C III]  	& 1.00 & 1.00 & 1.01 & 0.97 & 0.98 \\
1909\tablenotemark{b} &  C III]  	& 1.01 & 1.00 & 1.04\tablenotemark{a} & 1.02 & 0.98\\
3869 &  [Ne III] 	& 0.99 & 1.00 & 1.00 & 1.01 & 1.01 \\
4363\tablenotemark{b} &  [O III]  	& 0.99 & 1.02 & 1.03\tablenotemark{a} & 1.14\tablenotemark{a} & 1.09\\
4861 &  H$\beta$  	& 1.06\tablenotemark{a} & 1.00 & 0.90\tablenotemark{a} & 0.89\tablenotemark{a} & 0.91\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 0.98 & 1.28\tablenotemark{a} & 0.99 & 1.13\tablenotemark{a} & 1.25\tablenotemark{a}\\
5007 &  [O III]  	& 0.98\tablenotemark{a} & 0.99 & 1.02\tablenotemark{a} & 1.06\tablenotemark{a} & 1.04\tablenotemark{a} \\
5876 &  He I  	& 1.01 & 0.99 & 1.00 & 0.96\tablenotemark{a} & 0.97 \\
%Wave & & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
%\cline{3-7}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
%\tableline
7136 &  [Ar III]  	& 0.99\tablenotemark{a} & 1.00 & 1.00\tablenotemark{a} & 1.01\tablenotemark{a} & 1.01 \\
9532 &  [S III]  	& 0.96\tablenotemark{a} & 1.02 & 1.02\tablenotemark{a} & 1.08\tablenotemark{a} & 1.08\tablenotemark{a} \\
\tableline
\tablebreak
Wave & & NGC5882 Full & NGC5882 1 & NGC5882 2 & NGC5882 3 & \\
\cline{3-6}
 (\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed &  \\
 \tableline
1549 & C IV 		& 1.00 & 0.91 & 0.91 & 1.08 \\
1907 &  C III]  	& 1.00 & \nodata & \nodata & \nodata \\
1909\tablenotemark{b} &  C III]  	& 0.99 & 1.03\tablenotemark{c} & 1.07\tablenotemark{c} & 0.89\tablenotemark{c} \\
3869 &  [Ne III]  	& 1.02 & 1.02 & 1.04\tablenotemark{a} & 1.02 \\
4363\tablenotemark{b} &  [O III]  	& 1.13 & 1.22 & 1.00 & 0.94 \\
4686 &  He II  	& 0.98 & 0.92 & 0.84 & \nodata \\
4861 &  H$\beta$  	& 0.81\tablenotemark{a} & 0.84\tablenotemark{a} & 0.77\tablenotemark{a} & 0.82\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.33\tablenotemark{a} & 1.40\tablenotemark{a} & 1.25\tablenotemark{a} & 1.27\tablenotemark{a} \\
5007 &  [O III]  	& 1.12\tablenotemark{a} & 1.19\tablenotemark{a} & 1.07\tablenotemark{a} & 1.06\tablenotemark{a} \\
5876 &  He I  	& 0.98 & 0.95 & 0.94\tablenotemark{a} & 1.01 \\
6584 & [N II] 	& 1.00 & 1.00 & 1.01 & 1.01 \\
7136 &  [Ar III]  	& 1.00 & 0.99 & 1.03 & 1.01 \\
9532 &  [S III]  	& 1.02 & 1.00 & 1.02 & 1.01 \\
\tableline 
 & & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\
\cline{3-7} 
 & & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
1485 &  N IV]  	& 1.07\tablenotemark{a} & 1.01 & 1.03 & 1.00 & 0.97 \\
1549 & C IV 		& 1.00 & 0.96 & 0.82\tablenotemark{a} & 0.94 & 0.97 \\
1750 & N III] 	& 0.90 & \nodata & \nodata & \nodata & \nodata \\
1907 &  C III]  	& 0.96 & 1.01 & 1.12\tablenotemark{a} & 1.05 & 0.95 \\
1909\tablenotemark{b} &  C III]  	& 0.95 & 1.00 & 1.12\tablenotemark{a} & 1.04 & 0.96 \\
3727 & [O II] 	& 1.02 & \nodata & \nodata & \nodata & \nodata \\
3869 &  [Ne III]  	& 0.98 & 0.99 & 1.01 & 1.00 & 0.99 \\
4363\tablenotemark{b} &  [O III]  	& 0.83\tablenotemark{a} & 0.93 & 1.10 & 1.08\tablenotemark{a} & 0.93\tablenotemark{a} \\
4686 &  He II  	& 1.02\tablenotemark{a} & 1.06\tablenotemark{a} & 0.93\tablenotemark{a} & 0.99 & 0.47\tablenotemark{a} \\
4861 &  H$\beta$  	& 0.99 & 1.04\tablenotemark{a} & 0.89\tablenotemark{a} & 0.88\tablenotemark{a} & 1.08\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.02\tablenotemark{a} & 1.02\tablenotemark{a} & 1.07\tablenotemark{a} & 1.19\tablenotemark{a} & 1.02\tablenotemark{a} \\
5007 &  [O III]  	& 0.93\tablenotemark{a} & 0.93\tablenotemark{a} & 1.01 & 1.02\tablenotemark{a} & 0.93\tablenotemark{a} \\
5876 &  He I  	& 1.02 & \nodata & 0.97 & \nodata & 0.99 \\
Wave & & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\
\cline{3-7} 
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\
\tableline
7136 &  [Ar III]  	& 1.00 & 1.00 & 1.04 & 1.00 & 0.94 \\
9532 &  [S III]  	& 0.99 & 1.00 & 1.04 & 1.01 & 0.93 \\
\tableline
%\tablebreak
Wave & &  NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \\
\cline{3-6}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & \\
\tableline
1485 &  N IV]  	& 1.07 & 1.00 & 0.97 & 1.01 \\
1549 & C IV 		& 1.00 & 1.01 & 0.96 & 0.86\tablenotemark{a} \\
1750 & N III] 	& 0.91 & \nodata & \nodata & \nodata \\
1907 &  C III] 	& 0.98 & 0.97 & 0.98 & 0.98 \\
1909\tablenotemark{b} &  C III]  	& 0.97 & 0.97 & 0.99 & 0.93 \\
3727 & [O II] 	& \nodata & \nodata & 1.06 & \nodata \\
3869 &  [Ne III]  	& 0.96\tablenotemark{a} & 0.99 & 1.00 & 0.97 \\
4363\tablenotemark{b} &  [O III]  	& 0.91 & 0.90\tablenotemark{a} & 0.86\tablenotemark{a} & 0.80\tablenotemark{a} \\
4686 &  He II  	& 0.56\tablenotemark{a} & 0.95\tablenotemark{a} & 1.11\tablenotemark{a} & 1.13\tablenotemark{a} \\
4861 &  H$\beta$  	& 1.07\tablenotemark{a} & 1.08\tablenotemark{a} & 0.91\tablenotemark{a} & 1.20\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 0.98\tablenotemark{a} & 1.01\tablenotemark{a} & 1.00 & 0.73\tablenotemark{a} \\
5007 &  [O III]  	& 0.93\tablenotemark{a} & 0.92\tablenotemark{a} & 0.87\tablenotemark{a} & 0.72\tablenotemark{a} \\
5876 &  He I  	& 0.95 & 0.99 & 1.03 & \nodata \\
7136 &  [Ar III]  	& 0.97 & 0.99 & 0.97 & \nodata \\
9532 &  [S III]  	& 0.97 & 1.00 & 0.98 & \nodata \\
\enddata
\tablenotetext{a}{Modeled emission line intensity outside observed error bar.}
\tablenotetext{b}{This line was only included in a diagnostic for the rms calculation for reasons discussed in the text.}
\tablenotetext{c}{Blended 1907 and 1909.}
\end{deluxetable}
\end{landscape}
\begin{landscape}
\begin{deluxetable}{clcccccc}
\tabletypesize{\footnotesize}
\setlength{\tabcolsep}{0.07in}
\tablewidth{0in}
%\rotate
\tablecaption{Non-constant Density Model Emission Lines Compared to Observations For Full Regions\label{nmodline1}}
\tablehead{
\multicolumn{8}{c}{Non-constant Density Model Emission Lines Compared to Observations For Full Regions}
}
\startdata
 & & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
\cline{3-8}
 & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Wave & & & power-law & & power-law & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
\tableline
1485 &  N IV]  	& 1.00 & 1.00 & \nodata & \nodata & 0.77\tablenotemark{a} & 0.77\tablenotemark{a}\\
1549 & C IV 		& \nodata & \nodata & 1.01 & 1.01 & \nodata & \nodata \\
1907 &  C III]  	& 1.04 & 1.06 & 0.99 & 0.99 & 1.02 & 1.00  \\  
1909\tablenotemark{b} &  C III]  	& 1.12\tablenotemark{a} & 1.14\tablenotemark{a} & 1.08 & 1.06 & 1.04 & 1.02 \\
3727 &  [O II]  	& \nodata & \nodata & \nodata & \nodata & 0.83\tablenotemark{a} & 0.83\tablenotemark{a} \\  
3869 &  [Ne III]  	& 1.00 & 1.00 & 0.99 & 0.99 & 0.99 & 1.02\\
4363\tablenotemark{b} &  [O III]  	& 1.13\tablenotemark{a} & 1.15\tablenotemark{a} & 1.05 & 0.99 & 1.06 & 1.04 \\ 
4686 &  He II  	& 0.99 & 1.00 & \nodata & \nodata & 1.12\tablenotemark{a} & 1.10\tablenotemark{a} \\
4861 &  H$\beta$  	& 0.97\tablenotemark{a} & 0.98 & 0.99 & 1.02 & 1.03 & 1.02\\
4959\tablenotemark{b} &  [O III]  	& 1.08\tablenotemark{a} & 1.09\tablenotemark{a} & 1.19\tablenotemark{a} & 1.12\tablenotemark{a} & 1.10\tablenotemark{a} & 1.07\tablenotemark{a} \\ 
5007 &  [O III]  	& 1.06\tablenotemark{a} & 1.07\tablenotemark{a} & 1.06\tablenotemark{a} & 1.00 & 1.08\tablenotemark{a} & 1.06\tablenotemark{a}\\ 
5876 &  He I  	& 0.98 & 0.99 & 0.99 & 1.00 & 1.03 & 1.02 \\  
6584 &  [N II]	& \nodata & \nodata & \nodata & \nodata & 1.16\tablenotemark{a} & 1.16\tablenotemark{a} \\
7136 &  [Ar III]  	& 1.00 & 0.99 & 0.99 & 1.00 & 1.08\tablenotemark{a} & 1.07\tablenotemark{a} \\
9532 &  [S III]  	& 1.00 & 0.99 & \nodata & \nodata & 1.05\tablenotemark{a} & 1.04 \\ 
\tableline
\tablebreak
 & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC3242 Full}\\
\cline{3-8}
 & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
 Wave & & & power-law & & power-law & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
\tableline
1485 &  N IV] 	& \nodata & \nodata & \nodata & \nodata & 1.00 & 1.00 \\
1549 & C IV 		& 1.00 & 0.99 & 1.00 & 1.16 & \nodata & \nodata \\
1907 &  C III]  	& 0.99 & 0.99 & 1.00 & 1.00 & 1.10\tablenotemark{a} & 1.11\tablenotemark{a} \\
1909\tablenotemark{b} &  C III]  	& 1.07\tablenotemark{a} & 1.07\tablenotemark{a} & 1.00 & 0.99 & 1.10\tablenotemark{a} & 1.11\tablenotemark{a} \\
3727 & [O II] 	& \nodata & \nodata & \nodata & \nodata & 0.95 & 0.90 \\
3869 &  [Ne III]  	& 1.00 & 0.99 & 1.03 & 1.07\tablenotemark{a} & 1.05\tablenotemark{a} & 1.02 \\
4363\tablenotemark{b} &  [O III]  	& 1.05 & 1.02 & 1.12 & 1.14 & 1.13\tablenotemark{a} & 1.18\tablenotemark{a} \\
4686 &  He II  	& \nodata & \nodata & 0.99 & 0.96 & 0.90\tablenotemark{a} & 0.93\tablenotemark{a} \\
4861 &  H$\beta$  	& 1.03\tablenotemark{a} & 1.04\tablenotemark{a} & 0.81\tablenotemark{a} & 0.86\tablenotemark{a} & 0.92\tablenotemark{a} & 0.94\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.01\tablenotemark{a} & 1.00 & 1.32\tablenotemark{a} & 1.37\tablenotemark{a} & 1.09\tablenotemark{a} & 1.12\tablenotemark{a}\\
5007 &  [O III]  	& 0.99\tablenotemark{a} & 0.98\tablenotemark{a} & 1.11\tablenotemark{a} & 1.16\tablenotemark{a} & 1.11\tablenotemark{a} & 1.13\tablenotemark{a} \\
5876 &  He I  	& 1.01 & 1.00 & 0.99 & 1.05\tablenotemark{a} & 0.92\tablenotemark{a} & 0.95 \\
6584 & [N II] 	& \nodata & \nodata & 1.00 & 0.98 & \nodata & \nodata \\
7136 &  [Ar III]  	& 0.98\tablenotemark{a} & 1.00\tablenotemark{a} & 1.00 & 0.99 & 1.00 & 1.03 \\
% & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{3-8}
% & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Wave & & & power-law & & power-law & & power-law \\ 
%\cline{3-8}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
%\tableline
9532 &  [S III]  	& 0.95\tablenotemark{a} & 0.95\tablenotemark{a} & 1.01 & 1.01 & 1.02 & 1.03 \\
\tableline
\tablebreak
 & & \multicolumn{2}{c}{NGC7662 Full} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{}\\
\cline{3-8}
 & & Gaussian & Gaussian With \\
Wave  & & & power-law \\ 
\cline{3-8}
(\AA) & ID & Model/Observed & Model/Observed  \\ 
\tableline
1485 &  N IV] 	& 1.02 & 1.02 \\
1549 & C IV 		& 0.93\tablenotemark{a} & 0.91\tablenotemark{a} \\
1750 & N III] 	& 1.00 & 0.99 \\
1907 &  C III]  	& 1.04 & 1.04 \\
1909\tablenotemark{b} &  C III]  	& 1.06\tablenotemark{a} & 1.07\tablenotemark{a} \\
3727 & [O II] 	& 0.90 & 0.90 \\
3869 &  [Ne III]  	& 1.00 & 1.01 \\
4363\tablenotemark{b} &  [O III]  	& 0.91\tablenotemark{a} & 0.92\tablenotemark{a} \\
4686 &  He II  	& 1.04\tablenotemark{a} & 1.03\tablenotemark{a} \\
4861 &  H$\beta$  	& 0.97\tablenotemark{a} & 0.99\tablenotemark{a} \\
4959\tablenotemark{b} &  [O III]  	& 1.07\tablenotemark{a} & 1.09\tablenotemark{a}\\
5007 &  [O III]  	& 0.98\tablenotemark{a} & 0.99 \\
5876 &  He I  	& 1.03 & 1.02 \\
7136 &  [Ar III]  	& 1.00 & 1.00 \\
% & & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{3-8}
% & & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Wave & & & power-law & & power-law & & power-law \\ 
%\cline{3-8}
%(\AA) & ID & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed & Model/Observed \\ 
%\tableline
9532 &  [S III]  	& 1.00 & 1.01 \\
\enddata
\tablenotetext{a}{Modeled emission line intensity outside observed error bar.}
\tablenotetext{b}{This line was only included in a diagnostic for the rms calculation for reasons discussed in the text.}
\end{deluxetable}
\end{landscape}

Table~\ref{condenmods1} contains the best parameter values and associated errors for the constant density models.  Names of the stellar and nebular parameters that were used in the modeling are in the first column along with the values for each region in the subsequent columns. After the modeling parameters are the nebular temperatures, densities, ionization correction factors, and rms values for each region. For most of the regions, the model rms is below the observed rms, implying a good fit. The smallest model rms of 0.0063 from the full region of IC 2165 shows that the assumed model represented that region's structure quite well. In most cases, the modeled temperatures and densities of the gas are within the observed errors. Also, the model abundances for the regions agree within error with the observed abundances in most cases. The asymmetry in the errors is due to the $1-\frac{model}{observed}$ term in the equation for the rms having a lower bound of 1. The errors in stellar temperature and luminosity and nebular abundances are inversely related to overall signal strength in the emission lines, where the larger error corresponds to overall weaker signal strength.
\begin{landscape}
\begin{deluxetable}{cccccc}
\tabletypesize{\footnotesize}
\tablewidth{0in}
%%%\rotate
\tablecaption{Constant Density Models\label{condenmods1}}
\tablehead{
\multicolumn{6}{c}{Constant Density Models}
}
\startdata
Parameter & IC2165 Full & IC2165 1 & IC2165 2 & IC2165 3 & IC2165 4 \\
\tableline
$T_{star}$ (kK) & 110.0$^{+7.0}_{-17.0}$ & 110.0 & 110.0 & 110.0& 110.0  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.17$^{+0.20}_{-0.14}$ & 3.17 & 3.17 & 3.17 & 3.17  \\
$H_{den}$ (log[$H_{density}$]) & 3.79$^{+0.02}_{-0.03}$ & 3.75$^{+0.04}_{-0.04}$ & 4.06$^{+0.05}_{-0.07}$ & 3.70$^{+0.04}_{-0.04}$ & 3.75$^{+0.04}_{-0.05}$ \\
Inner Radius ($10^{-2}$pc) & 2.60$^{+0.06}_{-0.06}$ & 2.56$^{+0.11}_{-0.15}$ & 2.60$^{+0.05}_{-0.04}$ & 2.38$^{+0.15}_{-0.16}$ & 2.47$^{+0.13}_{-0.13}$ \\
Outer Radius ($10^{-2}$pc) & 3.09$^{+0.05}_{-0.05}$ & 3.09$^{+0.08}_{-0.07}$ & 2.73$^{+0.04}_{-0.05}$ & 3.11$^{+0.12}_{-0.11}$ & 2.96$^{+0.12}_{-0.12}$ \\
Filling Factor ($10^{-1}$) & 9.89$^{+0.11}_{-0.99}$ & 10.00$^{+0.00}_{-0.16}$ & 9.49$^{+0.51}_{-2.97}$ & 10.00$^{+0.00}_{-0.17}$ & 10.0$^{+0.00}_{-0.25}$ \\
He/H ($10^{-2}$) & 10.28$^{+1.41}_{-1.29}$ & 11.07$^{+2.58}_{-2.03}$ & 10.26$^{+4.20}_{-5.03}$ & 10.33$^{+2.55}_{-2.01}$ & 10.47$^{+3.33}_{-3.23}$ \\
C/H ($10^{-4}$) & 4.57$^{+2.41}_{-1.59}$ & 4.75$^{+5.55}_{-2.63}$ & 2.86$^{+5.15}_{-2.16}$ & 4.35$^{+4.78}_{-2.30}$ & 3.80$^{+5.97}_{-2.45}$ \\
N/H ($10^{-4}$) & 1.10$^{+0.43}_{-0.43}$ & 0.78$^{+0.56}_{-0.55}$ & 1.38$^{+1.52}_{-1.35}$ & 0.94$^{+0.34}_{-0.66}$ & 0.95$^{+0.91}_{-0.87}$ \\
O/H ($10^{-4}$) & 2.69$^{+0.91}_{-0.80}$ & 2.89$^{+1.95}_{-1.49}$ & 1.75$^{+1.80}_{-1.38}$ & 2.68$^{+1.89}_{-1.42}$ & 2.82$^{+2.43}_{-1.84}$ \\
Ne/H ($10^{-5}$) & 3.39$^{+1.32}_{-1.31}$ & 3.70$^{+2.70}_{-2.63}$ & 2.10$^{+2.14}_{-2.06}$ & 2.98$^{+2.15}_{-2.07}$ & 2.90$^{+2.72}_{-2.65}$ \\
S/H ($10^{-6}$) & 3.73$^{+1.42}_{-1.44}$ & 3.56$^{+2.53}_{-2.50}$ & 2.15$^{+2.11}_{-2.11}$ & 5.19$^{+3.72}_{-3.57}$ & 4.44$^{+4.08}_{-4.02}$ \\
Ar/H ($10^{-7}$) & 20.09$^{+7.58}_{-7.76}$ & 24.89$^{+17.77}_{-17.48}$ & 9.86$^{+9.86}_{-9.68}$ & 26.06$^{+17.6}_{-18.12}$ & 24.66$^{+22.65}_{-22.47}$ \\
\tableline
[O III] $T_{e}$ (K) & 13500 & 13900 & 14800 & 13700 & 14100 \\
\[[S II] N$_{e}$($cm^{-3}$) & 7900 & \nodata & \nodata & \nodata & \nodata \\
C III] $N_{e}$ ($cm^{-3}$) & 7200 & 6600 & 14000 & 5800 & 6700 \\
icf (O)  & 1.55 & 1.54 & 1.53 & 1.82 & 1.92 \\
icf (Ar)  & 1.30 & 1.30 & 1.25 & 1.36 & 1.37 \\
icf (Ne)  & 1.22 & 1.21 & 1.18 & 1.38 & 1.41 \\
icf (S)  & 4.30 & 4.43 & 3.30 & 6.07 & 5.98 \\
Model RMS ($10^{-2}$)  & 0.63 & 4.00 & 7.00 & 2.13 & 6.86 \\
Observed RMS ($10^{-2}$)  & 9.35 & 14.53 & 19.35 & 15.8 & 17.69\\
\tableline
%\tablebreak
 & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
\tableline
$T_{star}$ (kK) & 110.0 & 110.0 & 69.6$^{+15.0}_{-18.3}$ & 69.6 & 69.6 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.17 & 3.17 & 3.52$^{+0.74}_{-0.38}$ & 3.52 & 3.52 \\
$H_{den}$ (log[$H_{density}$]) & 3.62$^{+0.03}_{-0.03}$ & 3.99$^{+0.09}_{-0.18}$ & 3.70$^{+0.05}_{-0.05}$ & 3.76$^{+0.06}_{-0.08}$ & 3.59$^{+0.06}_{-0.08}$ \\
Inner Radius ($10^{-2}$pc) & 1.80$^{+0.24}_{-0.37}$ & 3.15$^{+0.23}_{-0.91}$ & 3.55$^{+0.08}_{-0.09}$ & 3.44$^{+0.09}_{-0.09}$ & 3.97$^{+0.21}_{-0.20}$ \\
Outer Radius ($10^{-2}$pc) & 3.32$^{+0.12}_{-0.11}$ & 3.57$^{+0.06}_{-0.07}$ & 3.93$^{+0.09}_{-0.08}$ & 3.74$^{+0.10}_{-0.10}$ & 4.66$^{+0.24}_{-0.23}$ \\
Filling Factor ($10^{-1}$) & 9.92$^{+0.08}_{-1.32}$ & 9.64$^{+0.36}_{-5.54}$ & 10.00$^{+0.00}_{-2.20}$ & 9.88$^{+0.12}_{-3.03}$ & 9.96$^{+0.04}_{-3.16}$ \\
Parameter & IC2165 5 & IC2165 6 & IC3568 Full & IC3568 1 & IC3568 2 \\
\tableline
He/H ($10^{-2}$) & 9.18$^{+1.78}_{-1.42}$ & 7.59$^{+9.40}_{-7.59}$ & 9.71$^{+4.42}_{-4.46}$ & 10.89$^{+6.89}_{-7.34}$ & 8.53$^{+5.59}_{-5.58}$ \\
C/H ($10^{-4}$) & 5.85$^{+5.63}_{-2.83}$ & 38.73$^{+212.46}_{-28.25}$ & 5.47$^{+2.85}_{-2.38}$ & 2.85$^{+2.05}_{-1.73}$ & 7.08$^{+5.51}_{-4.13}$ \\
N/H ($10^{-4}$) & 0.81$^{+0.54}_{-0.50}$ & 0.89$^{+105.96}_{-0.89}$ & \nodata & \nodata & \nodata \\
O/H ($10^{-4}$) & 2.54$^{+1.54}_{-1.19}$ & 5.31$^{+12.47}_{-4.71}$ & 4.72$^{+1.30}_{-0.92}$ & 4.25$^{+1.78}_{-1.01}$ & 5.02$^{+2.23}_{-1.21}$ \\
Ne/H ($10^{-5}$) & 4.27$^{+2.81}_{-2.64}$ & 10.94$^{+20.68}_{-10.94}$ & 8.05$^{+4.83}_{-4.34}$ & 2.02$^{+1.69}_{-1.57}$ & 9.14$^{+8.24}_{-6.90}$ \\
S/H ($10^{-6}$) & 5.05$^{+3.27}_{-3.10}$ & 2.30$^{+3.73}_{-2.30}$ & \nodata & \nodata & \nodata \\
Ar/H ($10^{-7}$) & 20.84$^{+6.07}_{-12.72}$ & 12.25$^{+20.11}_{-12.25}$ & 17.22$^{+9.39}_{-9.46}$ & 16.33$^{+13.18}_{-12.70}$ & 15.89$^{+12.95}_{-12.50}$ \\
\tableline
[O III] $T_{e}$ (K) & 12800 & 9500 & 10000 & 10800 & 9600 \\
C III] $N_{e}$ ($cm^{-3}$) & 4600 & 11100 & 5600 & 6500 & 4200 \\
icf (O)  & 1.31 & 1.02 & 1.07 & 1.08 & 1.07 \\
icf (Ar)  & 1.28 & 1.05 & 1.28 & 1.25 & 1.28 \\
icf (Ne)  & 1.10 & 0.91 & 0.94 & 0.94 & 0.93 \\
icf (S)  & 4.41 & 1.52 & \nodata & \nodata & \nodata \\
Model RMS ($10^{-2}$)  & 5.09 & 7.93 & 1.70 & 4.42 & 2.04 \\
Observed RMS ($10^{-2}$)  & 11.40 & 32.67 & 13.39 & 17.49 & 19.79 \\
\tableline
%\tablebreak
 & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
\tableline
$T_{star}$ (kK) & 69.6 & 169.8$^{+20.2}_{-17.7}$ & 169.8 & 169.8 & 169.8 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.52 & 2.74$^{+0.04}_{-0.04}$ & 2.74 & 2.74 & 2.74 \\
$H_{den}$ (log[$H_{density}$]) & 3.77$^{+0.11}_{-0.25}$ & 3.69$^{+0.02}_{-0.02}$ & 3.40$^{+0.03}_{-0.03}$ & 3.95$^{+0.08}_{-0.15}$ & 3.80$^{+0.03}_{-0.03}$ \\
Inner Radius ($10^{-2}$pc) & 3.83$^{+0.14}_{-3.83}$ & 2.30$^{+0.70}_{-1.20}$ & 3.86$^{+0.94}_{-1.06}$ & 2.46$^{+0.36}_{-0.86}$ & 2.28$^{+0.58}_{-0.78}$ \\
Outer Radius ($10^{-2}$pc) & 4.01$^{+0.10}_{-0.12}$ & 5.14$^{+0.12}_{-0.14}$ & 7.54$^{+0.50}_{-0.45}$ & 2.93$^{+0.12}_{-0.15}$ & 4.13$^{+0.16}_{-0.18}$ \\
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-7.00}$ & 1.76$^{+0.14}_{-0.16}$ & 3.01$^{+0.48}_{-0.44}$ & 2.42$^{+1.25}_{-1.40}$ & 2.09$^{+0.26}_{-0.30}$ \\
He/H ($10^{-2}$) & 9.73$^{+12.15}_{-9.73}$ & 12.27$^{+1.85}_{-2.04}$ & 14.93$^{+3.44}_{-3.34}$ & 12.25$^{+19.38}_{-5.94}$ & 11.40$^{+2.72}_{-2.69}$ \\
C/H ($10^{-4}$) & 24.89$^{+56.39}_{-24.89}$ & 2.54$^{+1.26}_{-1.06}$ & 3.56$^{+3.36}_{-2.33}$ & 1.08$^{+2.90}_{-1.08}$ & 2.45$^{+2.33}_{-1.62}$ \\
N/H ($10^{-4}$) & \nodata & 6.71$^{+2.00}_{-1.93}$ & 8.71$^{+4.78}_{-3.81}$ & 3.41$^{+4.91}_{-3.41}$ & 6.34$^{+3.43}_{-2.95}$ \\
O/H ($10^{-4}$) & 7.96$^{+31.85}_{-4.65}$ & 2.90$^{+0.77}_{-0.72}$ & 4.06$^{+2.10}_{-1.49}$ & 1.07$^{+1.22}_{-1.07}$ & 2.53$^{+1.10}_{-0.98}$ \\
Ne/H ($10^{-5}$) & 11.53$^{+25.62}_{-11.53}$ & 4.02$^{+1.61}_{-1.62}$ & 7.50$^{+5.38}_{-4.87}$ & 0.92$^{+1.71}_{-0.92}$ & 3.16$^{+2.09}_{-1.98}$ \\
S/H ($10^{-6}$) & \nodata & 1.64$^{+0.65}_{-0.64}$ & 2.09$^{+1.38}_{-1.33}$ & 0.59$^{+1.07}_{-0.59}$ & 1.37$^{+0.86}_{-0.85}$ \\
Ar/H ($10^{-7}$) & 24.38$^{+41.69}_{-24.38}$ & 14.96$^{+6.17}_{-5.84}$ & 23.44$^{+15.46}_{-14.93}$ & 7.59$^{+13.79}_{-7.59}$ & 12.79$^{+8.10}_{-8.01}$ \\
Parameter & IC3568 3 & NGC2440 Full & NGC2440 1 & NGC2440 2 & NGC2440 3 \\
\tableline
[O III] $T_{e}$ (K) & 8800 & 14400 & 13300 & 16900 & 14600 \\
\[[S II] N$_{e}$($cm^{-3}$) & \nodata & 6400 & 3400 & \nodata & 8200 \\
C III] $N_{e}$ ($cm^{-3}$) & 6700 & 5800 & 2800 & 11300 & 7600 \\
icf (O)  & 1.08 & 1.60 & 1.46 & 2.05 & 1.54 \\
icf (Ar)  & 1.26 & 1.21 & 1.24 & 1.39 & 1.20 \\
icf (Ne)  & 0.95 & 1.46 & 1.45 & 0.17 & 1.39 \\
icf (S)  & \nodata & 1.83 & 1.66 & 2.53 & 1.80 \\
Model RMS ($10^{-2}$)  & 1.00 & 1.49 & 8.45 & 9.20 & 6.97 \\
Observed RMS ($10^{-2}$)  & 49.97 & 7.44 & 8.35 & 35.57 & 8.75 \\
\tableline
%\tablebreak
 & NGC3242 Full & NGC3242 1 & NGC3242 2 & NGC3242 3 & NGC3242 4 \\
\tableline
$T_{star}$ (kK) & $89.7^{+7.3}_{-4.7}$ & $89.7$ & $89.7$ & $89.7$ & $89.7$  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & $3.36^{+0.28}_{-0.22}$ & $3.36$ & $3.36$ & $3.36$ & $3.36$  \\
$H_{den}$ (log[$H_{density}$]) & 3.62$^{+0.04}_{-0.06}$ & 3.25$^{+0.06}_{-0.06}$ & 3.77$^{+0.04}_{-0.03}$ & 3.50$^{+0.06}_{-0.07}$ & 3.50$^{+0.06}_{-0.07}$ \\
Inner Radius ($10^{-2}$pc) & 1.86$^{+0.74}_{-1.86}$ & 2.04$^{+1.36}_{-2.04}$ & 3.33$^{+0.12}_{-0.16}$ & 2.52$^{+0.48}_{-0.82}$ & 1.96$^{+0.74}_{-1.96}$ \\
Outer Radius ($10^{-2}$pc) & 3.80$^{+0.30}_{-0.30}$ & 10.50$^{+2.90}_{-2.40}$ & 3.90$^{+0.13}_{-0.09}$ & 4.59$^{+0.81}_{-0.59}$ & 10.20$^{+2.60}_{-2.10}$ \\
Filling Factor ($10^{-1}$) & 4.36$^{+1.14}_{-1.06}$ & 4.39$^{+1.31}_{-1.19}$ & 4.80$^{+1.00}_{-0.90}$ & 5.93$^{+1.77}_{-1.63}$ & 1.56$^{+0.54}_{-0.46}$ \\
He/H ($10^{-2}$) & 10.45$^{+4.34}_{-3.03}$ & 11.53$^{+4.34}_{-3.38}$ & 11.02$^{+3.11}_{-2.31}$ & 10.30$^{+4.15}_{-3.39}$ & 9.57$^{+4.23}_{-3.95}$ \\
C/H ($10^{-4}$) & 5.97$^{+7.52}_{-3.73}$ & 4.85$^{+4.92}_{-3.50}$ & 3.67$^{+2.35}_{-1.89}$ & 5.01$^{+5.46}_{-3.19}$ & 4.10$^{+4.03}_{-2.32}$ \\
O/H ($10^{-4}$) & 4.70$^{+2.71}_{-1.81}$ & 4.26$^{+2.35}_{-1.30}$ & 3.76$^{+1.25}_{-0.94}$ & 3.76$^{+2.41}_{-1.57}$ & 4.21$^{+2.55}_{-1.58}$ \\
Ne/H ($10^{-5}$) & 7.40$^{+6.73}_{-6.24}$ & 7.78$^{+7.36}_{-6.37}$ & 6.40$^{+3.60}_{-3.24}$ & 6.19$^{+5.03}_{-4.72}$ & 6.90$^{+5.40}_{-5.04}$ \\
\tableline
[O III] $T_{e}$ (K) & 11800 & 11100 & 11600 & 11800 & 11800 \\
C III] $N_{e}$ ($cm^{-3}$) & 4600 & 1500 & 6800 & 3500 & 3600 \\
icf (O)  & 1.57 & 1.13 & 1.22 & 1.56 & 1.51 \\
icf (Ne)  & 1.24 & 1.00 & 1.03 & 1.18 & 1.18 \\
Model RMS ($10^{-2}$)  & 6.26 & 2.40 & 3.75 & 4.46 & 1.63 \\
Observed RMS ($10^{-2}$)  & 15.02 & 20.91 & 10.68 & 17.06 & 18.57 \\
\tableline
 & NGC3242 5 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 \\
\tableline
$T_{star}$ (kK) & $89.7$ & $89.7$ & $89.7$ & $89.7$ & $89.7$  \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & $3.36$ & $3.36$ & $3.36$ & $3.36$ & $3.36$  \\
Parameter & NGC3242 5 & NGC3242 6 & NGC3242 7 & NGC3242 8 & NGC3242 9 \\
\tableline
$H_{den}$ (log[$H_{density}$]) & 3.60$^{+0.05}_{-0.06}$ & 3.60$^{+0.05}_{-0.06}$ & 3.90$^{+0.04}_{-0.04}$ & 3.55$^{+0.05}_{-0.06}$ & 3.25$^{+0.06}_{-0.07}$ \\
Inner Radius ($10^{-2}$pc) & 2.52$^{+0.48}_{-0.32}$ & 1.88$^{+0.52}_{-1.88}$ & 2.02$^{+0.08}_{-0.12}$ & 2.98$^{+0.22}_{-0.28}$ & 3.56$^{+0.84}_{-3.56}$ \\
Outer Radius ($10^{-2}$pc) & 4.21$^{+0.69}_{-0.41}$ & 6.49$^{+1.31}_{-0.96}$ & 2.52$^{+0.08}_{-0.12}$ & 3.72$^{+0.28}_{-0.22}$ & 8.40$^{+1.90}_{-1.50}$ \\
Filling Factor ($10^{-1}$) & 3.77$^{+1.03}_{-0.97}$ & 1.52$^{+0.48}_{-0.42}$ & 4.53$^{+0.87}_{-0.83}$ & 1.00$^{+0.00}_{-0.27}$ & 4.34$^{+1.36}_{-1.34}$ \\
He/H ($10^{-2}$) & 10.12$^{+3.69}_{-2.87}$ & 9.20$^{+3.68}_{-3.32}$ & 9.29$^{+2.19}_{-1.88}$ & 7.69$^{+2.78}_{-2.56}$ & 10.50$^{+4.64}_{-4.04}$ \\
C/H ($10^{-4}$) & 6.30$^{+6.29}_{-2.39}$ & 5.60$^{+5.12}_{-3.09}$ & 4.47$^{+4.04}_{-2.65}$ & 3.51$^{+3.91}_{-2.36}$ & 4.81$^{+5.19}_{-3.15}$ \\
O/H ($10^{-4}$) & 5.30$^{+2.65}_{-1.75}$ & 5.08$^{+2.68}_{-1.84}$ & 3.77$^{+1.60}_{-1.14}$ & 3.30$^{+1.94}_{-1.35}$ & 4.54$^{+2.38}_{-1.59}$ \\
Ne/H ($10^{-5}$) & 7.93$^{+6.20}_{-5.74}$ & 8.07$^{+6.38}_{-5.67}$ & 5.85$^{+3.92}_{-3.71}$ & 5.48$^{+4.52}_{-4.10}$ & 7.38$^{+6.42}_{-5.72}$ \\
\tableline
[O III] $T_{e}$ (K)  & 11500 & 11700 & 11700 & 11900 & 11500 \\
C III] $N_{e}$ ($cm^{-3}$) & 4500 & 4400 & 9200 & 3900 & 1600 \\
icf (O)  & 1.54 & 1.74 & 1.35 & 1.46 & 1.46 \\
icf (Ne)  & 1.19 & 1.30 & 1.09 & 1.07 & 1.16 \\
Model RMS ($10^{-2}$)  & 4.03 & 1.67 & 2.63 & 9.90 & 3.22 \\
Observed RMS ($10^{-2}$)  & 16.46 & 17.63 & 15.16 & 13.12 & 18.50 \\
\tableline
 & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\tableline
$T_{star}$ (kK) & 69.9$^{+6.5}_{-2.1}$ &  69.9 &  69.9 &  69.9 &  69.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 4.89$^{+0.16}_{-0.15}$ & 4.89 & 4.89 & 4.89 & 4.89 \\
$H_{den}$ (log[$H_{density}$]) & 4.71$^{+0.02}_{-0.02}$ & 4.76$^{+0.04}_{-0.05}$ & 4.72$^{+0.02}_{-0.02}$ & 4.71$^{+0.03}_{-0.03}$ & 4.53$^{+0.06}_{-0.09}$ \\
Inner Radius ($10^{-2}$pc) & 1.31$^{+0.01}_{-0.01}$ & 1.56$^{+0.03}_{-0.04}$ & 1.88$^{+0.01}_{-0.01}$ & 2.13$^{+0.01}_{-0.01}$ & 1.89$^{+0.25}_{-0.72}$ \\
Outer Radius ($10^{-2}$pc) & 1.46$^{+0.01}_{-0.01}$ & 1.63$^{+0.02}_{-0.02}$ & 1.98$^{+0.01}_{-0.01}$ & 2.15$^{+0.01}_{-0.01}$ & 2.33$^{+0.09}_{-0.11}$ \\
Filling Factor ($10^{-1}$) & 9.59$^{+0.41}_{-0.71}$ & 2.39$^{+0.58}_{-0.60}$ & 9.43$^{+0.57}_{-0.63}$ & 8.77$^{+1.23}_{-1.41}$ & 0.45$^{+0.18}_{-0.18}$ \\
He/H ($10^{-2}$) & 11.40$^{+1.78}_{-2.07}$ & 11.99$^{+5.38}_{-5.98}$ & 13.21$^{+2.28}_{-2.25}$ & 16.29$^{+4.60}_{-4.81}$ & 16.48$^{+10.43}_{-11.80}$ \\
C/H ($10^{-4}$) & 16.44$^{+3.51}_{-2.64}$ & 19.82$^{+11.09}_{-10.04}$ & 9.77$^{+1.71}_{-1.64}$ & 14.49$^{+5.01}_{-4.72}$ & 100.69$^{+50.66}_{-63.54}$ \\
%N/H ($10^{-5}$) & 5.74$^{+}_{-}$ & 2.12$^{+}_{-}$ & 11.89$^{+}_{-}$ & 11.91$^{+}_{-}$ & 1.87$^{+}_{-}$ \\
O/H ($10^{-4}$) & 6.31$^{+1.10}_{-0.81}$ & 6.81$^{+3.91}_{-2.24}$ & 7.46$^{+1.05}_{-0.86}$ & 9.93$^{+2.95}_{-1.80}$ & 15.31$^{+14.89}_{-6.40}$ \\
Ne/H ($10^{-5}$) & 14.59$^{+3.61}_{-3.37}$ & 10.79$^{+7.83}_{-7.07}$ & 18.24$^{+4.67}_{-4.11}$ & 18.97$^{+9.22}_{-8.25}$ & 3.33$^{+4.44}_{-3.04}$ \\
S/H ($10^{-6}$) & 421.70$^{+35.39}_{-32.65}$ & 287.08$^{+101.97}_{-82.90}$ & 248.89$^{+26.54}_{-25.01}$ & 245.47$^{+56.52}_{-41.30}$ & 314.05$^{+132.63}_{-95.27}$ \\
Ar/H ($10^{-7}$) & 954.99$^{+219.90}_{-196.42}$ & 743.02$^{+487.25}_{-447.90}$ & 603.95$^{+137.36}_{-136.21}$ & 623.73$^{+267.52}_{-252.20}$ & 961.61$^{+1033.65}_{-936.49}$ \\
\tableline
[O III] $T_{e}$ (K) & 8800 & 9600 & 8900 & 8600 & 7500 \\
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \nodata & 20000\tablenotemark{a} & 20000\tablenotemark{a} \\
Parameter & NGC5315 Full & NGC5315 1 & NGC5315 2 & NGC5315 3 & NGC5315 4 \\
\tableline
C III] $N_{e}$ ($cm^{-3}$) & 64000 & 73400 & 66300 & 67200 & 45400 \\
icf (O)  & 1.36 & 1.70 & 1.31 & 1.50 & 1.55 \\
icf (Ar)  & 1.96 & 2.23 & 1.85 & 2.03 & 1.52 \\
icf (Ne)  & 1.21 & 1.46 & 1.18 & 1.34 & 1.35 \\
icf (S)  & 47.27 & 38.16 & 21.26 & 20.11 & 29.07 \\
Model RMS ($10^{-2}$)  & 2.23 & 0.93 & 3.16 & 5.19 & 3.80 \\
Observed RMS ($10^{-2}$)  & 3.90 & 16.53 & 3.53 & 7.06 & 23.73 \\
\tableline
%\tablebreak
 & NGC5882 Full & NGC5882 1 & NGC5882 2 & NGC5882 3 & \\
\tableline
$T_{star}$ (kK) & 78.7$^{+3.3}_{-7.0}$ & 78.7 & 78.7 & 78.7 & \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.45$^{+0.20}_{-0.14}$ & 3.45 & 3.45 & 3.45 & \\
$H_{den}$ (log[$H_{density}$]) & 4.34$^{+0.05}_{-0.06}$ & 4.35$^{+0.05}_{-0.07}$ & 4.35$^{+0.04}_{-0.06}$ & 4.35$^{+0.06}_{-0.15}$ & \\
Inner Radius ($10^{-2}$pc) & 2.72$^{+0.03}_{-0.03}$ & 2.75$^{+0.03}_{-0.03}$ & 2.71$^{+0.03}_{-0.03}$ & 2.25$^{+0.63}_{-0.76}$ & \\
Outer Radius ($10^{-2}$pc) & 2.81$^{+0.03}_{-0.03}$ & 2.83$^{+0.03}_{-0.03}$ & 2.80$^{+0.03}_{-0.03}$ & 2.96$^{+0.08}_{-0.10}$ & \\
Filling Factor ($10^{-1}$) & 3.47$^{+0.94}_{-0.87}$ & 2.47$^{+0.76}_{-0.72}$ & 3.14$^{+0.78}_{-0.76}$ & 2.91$^{+0.95}_{-1.49}$ & \\
He/H ($10^{-2}$) & 12.59$^{+6.71}_{-5.39}$ & 12.19$^{+7.76}_{-6.02}$ & 12.97$^{+6.53}_{-5.39}$ & 11.35$^{+13.77}_{-11.35}$ & \\
C/H ($10^{-4}$) & 4.19$^{+3.72}_{-3.34}$ & 2.37$^{+1.90}_{-1.73}$ & 6.30$^{+3.70}_{-3.66}$ & 9.33$^{+16.37}_{-9.33}$ & \\
N/H ($10^{-4}$) & 2.89$^{+2.76}_{-2.78}$ & 4.28$^{+3.67}_{-3.65}$ & 1.43$^{+0.97}_{-1.01}$ & 1.48$^{+2.41}_{-1.48}$ & \\
O/H ($10^{-4}$) & 12.82$^{+6.13}_{-3.15}$ & 11.86$^{+6.34}_{-2.95}$ & 13.77$^{+5.28}_{-2.81}$ & 16.14$^{+31.72}_{-5.18}$ & \\
Ne/H ($10^{-5}$) & 23.23$^{+24.78}_{-19.43}$ & 19.05$^{+19.85}_{-15.16}$ & 29.04$^{+22.25}_{-18.08}$ & 3.08$^{+7.16}_{-3.08}$ & \\
S/H ($10^{-6}$) & 7.85$^{+6.94}_{-5.82}$ & 8.30$^{+7.55}_{-6.92}$ & 7.33$^{+4.97}_{-5.09}$ & 7.36$^{+12.14}_{-7.36}$ & \\
Ar/H ($10^{-7}$) & 38.90$^{+35.19}_{-35.04}$ & 36.81$^{+33.98}_{-31.32}$ & 40.46$^{+27.15}_{-28.71}$ & 40.64$^{+65.51}_{-40.64}$ & \\
\tableline
[O III] $T_{e}$ (K) & 8400 & 8600 & 8200 & 7700 & \\
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \\
C III] $N_{e}$ ($cm^{-3}$) & 26700 & \nodata & \nodata & \nodata & \\
icf (O)  & 1.12 & 1.12 & 1.13 & 1.10 & \\
icf (Ar)  & 1.18 & 1.17 & 1.19 & 1.10 & \\
icf (Ne)  & 0.98 & 0.99 & 0.99 & 0.97 & \\
icf (S)  & 1.89 & 1.86 & 1.88 & 1.58 & \\
Model RMS ($10^{-2}$)  & 5.58 & 7.60 & 9.20 & 7.50 & \\
Parameter & NGC5882 Full & NGC5882 1 & NGC5882 2 & NGC5882 3 & \\
\tableline
Observed RMS ($10^{-2}$)  & 14.20 & 16.48 & 11.56 & 41.36 & \\
\tableline
%\tablebreak
 & NGC7662 Full & NGC7662 1 & NGC7662 2 & NGC7662 3 & NGC7662 4 \\ 
\tableline
$T_{star}$ (kK) & 109.9$^{+9.1}_{-5.9}$ & 109.9 & 109.9 & 109.9 & 109.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.24$^{+0.18}_{-0.14}$ & 3.24 & 3.24 & 3.24 & 3.24 \\
$H_{den}$ (log[$H_{density}$]) & 3.42$^{+0.04}_{-0.04}$ & 3.54$^{+0.04}_{-0.04}$ & 3.70$^{+0.05}_{-0.08}$ & 3.60$^{+0.04}_{-0.04}$ & 3.32$^{+0.06}_{-0.08}$ \\
Inner Radius ($10^{-2}$pc) & 3.42$^{+0.36}_{-0.63}$ & 4.69$^{+0.11}_{-0.09}$ & 4.24$^{+0.10}_{-0.08}$ & 3.81$^{+0.06}_{-0.09}$ & 3.34$^{+0.54}_{-3.34}$ \\
Outer Radius ($10^{-2}$pc) & 5.28$^{+0.36}_{-0.34}$ & 5.47$^{+0.19}_{-0.18}$ & 4.55$^{+0.13}_{-0.12}$ & 4.37$^{+0.16}_{-0.15}$ & 8.49$^{+1.61}_{-1.69}$ \\
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-1.80}$ & 9.40$^{+0.60}_{-1.80}$ & 10.00$^{+0.00}_{-3.38}$ & 10.00$^{+0.00}_{-1.87}$ & 10.00$^{+0.00}_{-3.1}$ \\
He/H ($10^{-2}$) & 9.53$^{+2.77}_{-2.61}$ & 9.10$^{+8.28}_{-4.83}$ & 10.35$^{+4.78}_{-4.98}$ & 8.32$^{+5.49}_{-3.75}$ & 5.02$^{+3.29}_{-3.54}$ \\
C/H ($10^{-4}$) & 5.94$^{+5.81}_{-2.99}$ & 4.86$^{+2.90}_{-2.05}$ & 3.66$^{+5.25}_{-2.79}$ & 4.89$^{+3.15}_{-3.55}$ & 3.19$^{+5.13}_{-2.12}$ \\
N/H ($10^{-4}$) & 0.77$^{+0.44}_{-0.41}$ & 0.75$^{+0.40}_{-0.39}$ & 0.77$^{+0.82}_{-0.77}$ & 0.85$^{+0.50}_{-0.46}$ & 0.38$^{+0.45}_{-0.38}$ \\
O/H ($10^{-4}$) & 4.11$^{+1.78}_{-1.48}$ & 4.10$^{+1.15}_{-0.94}$ & 3.62$^{+2.69}_{-1.80}$ & 4.63$^{+1.39}_{-1.17}$ & 2.70$^{+2.67}_{-1.83}$ \\
Ne/H ($10^{-5}$) & 6.85$^{+5.73}_{-5.16}$ & 7.52$^{+3.97}_{-3.80}$ & 5.42$^{+6.33}_{-5.42}$ & 6.17$^{+3.38}_{-3.28}$ & 4.60$^{+5.17}_{-4.60}$ \\
S/H ($10^{-6}$) & 3.54$^{+2.77}_{-2.69}$ & 2.29$^{+1.18}_{-1.17}$ & 3.56$^{+3.67}_{-3.56}$ & 3.46$^{+1.79}_{-1.87}$ & 1.81$^{+2.17}_{-1.81}$ \\
Ar/H ($10^{-7}$) & 25.18$^{+19.49}_{-19.15}$ & 16.94$^{+8.76}_{-8.63}$ & 18.58$^{+19.44}_{-18.58}$ & 28.64$^{+15.10}_{-15.46}$ & 10.47$^{+12.44}_{-10.47}$ \\
\tableline
[O III] $T_{e}$ (K) & 12200 & 12300 & 13100 & 12600 & 13400\\
C III] $N_{e}$ ($cm^{-3}$) & 2800 & 3800 & 5800 & 4400 & 1900\\
icf (O)  & 1.62 & 1.39 & 1.43 & 1.78 & 1.74\\
icf (Ar)  & 1.36 & 1.27 & 1.26 & 1.38 & 1.29 \\
icf (Ne)  & 1.27 & 1.11 & 1.12 & 1.31 & 1.35\\
icf (S)  & 4.83 & 3.03 & 3.01 & 4.28 & 3.48 \\
Model RMS ($10^{-2}$)  & 4.67 & 3.17 & 10.99 & 4.95 & 18.65 \\
Observed RMS ($10^{-2}$)  & 12.42 & 10.17 & 17.98 & 9.55 & 12.60 \\
\tableline
%\tablebreak
 & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \\
\tableline
$T_{star}$ (kK) & 109.9 & 109.9 & 109.9 & 109.9 & \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.24 & 3.24 & 3.24 & 3.24 & \\
$H_{den}$ (log[$H_{density}$]) & 3.34$^{+0.05}_{-0.07}$ & 3.54$^{+0.03}_{-0.03}$ & 3.37$^{+0.04}_{-0.04}$ & 3.42$^{+0.05}_{-0.07}$ & \\
Inner Radius ($10^{-2}$pc) & 3.05$^{+0.64}_{-3.05}$ & 3.33$^{+0.10}_{-0.08}$ & 1.84$^{+0.76}_{-1.84}$ & 3.70$^{+0.25}_{-0.17}$ & \\
Outer Radius ($10^{-2}$pc) & 7.53$^{+1.11}_{-1.34}$ & 4.86$^{+0.22}_{-0.21}$ & 5.45$^{+0.55}_{-0.61}$ & 5.22$^{+0.56}_{-0.45}$ & \\
Parameter & NGC7662 5 & NGC7662 6 & NGC7662 7 & NGC7662 8 & \\
\tableline
Filling Factor ($10^{-1}$) & 10.00$^{+0.00}_{-2.94}$ & 10.00$^{+0.00}_{-1.25}$ & 10.00$^{+0.00}_{-1.80}$ & 10.00$^{+0.00}_{-2.59}$ & \\
He/H ($10^{-2}$) & 6.46$^{+4.01}_{-3.83}$ & 8.83$^{+1.88}_{-1.75}$ & 12.05$^{+3.44}_{-2.72}$ & 4.89$^{+4.23}_{-2.54}$ & \\
C/H ($10^{-4}$) & 3.77$^{+5.35}_{-2.25}$ & 4.56$^{+2.36}_{-1.61}$ & 5.48$^{+6.82}_{-3.19}$ & 4.28$^{+3.85}_{-2.04}$ & \\
N/H ($10^{-4}$) & 0.51$^{+0.38}_{-0.37}$ & 0.55$^{+0.25}_{-0.24}$ & 0.56$^{+0.54}_{-0.27}$ & 0.55$^{+0.37}_{-0.33}$ & \\
O/H ($10^{-4}$) & 2.82$^{+2.42}_{-1.62}$ & 3.56$^{+1.11}_{-0.93}$ & 3.44$^{+1.93}_{-1.53}$ & 3.18$^{+1.60}_{-1.18}$ & \\
Ne/H ($10^{-5}$) & 4.70$^{+5.53}_{-4.70}$ & 5.25$^{+2.51}_{-2.30}$ & 6.34$^{+3.48}_{-5.31}$ & 6.27$^{+4.45}_{-4.03}$ & \\
S/H ($10^{-6}$) & 2.32$^{+2.58}_{-2.32}$ & 2.54$^{+1.18}_{-1.12}$ & 3.12$^{+2.91}_{-2.72}$ & 2.05 & \\
Ar/H ($10^{-7}$) & 13.87$^{+14.97}_{-13.87}$ & 18.11$^{+8.19}_{-7.88}$ & 23.50$^{+22.21}_{-20.68}$ & 14.72 & \\
\tableline
[O III] $T_{e}$ (K) & 13100 & 12800 & 12400 & 13300 & \\
C III] $N_{e}$ ($cm^{-3}$) & 2100 & 3700 & 2500 & 2600 & \\
icf (O)  & 1.72 & 1.62 & 1.35 & 1.67 & \\
icf (Ar)  & 1.30 & 1.32 & 1.33 & 1.47 & \\
icf (Ne)  & 1.34 & 1.26 & 1.10 & 1.59 & \\
icf (S)  & 3.96 & 4.46 & 5.21 & 5.51 & \\
Model RMS ($10^{-2}$)  & 14.78 & 3.41 & 7.16 & 11.80 & \\
Observed RMS ($10^{-2}$)  & 13.29 & 7.61 & 13.83 & 9.35 & 
\enddata
\tablenotetext{a}{High Density Limit Default.}
\end{deluxetable}
\end{landscape}

The oxygen and argon model ionization correction factors for IC 3568, NGC 5315, and NGC 5882 are larger than their observed counterparts, while the same ICFs are smaller for IC 2165, NGC 2440, NGC 3242, and NGC 7662. Also, IC 3568, NGC 5315, and NGC 5882 have lower stellar temperatures than IC 2165, NGC 2440, NGC 3242, and NGC 7662. Therefore, the ICF equations employed by ELSA could be under-correcting for PN with lower stellar temperatures and over-correcting for those with higher stellar temperatures. Both of the ICF equations for argon and oxygen depend on the ratio (He$^{+}$+He$^{+2}$)/He$^{+}$. For lower stellar temperatures, the He$^{+}$ ionic state will be populated more than in the case of a higher stellar temperature, reducing the ratio and subsequent ICF value. The neon model ICFs are smaller in all PNe except for NGC 5315, and upon inspection of the ICF equation, no clear reason can be found to explain the differences. Calculating the average observed Ne/O for this sample and comparing to the average modeled Ne/O shows a discrepancy of about 10\%, 0.20$\pm$0.02 and 0.18 for the observed and modeled ratio, respectively. Thus, on average, the systematic error introduced by using ICFs seems to be minor in this case. Interestingly for neon, many regions have ICFs less than 1, which points to a problem in the neon abundance calculations. This could indicate that the atomic constants such as the collision strengths or Einstein A values are slightly off from their true values, resulting in an ionic abundance of neon that is too large. Lastly, all PN except NGC 5882 have model ICFs of sulphur larger than their observed ICFs with the largest discrepancy seen in NGC 5315. 

To further investigate the ICFs of oxygen, argon and neon, a suite of over 400 Cloudy models provided by Gary Ferland was used. This suite covers a large range of stellar temperatures (50-500 kK, $\bigtriangleup$ = 0.1 dex), metallicities (10$^{-0.6}$-10$^{0.4}$ times solar, $\bigtriangleup$ = 0.2 dex), and nebular densities (10$^{2}$-10$^{5}$ cm$^{-3}$, $\bigtriangleup$ = 0.5 dex). Each model uses the Rauch H-Ca atmospheric simulation and typical planetary nebula values for all other input parameters. For each model, the ICFs for O, Ar, and Ne from the equations used by ELSA and the value from the model are compared in Figure~\ref{icfcomp}. The stellar temperature is limited to include only up to 200 kK as none of the stars in this sample are above this value. The models increase in stellar metallicity first (repeats every 6th model), then nebular density (repeats every 36th model), and finally stellar temperature for each successive model number. For the majority of models, the oxygen ICF from the ELSA equation is smaller than the model ICF and vice versa for neon. This is what is seen for the PN in this sample, albeit at different stellar temperatures and smaller percent differences. Also, all of the model argon ICFs are smaller than the ELSA equation counterparts, which is not observed in this PN sample. These discrepancies may be the result of the boundaries of the nebular gas and the stellar atmosphere model being different and warrants further investigation. 
%\begin{landscape}
\begin{figure}
\caption{Relative percent error of the oxygen, argon, and neon ICFs calculated with the equations in ELSA with respect to the ICF from each model. The models increase in stellar metallicity first (repeats every 6th model), then nebular density (repeats every 36th model), and finally stellar temperature for each successive model number.\newline}
\includegraphics[scale=0.30]{icfcomp.png}
\label{icfcomp}
\end{figure}
%\end{landscape}

The parameters for the best fit models for the Gaussian and Gaussian with a power-law density profiles are in Table~\ref{gaudenmods1}. This table has the same format as Table~\ref{condenmods1} but only contains the full regions. The difference between these stellar parameters and the constant density models is small in most cases. Only IC 3568 had a somewhat large change in the luminosity of 0.16 dex. However, this is small compared to the errors estimated for the best fit constant density model. Therefore, the choice of density structure only has a minor effect on the final stellar temperature and luminosity and the adoption of the stellar parameters from the constant density models is reasonable. The Gaussian and Gaussian with a power-law density profiles also generate similar electron temperatures but higher electron densities when compared with the constant density profile. This makes sense, since these two profiles have peak density values significantly above the constant density profile (see Figures~\ref{densfig1}~\&~\ref{densfig2}). The ionization correction factors are either slightly larger or smaller than the constant density ICFs as well. This could be an indication that the choice of density structure affects the ICFs. Lastly, the rms values for IC 2165 and NGC 2440 are considerably larger than their constant density counterparts while the Gaussian profile for NGC 5882 is smaller than the constant density rms value. This indicates that IC 2165 and NGC 2440 are better represented using a constant density model while a Gaussian density profile appears more suitable in the case of NGC 5882.
\begin{landscape}
\begin{deluxetable}{ccccccc}
\tabletypesize{\footnotesize}
\tablewidth{0in}
%%%\rotate
\tablecaption{Non-constant Density Models\label{gaudenmods1}}
\tablehead{
\multicolumn{7}{c}{Non-constant Density Models}
}
\startdata
 & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
\cline{2-7}
 & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Parameter & & power-law & & power-law & & power-law \\ 
\tableline
$T_{star}$ (kK) & 110.0 & 110.0 & 69.2 & 66.6 & 171.8 & 171.9 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.19 & 3.19 & 3.67 & 3.68 & 2.74 & 2.73\\
Filling Factor ($10^{-1}$) & 9.51 & 9.45 & 9.70 & 8.67 & 1.76 & 1.71\\
He/H ($10^{-2}$) & 10.19 & 10.14 & 9.27 & 9.04 & 12.27 & 12.27\\
C/H ($10^{-4}$) & 3.84 & 3.92 & 5.35 & 5.24 & 2.54 & 2.54\\
N/H ($10^{-4}$) & 1.18 & 1.15 & 0.15 & 0.17 & 0.74 & 0.74\\
O/H ($10^{-4}$) & 2.54 & 2.54 & 4.83 & 4.45 & 2.71 & 2.69\\
Ne/H ($10^{-5}$) & 3.04 & 3.00 & 7.69 & 7.57 & 3.42 & 3.58\\
S/H ($10^{-6}$) & 2.80 & 2.82 & 12.08 & 13.30 & 1.49 & 1.49\\
Ar/H ($10^{-7}$) & 14.26 & 14.35 & 15.35 & 16.11 & 13.03 & 13.00\\
\tableline
\[O III] $T_{e}$ (K) & 13700 & 13700 & 10000 & 10000 & 14200 & 14200\\
\[[S II] N$_{e}$($cm^{-3}$) & 12600 & 12500 & \nodata & \nodata & 8700 & 8500\\
C III] $N_{e}$ ($cm^{-3}$) & 11800 & 11700 & 9100 & 8500 & 8300 & 8100\\
icf (O) & 1.45 & 1.45 & 1.09 & 1.08 & 1.44 & 1.43\\
icf(Ar) & 1.26 & 1.26 & 1.27 & 1.32 & 1.16 & 1.16\\
icf (Ne) & 1.14 & 1.15 & 0.94 & 0.95 & 1.26 & 1.27\\
% & \multicolumn{2}{c}{IC2165 Full} & \multicolumn{2}{c}{IC3568 Full} & \multicolumn{2}{c}{NGC2440 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\ 
%\tableline
icf(S) & 3.29 & 3.36 & \nodata & \nodata & 1.64 & 1.62\\
RMS ($10^{-2}$) & 3.40 & 3.60 & 3.13 & 2.31 & 10.25 & 9.97 \\
\tableline
\tablebreak
 & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC3242 Full}\\
\cline{2-7}
 & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
Parameter & & power-law & & power-law & & power-law \\
\tableline
$T_{star}$ (kK) & 69.9 & 69.9 & 79.2 & 78.7 & 91.6 & 91.2 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 4.92 & 4.94 & 3.42 & 3.42 & 3.26 & 3.29\\
Filling Factor ($10^{-1}$) & 9.68 & 9.75 & 8.30 & 8.26 & 9.77 & 9.83\\
He/H ($10^{-2}$) & 11.94 & 11.80 & 12.62 & 12.59 & 9.84 & 9.93\\
C/H ($10^{-4}$) & 16.87 & 17.82 & 4.29 & 4.29 & 5.28 & 5.21\\
N/H ($10^{-4}$) & 0.57 & 0.57 & 2.41 & 0.24 & \nodata & \nodata\\
O/H ($10^{-4}$) & 6.59 & 6.52 & 12.88 & 12.88 & 4.54 & 4.46\\
Ne/H ($10^{-5}$) & 14.89 & 14.83 & 23.66 & 23.66 & 7.11 & 6.61\\
S/H ($10^{-6}$) & 431.52 & 454.99 & 7.66 & 7.69 & \nodata & \nodata\\
Ar/H ($10^{-7}$) & 959.40 & 1016.25 & 38.11 & 38.46 & \nodata & \nodata\\
\tableline
\[O III] $T_{e}$ (K) & 8900 & 8900 & 8400 & 8300 & 11900 & 12000\\
% & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\
%\tableline
\[[S II] N$_{e}$($cm^{-3}$) & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & 20000\tablenotemark{a} & \nodata & \nodata \\
C III] $N_{e}$ ($cm^{-3}$) & 72100 & 72200 & 27400 & 26700 & 4700 & 4700\\
icf (O) & 1.39 & 1.40 & 1.12 & 1.12 & 1.52 & 1.53\\
icf(Ar) & 1.98 & 1.99 & 1.17 & 1.22 & \nodata & \nodata\\
icf (Ne) & 1.23 & 1.24 & 0.99 & 0.99 & 1.22 & 1.23\\
icf(S) & 47.57 & 50.88 & 1.84 & 1.96 & \nodata & \nodata\\
RMS ($10^{-2}$) & 3.32 & 3.45 & 5.52 & 7.97 & 7.88 & 8.61\\ 
\tableline
\tablebreak
 & \multicolumn{2}{c}{NGC7662 Full} & \multicolumn{2}{c}{} & \multicolumn{2}{c}{}\\
\cline{2-7}
 & Gaussian & Gaussian With \\
Parameter & & power-law  \\
\tableline
$T_{star}$ (kK) & 108.8 & 108.8 \\
$L_{star}$ (log[L/$L_{\astrosun}$]) & 3.36 & 3.36\\
Filling Factor ($10^{-1}$) & 10.00 & 10.00\\
He/H ($10^{-2}$) & 9.84 & 9.59\\
C/H ($10^{-4}$) & 5.81 & 5.78\\
N/H ($10^{-4}$) & 0.75 & 0.74\\
O/H ($10^{-4}$) & 3.94 & 3.94\\
Ne/H ($10^{-5}$) & 6.44 & 6.35\\
S/H ($10^{-6}$) & 3.43 & 3.48\\
Ar/H ($10^{-7}$) & 24.89 & 25.23\\
\tableline
\[O III] $T_{e}$ (K) & 12400 & 12400\\
% & \multicolumn{2}{c}{NGC5315 Full} & \multicolumn{2}{c}{NGC5882 Full} & \multicolumn{2}{c}{NGC7662 Full}\\
%\cline{2-7}
% & Gaussian & Gaussian With & Gaussian & Gaussian With & Gaussian & Gaussian With\\
%Parameter & & power-law & & power-law & & power-law \\
%\tableline
C III] $N_{e}$ ($cm^{-3}$) & 4300 & 4200\\
icf (O) & 1.51 & 1.51\\
icf(Ar) & 1.36 & 1.36\\
icf (Ne) & 1.19 & 1.19\\
icf(S) & 2.22 & 4.75\\
RMS ($10^{-2}$) & 4.87 & 5.50 
\enddata
\tablenotetext{a}{High Density Limit Default.}
\end{deluxetable}
\end{landscape}