\begin{table}%t6
 \caption{\label{tab6}Proper motions constraints of SDSS L dwarfs that were also found in UKIDSS DR4.}
%\centerline
 {\begin{tabular}{cllclclcl}
\hline\hline
SDSS Name & Proper motion$^{{a}}$ & Proper motion & Proper motion$^{{b}}$ & Proper motion & Proper motion$^{{c}}$ & Proper motion & Proper motion$^{{d}}$ & Proper motion \\
 & ($^{\prime\prime}$yr$^{-1}$) & Angle$^{{a}}$ & ($^{\prime\prime}$yr$^{-1}$) & Angle$^{{e}}$ & ($^{\prime\prime}$~yr$^{-1}$) & Angle$^{{e}}$ & ($^{\prime\prime}$yr$^{-1}$) & Angle$^{{e}}$       \\
\hline
SDSS J004759.59$+$135332.0 & ~~~~~~~~...$^{{h}}$ & ~~~~~~~~... &0.13~$\pm$~0.02 &208~$\pm$~10&0.13~$\pm$~0.03 &234~$\pm$~14&0.47~$\pm$~0.27 &300~$\pm$~36 \\
SDSS J015141.04$-$005156.5 & 0.044~$\pm$~0.012  & 274.8~$\pm$~14.2  &0.07~$\pm$~0.06 &285~$\pm$~57&0.04~$\pm$~0.03 &257~$\pm$~72&0.07~$\pm$~0.15 &150 ... \\
SDSS J022927.95$-$005328.5 & 0.068~$\pm$~0.012  & 104.8~$\pm$~25.1  &0.02~$\pm$~0.03 &~~57 ...&0.04~$\pm$~0.04 &136 ...&0.10~$\pm$~0.09 &143~$\pm$~63 \\
SDSS J073241.77$+$264558.9 & 0.002 ... & ~~30.3 ... &0.04~$\pm$~0.02 &359~$\pm$~32&0.02~$\pm$~0.03 &230 ...&0.12~$\pm$~0.06 &206~$\pm$~30 \\
SDSS J074436.02$+$251330.5 & 0.033 ... & 262.6 ... &0.04~$\pm$~0.03 &296~$\pm$~50&0.06~$\pm$~0.06 &296 ...&0.05~$\pm$~0.28 &322 ... \\
SDSS J075754.16$+$221604.9 & 0.016 ... & ~~74.6 ... &0.02~$\pm$~0.04 &~~63 ...&0.05~$\pm$~0.04 &116~$\pm$~59&0.11~$\pm$~0.07 &124~$\pm$~38 \\
SDSS J081303.96$+$243355.9 & 0.066 ... & 251.3 ... &0.06~$\pm$~0.03 &254~$\pm$~30&0.08~$\pm$~0.03 &228~$\pm$~25&0.09~$\pm$~0.06 &216~$\pm$~42 \\
SDSS J081409.45$+$260250.4 & 0.057 ... & 278.5 ... &0.06~$\pm$~0.03 &304~$\pm$~35&0.03~$\pm$~0.03 &217~$\pm$~59&0.08~$\pm$~0.05 &170~$\pm$~36 \\
SDSS J083613.45$+$022106.2 & 0.096~$\pm$~0.003  & 285.0~$\pm$~1.6  &0.07~$\pm$~0.02 &311~$\pm$~17&0.11~$\pm$~0.03 &291~$\pm$~14&0.36~$\pm$~0.16 &263~$\pm$~26 \\
SDSS J092745.81$+$010640.4 & 0.100~$\pm$~0.001  & 274.1~$\pm$~2.0  &0.12~$\pm$~0.02 &272~$\pm$~~~9&0.10~$\pm$~0.03 &302~$\pm$~19& ...$^{{g}}$ &~~37~$\pm$~58 \\
SDSS J094624.37$+$344639.8 & 0.083 ... & 293.8 ... &0.09~$\pm$~0.03 &304~$\pm$~22&0.07~$\pm$~0.04 &298~$\pm$~33&0.05~$\pm$~0.07 &295 ... \\
SDSS J095941.47$+$114146.0 & 0.148 ... & 254.1 ... &0.15~$\pm$~0.03 &259~$\pm$~12&0.14~$\pm$~0.04 &257~$\pm$~18&0.11~$\pm$~0.10 &252~$\pm$~67 \\
SDSS J121238.73$+$000721.6 & 0.037 ... & 278.5 ... &0.03~$\pm$~0.02 &342~$\pm$~38&0.04~$\pm$~0.05 &282 ... & ~0.13~$\pm$~0.27$^{{f}}$  &~~20 ... \\
SDSS J133131.70$+$122531.4 & 0.182~$\pm$~0.006  & 193.7~$\pm$~1.4  &0.16~$\pm$~0.03 &188~$\pm$~11&0.12~$\pm$~0.02 &207~$\pm$~~~8& 0.12~$\pm$~0.03  &243~$\pm$~14 \\
SDSS J134531.43$+$001551.2 & 0.047~$\pm$~0.006  & ~~95.2~$\pm$~1.9  &0.05~$\pm$~0.02 &~~77~$\pm$~22&0.04~$\pm$~0.05 &124 ...& ~0.25~$\pm$~0.27$^{{f}}$  &~~34 ... \\
SDSS J150153.00$-$013507.1 & 0.236~$\pm$~0.002  & 255.3~$\pm$~0.7  &0.26~$\pm$~0.03 &264~$\pm$~~~6&0.24~$\pm$~0.02 &258~$\pm$~~~5&0.21~$\pm$~0.07 &241~$\pm$~19 \\
SDSS J154236.26$-$004545.9 & 0.531~$\pm$~0.001  & 258.5~$\pm$~0.1  &0.52~$\pm$~0.02 &259~$\pm$~~~2&0.60~$\pm$~0.05 &252~$\pm$~~~5& ...$^{{g}}$ &~~40~$\pm$~25 \\
SDSS J154432.77$+$265551.2 & 0.141 ... & 311.9 ... &0.16~$\pm$~0.04 &310~$\pm$~15&0.15~$\pm$~0.03 &304~$\pm$~11&0.18~$\pm$~0.05 &295~$\pm$~16 \\
SDSS J154740.16$+$053208.3 & 0.047~$\pm$~0.006  & 293.1~$\pm$~3.9  &0.06~$\pm$~0.05 &327~$\pm$~46&0.06~$\pm$~0.05 &243~$\pm$~54&0.16~$\pm$~0.11 &209~$\pm$~43 \\
SDSS J161711.68$+$322249.5 & 0.099 ... & 213.0 ... &0.04~$\pm$~0.04 &~~61 ...&0.02~$\pm$~0.04 &107 ...&0.02~$\pm$~0.06 &173 ... \\
SDSS J232715.71$+$151730.4 & 0.160~$\pm$~0.001  & 202.4~$\pm$~0.7 &0.20~$\pm$~0.02 &216~$\pm$~~~5&0.18~$\pm$~0.02 &211~$\pm$~~~5&0.10~$\pm$~0.04 &210~$\pm$~28 \\
SDSS J234040.33$-$003337.2 & 0.028~$\pm$~0.003  & 258.8~$\pm$~6.4  &0.05~$\pm$~0.04 &~~49~$\pm$~57&0.01~$\pm$~0.04 &199 ...&0.05~$\pm$~0.08 &214 ... \\
SDSS J234513.85$+$002441.6 & 0.092~$\pm$~0.001  & 200.1~$\pm$~4.2  &0.29~$\pm$~0.03&189~$\pm$~7&0.05~$\pm$~0.05 &221 ...&1.04~$\pm$~0.26 &~~~~4~$\pm$~14 \\
\hline
\end{tabular}}
\par
\smallskip
$^{{a}}$ SDSS-UKIDSS relative proper motions -- found by specifically measuring the relative
movement of the ultracool dwarfs with respect to nearby reference objects in the SDSS and UKIDSS 
images;
$^{{b}}$ SDSS-UKIDSS data-base proper motions -- found by dividing the difference between
the SDSS and UKIDSS coordinates (from the respective databases) by
the observational epoch difference.
Standard errors are calculated using the major axes of the position error ellipses from SDSS and 
UKIDSS;
$^{{c}}$ 2MASS-UKIDSS database proper motions -- as for $b$ except using 2MASS and UKIDSS;
$^{{d}}$ 2MASS-SDSS database proper motions -- as for $b$ except using 2MASS and SDSS. We do not present
the proper motions calculated with a baseline 10 months;
$^{{e}}$ error ellipses of 2MASS and SDSS overlap for some objects for which position angle
errors are not meaningful;
$^{{f}}$ objects with a 2MASS-SDSS baseline $<$1~year;
$^{{g}}$ we do not present their proper motions for they have a short 2MASS-SDSS baseline 
($<$2~months);
$^{{h}}$ We do not measure its proper motion for it is very faint in SDSS {\it z}-band
image.
\end{table}