\begin{table}%t1
\caption{Characteristic luminosity  $L_{*}$ in units  of $L_\odot$ at
12~$\mu$m  (Col.~3)  and 24~$\mu$m  (Col.~4)  of  the $z=0$ luminosity
functions used here, as a  function of galaxy type (Col.~1).  Column~2  gives  the  value of  the  parameter~$p_2$,  the rate  defined  by $\textit{SFR}_i(t)=M_{{\rm gas}}(t)/{p_2}$.  Galactic winds occur at an age of 3~Gyr in ellipticals of type~E  and ULIRG, and at 1~Gyr in ellipticals
of type~E2; there are no galactic winds in spirals.  Infall time scale
of ULIRGs is 100~Myr as for  ellipticals of type~E or E2; it regularly
increases for spirals from 2.8~Gyr  (Sa) to 8.0~Gyr (Im) (see text for
details and references).  The $L_{*}$(12~$\mu$m) for the normal types
(other than ULIRG) are derived  from the $L_{*}(B_J)$ of the observed
optical  luminosity  functions  from   Heyl  et~al.  (\cite{heyl})  and  the
$B_J-12~\mu$m  and  $B_J-24~\mu$m  colours,  in the  $AB$~magnitude
system, are computed at $z\simeq0$  with P\'EGASE.3 (Cols.~5 and~6).
The value of $L_{*}(12~\mu$m) assigned to Sbc~galaxies, the brightest
emitters in  this band,  is that of  the observed  luminosity function
measured with $IRAS$  (Rush et~al. \cite{rush}; Shupe et~al. \cite{shupe}); the same
offset as for Sbc is then  applied to all types.  The last two columns
show  the adopted  number density  fraction by  type: model~1 (normal
galaxies only, Col.~7) uses the type distribution  derived from the
UV-optical-near IR  faint counts  (Fioc et~al.  1999a)  while  model~2
(normal  galaxies~+  ULIRGs, Col.~8) is  built by  replacing  1/3 of
normal dust-poor ellipticals (9\% of all galaxies) with ultra luminous
elliptical  galaxies (called  ULIRGs). These  last galaxies  evolve as
dusty ellipticals, they are $\simeq$$2.5$ to $\simeq$$5$~mag brighter
than normal  ellipticals (depending on  wavelength), and are  thus as
luminous as spirals Sbc in the mid-IR at  $z=0$.  The number densities for the other
galaxy types are identical in both models. }\label{table:parameters}
%%\centering
\par
\small
\begin{tabular}{cccccccc}
\hline\hline
Type &$p_2$&$\log_{10}$&$\log_{10}$ & Colour& Colour&Model 1 &Model 2  \\ 
 &(Myr)&$[L_{*}(12~\mu {\rm m})/L_{\odot}]$& $[L_{*}(24~\mu {\rm m})/L_{\odot}]$&$B_J-12~\mu$m&$B_J-24~\mu$m&normal& normal\\
  & & & & $_{AB}$& $_{AB}$& only & + ULIRGs \\
\hline 
ULIRG&100&9.9&9.7&$-$&$-$&0\%& 9.0\%\\  
E&100&8.9&7.7& --1.00&--2.60&9\%& 0\%\\  
E2 &300&9.0&7.8&--1.20&--2.82&17.5\%&17.5\%\\  
Sa &1400&9.0&8.8& --0.45&+0.21& 7.9\%& 7.9\%\\  
Sb &2500&9.4&9.2&+0.37&+1.28& 7.9\%& 7.9\% \\  
Sbc &5714&9.8&9.6&+1.38&+2.30&7.9\%& 7.9\%\\  
Sc &10000&9.6&9.4&+1.57&+2.46&16.6\% & 16.6\%\\  
Sd &14286&9.6&9.4&+1.61&+2.48&16.6\%& 16.6\%\\  
Im &16000&8.8&8.5&+1.57&+2.42&16.6\%& 16.6\%\\ 
\hline
\end{tabular}
\end{table}