**2.1.1. Luminosity Fractions**

We consider first the luminosity fractions *f* in
equation (2).
In Table 1 we show the bulge fraction of galaxies in
luminosity, =
*L*_{bulge} / (*L*_{bulge} +
*L*_{disk}), for each morphological type,
from the bulge-disk decomposition of
Kent (1985)
based on his accurate Gunn
*r* band CCD photometry. We take the median of the distribution
presented by Kent.
The bulge fraction in *r* band is converted into that in the
*B* band using the color transformation law *B - r* = 1.19
for elliptical galaxies and bulges
(Fukugita, Shimasaku &
Ichikawa 1995).
The values of thus obtained in the
*B* band are consistent with the result of
Whitmore and Kirshner
(1981),
although the latter sample is not as large as that of
Kent and the decomposition, based on photography, may be less
accurate. The bulge fraction is well correlated with the morphology
(Morgan 1962;
Dressler 1980;
Meisels & Ostriker 1984;
Kent 1985),
but the morphologies at given bulge fraction overlap neighboring classes.

Parameter | E | S0 | Sab | Sbc | Scd | Irr |

Bulge fraction (r)............
| 1 | 0.75 | 0.40 | 0.24 | 0.10 | 0 |

Bulge fraction (B)...........
| 1 | 0.64 | 0.33 | 0.16 | 0.061 | 0 |

Morphology fraction µ(B).... | 0.11 | 0.21 | 0.28 | 0.29 | 0.045 | 0.061 |

HI typical mass (10^{9} M_{})...
| 0 | 0.64 | 2.5 | 4.0 | 2.9 | 1.8 |

H_{2} / HI...........................
| ... | 2.5 | 1.0 | 0.63 | 0.25 | 0.06 |

Row (3) in Table 1 is our adopted distribution of
morphologies, expressed as the fraction *µ _{t}* of the
mean luminosity density contributed by galaxies of morphological
type

The sum in the second expression is from SOs through
spirals. Because the mass in S0 discs is so small
we make little error in treating the disks of spirals
and S0s as the same population.
The separation into each morphological type is ambiguous, and the
classification depends much on the author. To model such error,
we recalculate the fractions *f* after reclassifying 1/3 of the
galaxies in each type systematically to the neighboring later
type, or else to the neighboring earlier type. This produces the
range (0.324-0.459):(0.599-0.499): (0.076-0.041). When we use
a morphological fraction or a bulge-to-disk
ratio taken from other authors, we find the
luminosity fractions *f* fall within this range in most cases.
In particular these estimates, when translated into the *V* pass
band, agree with the survey of
Schechter and Dressler
(1987).
This spread of values of the *µ _{t}* is taken into account in
our assignment of errors in estimates of the mean mass density.