The Goddard High Resolution Spectrograph aboard the Hubble Space Teles
cope was used with the G160M grating to obtain high-resolution (0.2 An
gstrom) spectra of three very bright active galactic nuclei located be
hind voids in the nearby distribution of bright galaxies (i.e., CfA an
d Arecibo redshift survey regions). A total of eight definite (greater
than or equal to 4 sigma) Ly alpha absorption lines were discovered r
anging in equivalent width from 26 to 240 m Angstrom at Galactocentric
velocities 1740-7740 km s(-1). Of these eight systems, we locate seve
n in supercluster structures and one, in the sight line of Mrk 501 at
7740 km s(-1), in a void. In addition, one of two tentative (3-4 sigma
) Ly alpha absorption lines are found in voids. Thus, the voids are no
t entirely devoid of matter, and not all Ly alpha clouds are associate
d with galaxies. Also, since the path lengths through voids and superc
lusters probed by our observations thus far are nearly equal, there is
some statistical evidence that the Ly alpha clouds avoid the voids. T
he nearest galaxy neighbors to these absorbing clouds are 0.45-5.9 Mpc
away, too far to be physically associated by most models. The lower e
quivalent width absorption lines (W(lambda)less than or equal to 100 m
Angstrom) are consistent with random locations with respect to galaxi
es and may be truly intergalactic, similar to the bulk of the Ly alpha
forest seen at high z. These results on local Ly alpha clouds are in
full agreement with those found by Morris et al. (1993) for the 3C 273
sight line but are different from the results for higher equivalent w
idth systems where closer cloud-galaxy associations were found by Lanz
etta et al. (1994). Pencil-beam optical and 21 cm radio line observati
ons of the area of sky surrounding Mrk 501 fail to find faint galaxies
near the velocities of the Ly alpha clouds in that sight line. Specif
ically, for the ''void absorption'' system at 7740 km s(-1) we find no
galaxy at comparable redshift to the absorber within 100 h(75)(-1) kp
c(H-0 = 75 h(75) km s(-1) Mpc(-1)) with an absolute magnitude of B les
s than or equal to -16 and no object with H I mass greater than or equ
al to 7 x 10(8) h(75)(-2) M. within 500 h(75)(-1) kpc. Thus, neither a
faint optical galaxy nor a gas-rich, optically dim or low surface bri
ghtness galaxy is present close to this absorber.