We have obtained deep ROSAT images of three regions within the Pleiade
s open cluster. We have detected 317 x-ray sources in these ROSA T PSP
C images, 171 of which we associate with certain or probable members o
f the Pleiades cluster. We detect nearly all Pleiades members with spe
ctral types later than G0 and within 25 arcminutes of our three field
centers where our sensitivity is highest. This has allowed us to deriv
e for the first time the luminosity function for the G, K, and M dwarf
s of an open cluster without the need to use statistical techniques to
account for the presence of upper limits in the data sample. Because
of our high X-ray detection frequency down to the faint limit of the o
ptical catalog, we suspect that some of our unidentified X-ray sources
are previously unknown, very low-mass members of the Pleiades. A larg
e fraction of the Pleiades members detected with ROSAT have published
rotational velocities. Plots of L(X)/L(Bol) versus spectroscopic rotat
ional velocity show tightly correlated ''saturation'' type relations f
or stars with (B - V)0 greater-than-or-equal-to 0.60. For each of seve
ral color ranges, X-ray luminosities rise rapidly with increasing rota
tion rate until upsilon sin i congruent-to 15 km s-1, and then remain
essentially flat for rotation rates up to at least upsilon sin i appro
ximately 100 km s-1. The dispersion in rotation among low-mass stars i
n the Pleiades is by far the dominant contributor to the dispersion in
L(X) at a given mass. Only about 35% of the B, A, and early F stars i
n the Pleiades are detected as X-ray sources in our survey. There is n
o correlation between X-ray flux and rotation for these stars. The X-r
ay luminosity function for the early-type Pleiades stars appears to be
bimodal-with only a few exceptions, we either detect these stars at f
luxes in the range found for low-mass stars or we derive X-ray limits
below the level found for most Pleiades dwarfs. The X-ray spectra for
the early-type Pleiades stars detected by ROSA T are indistinguishable
from the spectra of the low-mass Pleiades members. We believe that th
e simplest explanation for this behavior is that the early-type Pleiad
es stars are not themselves intrinsic X-ray sources and that the X-ray
emission actually arises from low-mass companions to these stars.