We use the method developed by Blakeslee & Tonry (1995, ApJ, 442, 579)
to study the globular cluster (GC) populations of 21 giant elliptical
galaxies in 19 Abell clusters. This method, applied here primarily in
the R band, is based on the surface brightness fluctuations technique
of extragalactic distance measurement. The sample galaxies range in r
edshift from 5000 to 10.000 hn s(-1). and were selected primarily from
the Lauer & Postman (1994, ApJ, 425, 418) survey of brightest cluster
galaxies (BCGs), We find a tight correlation between the GC specific
frequency S-N of the central bright galaxy in the cluster and the clus
ter velocity dispersion. S-N also correlates well with the cluster X-r
ay temperature and with the number of bright neighboring galaxies, les
s well with the galaxy profile, and only marginally with galaxy lumino
sity and overall cluster richness. It does not correlate with cluster
morphology class. Thus, unlike galaxy luminosity, S-N is determined by
the cluster mass, or density. To account for this situation, we propo
se that the GCs formed early and in proportion to the available mass,
while the luminosity growth of the galaxy was later halted, yielding t
he observed correlations of S-N with density. We introduce a quantity
called eta(GC), the number of GCs per unit local cluster mass. For a s
imple cluster mass model, eta(GC) is found to be constant, indicating
a uniform GC production rate per unit available mass. A measurement of
the Gaussian width sigma of the GC luminosity function (GCLF) is one
of the by-products of our analysis. In the cosmic microwave background
frame. the mean width for this sample is [sigma] = 1.43 mag, virtuall
y identical to the HST value for M87, the galaxy used to calibrate the
mean of the GCLF in this analysis. (C) 1997 American Astronomical Soc
iety.