We study the rms peculiar velocity of clusters as a convenient statistic to put constraints on cosmological models .
This statistic is easy to compute theoretically given a model for the power spectrum ; we show that with some assumptions it can be directly related to the quantity \Omega _ { 0 } ^ { 0.6 } \sigma _ { 8 } .
We develop a likelihood method for estimating the rms peculiar velocity of clusters from line-of-sight velocity measurements and their associated errors .
We apply our method to two samples of cluster peculiar velocities ; a new sample known as the SCI sample and a subsample of the Mark III catalog .
Although these two samples initially give results which are inconsistent , we show that they can be put into good agreement by the removal , particularly from the Mark III sample , of a set of clusters with multiple mass concentrations , cluster membership ambiguities , or excessive obscuration , properties which may have introduced unaccounted for errors into measurements of their peculiar velocities .
Once these clusters are removed from the samples , they both favor a relatively low value for the 1-D rms peculiar velocity of clusters \sigma _ { v } = 265 ^ { +106 } _ { -75 } { km s } ^ { -1 } ( at 90 \% confidence ) , leading to the constraint \Omega _ { 0 } ^ { 0.6 } \sigma _ { 8 } = 0.44 ^ { +0.19 } _ { -0.13 } , consistent with cluster abundance studies but inconsistent with \Omega _ { 0 } = 1 CDM normalized to COBE at the 99.7 \% confidence level .