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Let me conclude by looking forward into the distant cosmic future. As the universe continues to expand, the scale of clustering will grow. In a simple model with Omega = 1 and scale independent initial perturbations, the typical mass scale of clustering rises in direct proportion to the age of the universe. In this particular model, the virial velocities and temperatures of typical clusters are independent of time. The typical number of galaxies in a rich cluster is now about 103. At a much later time, this number will, instead, be

Equation 4 (4)

The typical number of galaxies in the mean correlation scale is now only about 10. It is the smallness of this number which makes it hard to study clusters; for instance, we cannot map out their shapes, isodensity contours, etc., with any precision because of discreteness effects. But at later times this number will also have risen in proportion to the size of rich clusters. Moreover, the characteristic cooling time for the gas in a cluster increases as t3, even if Omegagas does not decrease. Therefore, one will not need to worry about the complications of cooling flows in the remote future.

In a cosmic perspective and time-frame we may be observing clusters at a confusing stage in their development, but if we view astronomical advances on a human timescale we can feel very encouraged. Progress in delineating largescale structures, streaming velocities, and the optical and X-ray properties of individual clusters, not only locally but far enough away to see evolution, is rapid and encouraging. Now is therefore the best of times for a conference like this.

NOTE The topics mentioned in this introductory survey are all treated more fully in later chapters. For this reason, and to avoid duplication, literature references are not given here.