THE ART OF N-BODY BUILDING

Ever since the early work of Jeans ( 19 15), astronomers have struggled with the dynamical problems posed by large aggregates of stars. As more observational data have poured in, the problems have become still harder . For example, elliptical galaxies now appear to be triaxial objects supported by anisotropic velocity dispersions, presenting great difficulties in con­ structing even an equilibrium model. Galaxies may also be embedded in unseen halos of material whose distribution and extent can only be probed indirectly. This discovery does nothing to simplify the old problems of spiral structure and bar stability, and makes it very difficult to estimate total masses for galaxies and consequently the extent to which their inter­ actions might be significant . We are also currently faced with trying to understand how groups and clusters of galaxies form in a universe that appears so uniform on yet larger scales. Analytical treatments of these problems are characterized by simplifying approximations, linearizations, etc., and are still far from clear answers to many of the major questions that arise. Holmberg ( 1941) recognized that simulations could break free from this type of restriction and offer new insight . With the advent of modern computers, this approach has opened up a whole new industry; scarcely an issue of a current major journal appears without a paper reporting new results from simulations. However, simulations can only complement , not replace, analytical studies; they usually possess a different set of weaknesses. Understanding is most rapidly advanced when the numerical and analytical approaches are used in concert, each guiding the other in small steps. It is neither necessary nor desirable to use a full-blooded N-body simu-