On his return to Austin he took Moore's summer geometry course followed by Moore's graduate topology classes and seminars. Upon finishing his Ph.D. at Texas in 1952, he took a position at The University of Virginia. But the bulk of his academic career was spent at the University of Georgia, from 1959 until his retirement in 1986. Joe Ball's dissertation, "Continuous and equicontinuous collections of arcs", appeared in the Duke Mathematical Journal in 1952. He showed that if the union, G * , of such a collection is a planar continuum, then G * is either a 2-cell or an annulus, and there is an autohomeomorphism on the plane taking each element of the collection onto a straight line interval. In reviewing the paper for Mathematical Reviews, E.E. Moise commented that the argument required 11 pages. Ball also noted that if G * is not assumed to be planar but is still a continuum, then the union of the endpoints of the collection is compact and has at most two components. In E 3 such a collection could form a MΓΆbius band, and the set of endpoints would have exactly one component. His next paper, "Some theorems concerning spirals in the plane", appeared in the American Journal of Mathematics in 1954 and reflected the interest of many of Moore's students of the 1950s in planar spirals.
There followed three papers on ordered spaces, no doubt a result of his interest in the Souslin Problem. He was apparently the first to observe that point-countable open covers of ordered spaces have locally finite open refinements, and thus such spaces are countably paracompact. In another paper he gave three conditions each of which guarantees the separability of connected ordered spaces, and he also gave conditions ensuring that the product of ordered spaces be normal.