We adapt several parallel sorting algorithms (block sorting algorithms) and distributed sorting algorithms for implementation on an Ethernet network with diskless Sun workstations. We argue that the performance of sorting algorithms on local area networks (LANs) should be analyzed in a manner that is different from the ways that parallel and distributed sorting algorithms are usually analyzed. Consequently, we propose an empirical approach which will provide more insight into the performance of the algorithms. We obtain data on communication time, local processing time, and response time (i.e. total running time) of each algorithm for various file sizes and different numbers of processors. Comparing the performance data with our theoretical analysis, we attempt to provide rationale for the behaviour of the algorithms and project the future behaviour of the algorithms as file size, number of processors, or interprocessor communication facilities change.