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To explain is to make clear or plain, to change something not understood to something that is understood. This document defines explanation; makes clear the differences between explanation and related subjects; describes and illustrates over 50 factors affecting the quality of an explanation; discusses the classes of words in an explanation and gives a program for vocabulary analysis with a computer; explains methods for revising and improving an explanation and gives three illustrations at length; discusses practical aspects of improved explanation; states in full a powerful 'Vocabulary Analysis Program' which has been worked out and aids explaining (this program runs on the PDP-7 computer of Digital Equipment Corporation, and a copy of the program tape is available on request); states half a dozen more computer programs for aiding explanation; gives eight sample explanations and their assessment; gives an annotated bibliography of 18 references relating to better explanation; and contains a glossary and an index.