Excerpt from The American Mathematical Monthly, Vol. 21 Note BY the editors. - This article illustrates the reference in the editorial of this issue concerning papers of a somewhat more technical character in which, however, we have tried to have the technical terms explained for the benefit of the general reader. Professor Bussey has met this request most admirably. The study of tactical configurations known as triple systems had its origin in two related problems proposed independently by T. P. Kirkman1 and J. Steiner.2 Kirkman's problem is to arrange fifteen school girls in parties of three for seven consecutive days' walk so that every two of the girls walk together once and only once during the seven days. There is a good account of the history of the problem with several methods of solution in Ball's Mathematical Recreations and Essays, 5th edition, Chapter 9. An arrangement of a number of elements in sets of three so that every set of two is contained in one and only one set of three is called a triple system. The sets of three are called triples or triads. The problem of the fifteen school girls involves a triple system of 15 elements and 35 triads. The simplest triple system is the following well-known one of 7 elements and 7 triads. The digits 0, 1, 2, 3, 4, 5, 6 are the elements and the columns are the triads. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.