During World War II, the Ballistic Research Laboratory of the U.S. Army was charged with the responsibility of preparing firing tables for the various new weapons under development. The computations required for the preparation of these firing tables were so time-consuming that they overwhelmed the facilities available at the laboratory. In spite of the extensive arrangements the laboratory made with the University of Pennsylvania for assistance, the backlog continued to grow. At one point, more than 100 female students were engaged to carry out firing table calculations. It was to relieve this bottleneck that John W. Mauchly and J. Presper Eckert, two members of the faculty of the Moore School of Engineering, the University of Pennsylvania, proposed the construction of the ENIAC, which was funded by the U.S. Army. In this article, I describe the nature of the computations required in the preparation of firing tables and explain the reasons why these calculations were so burdensome.