The nature of warfare has always been largely determined by contemporary technology. Instances of technological change undertaken for the sake of military advantage have also been relatively common in history. The relationships between science and warfare, however, have been much more variable and ambiguous. The papers and discussions of the Symposium investigate selected aspects of the complex relationships between science and technology on the one hand, and warfare on the other, from the Renaissance to the 1960s. In the first session, Professor Hall takes up in turn the possible areas of interaction between science (exterior ballistics, engineering, explosives, mechanics, and metallurgy) and military technology (edge weapons, cannons and mortars, fortification and siege warfare, and small arms) in the 15th, 16th, and 17th centuries. The notion that science is pursued for utilitarian ends, Hall finds, is an unhistorical projection backward from our own age." He excludes navigation and medicine from consideration, because they were civil as well as military concerns. In spite of the pleading of certain early propagandists of the Empire of Man over Nature," and in spite of the elaborate sketches of military engines in Leonardo's notebooks, military technology was largely innocent of scientific method. The developments in fortification required mathematical skills, but nothing more than elementary geometry and arithmetic. Mathematicians studied the ancient problem of the trajectory of projectiles, but their efforts affected neither the design nor the use of guns. The range tables they provided were not even usable with the guns of the time. The solution of the trajectory problem would await Benjamin Robins and the 18th century. Professor Hale supports Hall's conclusion with three arguments. In the 16th and 17th centuries, armies were so organized as to preclude any productive contact with the worlds of science and technology.