Under certain conditions, an explosion results when a material in the molten state falls into a much colder liquid. These accidental explosions, although infrequent, are violent enough to cause extensive damage. Although previous investigators have studied this phenomenon, their studies have been restricted to the particulars affecting their own industry. Moreover, in only one case, that of the metal industry, has a satisfactory remedy to this problem been found; and even in this case, no satisfactory explanation of the phenomena has been obtained. Neither the paper industry nor the nuclear reactor industry, both plagued by these explosions, have found an answer to them. In this thesis the problem of break-up of moltem materials in a cool liquid has been studied both theoretically and experimentally. The theoretical study was based purely on fundamental principles stated as axioms. The theoretical study lead to the conclusion that the rate of cooling is the important factor in whether, a molten mass breaks up into many smaller pieces. The agreement of the theoretical results to experimental results lends credence to the theory. The experiments involved dropping small amounts of aluminim, zinc, lead, bismuth and tin in water and liquid nitrogen. This research program has not produced all the answers to this problem, because, if nothing else, it is impossible for our intelligence to understand nature to perfection. Many aspects of these phenomena, still remain obscure. It is claimed, however, that this paper contains a rational interpretation of the phenomena, and considers, as a unit, a problem that is common to many industries.