The conception which had been held from the earliest times that the three recognised states of matter were clearly separated from each other received a rude blow from the interpretation put upon the work of Andrews, that the liquid and gaseous states were really continuous, and that the two states could only be classified under one head—the fluid state. Andrews demonstrated that by placing a liquid under a pressure greater than the critical, and then raising the temperature, the liquid might be made to pass to an undoubtedly gaseous state without any sudden change having been visible. Thus the continuity of the liquid and gaseous states seemed established. I say seemed, because I have shown in former papers that under any pressure the fluid passes at a given temperature from a state where it possesses cohesion, capillarity, or surface tension—the distinguishing property of liquid, which prevents it freely mixing with a true gas—to a state where it possesses no cohesion, capillarity, nor surface tension, and where it mixes freely with any gas—in fact, to the gaseous state; and this change takes place at a fixed temperature independent of pressure. As MM. Cailletet and Hautefeuille have recently come to the conclusion that the continuity claimed by Andrews does not exist, and have thus corroborated my work, I wish to place on record more fully the conclusions to which this work has led me.