This paper contains some results of a study of the freezing points of binary alloys, the freezing points being traced for all proportions of the two metals, so that the results when plotted give a complete freezing-point curve. The freezing point, properly speaking, is the temperature at which a liquid and some solid that can be formed from it are in equilibrium. In practice, at all events when working with alloys, it is necessary to take as the freezing point the temperature at which solid matter begins to separate from a liquid that is being slowly cooled. The first indication of this formation of solid is generally afforded by a thermometer immersed in the liquid, the heat given out when solid matter separates arresting the fall in temperature and causing the thermometer to register a constant temperature for a shorter or longer time. It is evident that, except when we are dealing with a pure substance, the freezing point obtained in this way must be below the true freezing point. This cause of error can be diminished by using a sensitive thermometer, by using a large mass of substance, and by causing the rate of fall to be very slow. Surfusion also, where it occurs, must be prevented by the usual method of dropping in nuclei. When the freezing point changes a good deal for a small change in the concentration, this method is liable to give values of the freezing point considerably below the true value.