[Illustration: FIG. 2.] It will be seen that the subject of eutexia embraces many points of practical importance and of theoretical interest. Thus it has been shown by Dr. Guthrie that the desilverizing of lead in Pattinson's process is but a case of eutexia, the separation of lead on cooling a bath of argentiferous lead poor in silver being analogous to the separation of ice from a salt solution. Dr. Guthrie has also shown that eutexia may reasonably be supposed to have played an important part in the production and separation of many rock-forming minerals. It is with considerable diffidence that I suggest the following as an explanation of the multitude of facts to which previous reference has been made. In a mixture of two substances, A and B, we have the following forces active, tending to produce solidification: 1. The cohesion between the particles of A. 2. The cohesion between the particles of B. 3. The cohesion between the particles of A and the particles of B. With regard to this last factor, it will be seen that there are three cases possible: 1. The cohesion of the mixture A B may be greater than the cohesion of A + the cohesion of B. 2. The cohesion of A B may be equal to the cohesion of A + the cohesion of B. 3. The cohesion of A B may be less than the cohesion of A + the cohesion of B. Now, since cohesion tends to produce solidification, we should in the first case expect to find the melting-point of the mixture _higher_ than the mean of the melting-points of its constituents, or the curve of melting-points would be of the form given in _a_, Fig. 3. Here no eutectic mixture is possible. [Illustration: FIG. 3.] In the second case, where cohesion A B = cohesion A + B, we should obtain melting-points for the mixture which would agree with the mean of the melting-points of the constituents, the curve of melting-points would be a straight line, and again no eutectic mixture would be possible. In the third case, however, where cohesion A B is less than cohesion A + B, we should find the melting-points of the mixture lower than the mean of the melting-points of its constituents, and the curve of melting-points would be of the form given in _e_, Fig. 3. Here, in those cases where the difference of cohesion on mixture is considerable, the curve of melting-points may dip below the line _e f_. This is the _only case_ in which a eutectic mixture is possible, and it is, of course, found at the lowest point of the curve. If it be true, as above suggested, that the force of cohesion is at its minimum in the eutectic alloy, we should expect to find, in preparing a eutectic substance, either that actual expansion took place, or that the molecular volume would gradually increase in passing along our curve of melting-points, from either end, for each molecule added, and that it would obtain its greatest value at the point corresponding to the eutectic alloy.