1. The word contour is largely used in ordinary language, but its meaning, when so used, is in general very different from its meaning as a scientific term. We speak of the contour of a hill, a cloud, a country, and so on; meaning usually a profile or an outline,—sometimes a particular outline only. Yet, even in this popular use of the word, we have an indication of its more exact significance. Thus, we see that the visible horizon, if we consider it to be a contour line, is the curve in which the earth's surface is met by its tangent-cone the vertex of which is at the observer's eye. The tangent-surface has a constant characteristic; and it is this possession of a distinctive property by all surfaces which give rise to contour lines, which furnishes the reason for the peculiar applicability of the method of contours to physical problems.