If the field of observation were cylindrical in shape, if it had parallel sides, if its projection were a rectangle or a parallelogram, the height at which birds are flying would not be a factor in finding out their number. Then the sample would be of equal breadth throughout, with an equally wide representation of the flight at all levels. Since the field of observation is actually an inverted cone, triangular in section, with diverging sides, the opportunity to detect birds increases with their distance from the observer. The chances of seeing the birds passing below an elevation midway to the flight ceiling are only one-third as great as of seeing those passing above that elevation, simply because the area of that part of the triangle below the mid-elevation is only one-third as great as the area of that part above the mid-elevation. If we assume that the ratio of the visible number of birds to the number passing through the density plane is the same as the ratio of the triangular section of the cone to the total area of the plane, we are in effect assuming that the density plane is made up of a series of triangles the size of the sample, each intercepting approximately the same number of birds. We are assuming that the same number of birds pass through the inverted triangular sample as through the erect and uninvestigable triangle beside it (as in Figure 11, Diagram II). In reality, the assumption is sound only if the altitudinal distribution of migrants is uniform. [Illustration: FIG. 11. Theoretical possibilities of vertical distribution. Diagram I shows the effect of a uniform vertical distribution of birds. The figures indicate the number of birds in the respective areas. Here the sample triangle, ABD, contains the same number of birds as the upright triangle, ACD, adjacent to it; the density plane may be conceived of as a series of such alternating triangles, equal in their content of birds. Diagram II portrays, on an exaggerated scale, the situation when many more birds are flying below the median altitude than above it. In contrast to the 152 birds occurring in the triangle A´C´D´, only seventy-two are seen in the triangle A´B´D´. Obviously, the latter triangle does not provide a representative sample of the total number of birds intersecting the density plane. Diagram III illustrates one method by which this difficulty may be overcome. By lowering the line F´G´ to the median altitude of bird density, F´´G´´ (the elevation above which there are just as many birds as below), we are able to determine a rectangular panel, HIJK, whose content of birds provides a representative sample of the vertical distribution.]