Our work on the collection and generalization of morphometric data was begun several years ago. A work of this kind encounters great difficulties. The morphometric relief data available in literature are scattered through innumerable papers; moreover, these data are usually quite inaccurate (because averaged numerical data are reported) and incomplete. Many papers and special works provide information only on the length and width of the relief forms, but not on their height nor depth; other papers only describe the width and height without referring to length; still others only mention the steepness of slopes, without providing any other dimensions, and so on. In spite of the difficulties encountered, our preliminary processing of the collected data enabled us, in 1959, to discern patterns in the ratios of the basal area (length and width) and the vertical develop ment (height and depth) for a considerable number of relief forms including the tectonic structural forms, i. e., forms deriving from movements of the Earth's crust.
In classifying relief forms and tectonic structures according to their morphometric indexes, we found a regular repetition of the ratios of these indexes, while the forms themselves could be grouped in a general morphometric series consisting of 18 orders (Table 1). In these orders the ratios of length, width, and vertical development are constant (1 : 3 and 1:10), and they comprise the most common relief forms and tectonic structures of the Earth.
Obviously some of the forms differ in their dimensions from those indicated in the orders of the general morphometric series. However, further processing of the data made it possible to establish the limits of deviation and to find out that wide forms (rounded in plan) deviate by 20-30% from the linear indexes of the series, whereas their areas largely conform to those of the series, In very long forms, the ratio of width to length reached 1 : 10 in isolated cases, but their areas were similar to those of the forms of the respective order in the general series.
The first order of the general morphometric series comprise the smallest relief forms of the type of sand ripples and the smallest folds occurring in plastic clays, shales, etc. The last orders of the series include entire highlands, continents, and oceanic depressions (Gerassimov's "geotectures", 1946). Order XVIII comprises forms which are commen surable with the Earth itself, their areas approaching those of the hemi spheres.
The general rr:orphometric series is simple and consistent (see Table 1), the transition from one order to another being completely uniform over the entire series and with respect to all the indexes (length, width, height, and area). The uniformity is expressed by the same ratios as in every
individual order (1 : 3 and 1 :10) but with a certain difference. The difference consists in the ratio of 1 : 3 alternating with the ratio of 1 : 3.3 for every other order (10, 30, 100, 300, etc.). The index for areas increases regularly by a factor of 10 in transition from one order to the next.
The general morphometric series p_oved to withstand various trans formations to other ratios (1X2, 2X3, 3X5, etc.); the attempts to eliminate the existing ratio of 1 : 3.3 also failed, In such attempts the actual relief forms are satisfactorily arranged in two or three adjacent orders but after that the theoretically calculated values disagree with the factual data. The regularity involved in the transition from forms of a certain order to the next order (i.e., their trebling) is especially evident in relief forms which definitely derive from wave action (sand ripples, barchan ridges, etc.). When enlarged threefold, these forms undergo the most successful transition to geometrically similar bodies of the next order with the least rearrangement of their original elements. The elements are preserved when the slopes of the small ridges are taken over by the larger ridges, as shown in Figure 1, while the material is transported over short distances (from negative relief forms to crests of the nearest ridges).
Figure 1 presents a scheme of sand ripples formed from local material on a horizontal surface, preserving the general basic level. The scheme must be somewhat modified for large relief forms developed on the Earth's spherical surface and for forms whose genesis involves influx of additional material (or loss of material), yet the general principle and the derived ratios are preserved.
It will be seen from Figure 1 that if two adjacent forms — a positive and a negative one (i. e., crest and trough) — are taken as the basic ones (as single "wave"), then the next order is obtained by combining three such "waves". Moreover, the scheme shows that the "momentum" stored between the large positive forms (in the "trough") is capable of producing a smaller ridge. In the crest portion of the large ridge there is a "momentum" tending to flatten it and subdivide it into two smaller crests. Both cases are observed in nature when the spacing of ridges are changed, and when individual large forms become excessively wide. Thus, the transition of forms from one order to another is effected with relative simplicity, while their similarity is partially maintained by the common element of slopes and by certain permanent properties of rocks (shear angles, angles of repose, etc.).