It is perhaps generally true of very high ranges that their highest peaks and ridges are arranged so as to be in accordance. If we imagine a surface which shall everywhere touch these summit-levels, it will be found to form a gently arching dome, with major axis coinciding with the general trend of the mountains and highest in the interior of the range. This accordance has been observed in many alpine ranges, such as the Pyrenees, Alps, and Caucasus, the Sierra Nevada and Cascades, the Selkirks and Coast Range of British Columbia, and the mountains of Alaska.

In attempting to explain this remarkable coincidence, the hypothesis of peneplanation and subsequent upwarping, which is so satisfactory and so widely accepted as applied to the Appalachians and similar cases in Europe, has also been employed for alpine ranges of comparatively recent geological date. This explanation has not, however, found so general an acceptance for the high mountains, and other hypotheses should be considered as possible alternatives in each case. These rival hypotheses may be grouped into two classes: (1) those which regard the accordance as due to original structure in the processes of upheaval, and (2) those which refer the phenomenon to the spontaneous action of the denuding forces.

(1) There is no reason to believe that mountains could, or ever did, rise to indefinite heights; on the contrary, their height must be limited by the ability of their foundations to sustain them, and the principle of isostatic adjustment might well operate to produce some rough accordance of height, while denudation during the slow upheaval would tend to remove the higher summits faster than the lower ones. "The downcrushing of higher, heavier blocks with the simultaneous rise of their lower, lighter neighbors, coupled with the likewise simultaneous, especially rapid loss of substance on the higher summits, form a compound process leading toward a single, relatively simple result." (Daly).

(2) The core of many high ranges is a granite batholith, from which are carved the higher peaks and ridges, the original covering of strata having been swept away by denudation. The form of the uneroded batholith was that of a gently arching dome, such as might be expected to give rise to accordant summits in the peaks carved from it. In ranges, like the Alps, which have no batho-lithic core, there is yet almost always great metamorphism due to the compression of the rocks and the weight of overlying masses.

The surface of the metamorphic core was probably quite regular before the covering strata were removed, and would tend to result in accordant summits among the peaks which are sculptured out of it. The thoroughly metamorphosed rocks, such as gneisses, schists, quartzites, marbles, etc., are not very different from one another in their resistance to weathering, and hence denudation would tend, in a general way, to maintain the accordance. Indeed, many investigators of the Alps ascribe the accordant summits to denudation alone. "The longer a mountainous region is exposed to denudation, the more completely do the indications of original inequalities in the relative heights of its peaks disappear, till finally the summits are determined entirely by the character of the rocks, the most resistant rocks forming the highest peaks." (Penck).

It is not necessary to assume that any of these alternative hypotheses is true to the exclusion of the others. All the factors mentioned may cooperate to a common end, and for every mountain range the problem should be regarded as an individual one, without taking for granted that one explanation will cover all cases.