184 G. K. GILBERT — CONTINENTAL TROBLEMS. 



congelation, having been initiated by an otherwise unimportant ine- 

 quality, would be perpetuated by any of those cumulative processes 

 which are of such importance in various departments of physics ? And 

 can it be shown that such a process of continent-building would segre- 

 gate in the continental tract certain kinds of matter, and thus institute 

 the conditions essential to isostatic equilibrium? To the first of these 

 questions no answer is apparent, but I incline to the opinion that the 

 second may be answered in the affirmative. If we assume the liquid 

 envelope to consist of various molten rocks arranged in the order of their 

 densities, and if we assume, further, that their order of densities in the 

 liquid condition corresponds to their order of densities in the solid con- 

 dition, then the successive crusts whose heaping built up the continents 

 would all be formed from the lightest material, and the isostatic condi- 

 tion would be satisfied. 



It was the fashion of the last generation of physical geographers to 

 study the forms of continents as delimited by coasts, seeking analogies 

 of continental forms with one another, and also with various geometric 

 figures, especially the triangle. The generalizations resulting from these 

 studies have not yielded valuable ideas, and the modern student is apt 

 to smile at the effort of his predecessor to discover the ideal geometric 

 figure where the unbiased eye sees only irregularity. But barren as 

 were those studies I am not satisfied that their method was faulty ; and 

 as a physiographer I have such appreciation of the ideas that sometimes 

 grow from studies of form that I have attempted to apply the old method 

 to the new conception of the continental plateau. Confessing in advance 

 that my only result has been negative, I nevertheless recite what I have 

 done, partly because negative contributions to an obscure subject are not 

 entirely valueless, and partly with the thought that the forms whose 

 meanings I failed to discover may nevertheless prove significant to some 

 other eyes. 



What I did was to draw upon a globe the outline of the continental 

 plateau and then view it from every direction. Afterwards I developed 

 the figure upon a plane surface, employing for that purpose a mode of 

 projection which is probably novel. As this mode is not susceptible of 

 mathematical formulation, and therefore will not find place in the litera- 

 ture of cartography, I may be pardoned for applying a trivial name and 

 calling it the orange-peel projection. The name almost explains it. Con- 

 ceive the continental plateau to be outlined upon a spherical orange and 

 the rind of the orange to be divided by a sharp knife along the sinuosi- 

 ties of the outline; conceive then that the portion of the rind thus cir- 

 cumscribed is peeled from the orange and is spread upon a flat surface, 

 the different parts being stretched and compressed so as to pass from 



