472 



0. FISHER ON MR. MALLET S 



a crust, then the explanation fails that they were caused by unequal 

 radial contraction when the crust was first permanently formed and 

 thin. . Neither do I understand how Mr. Mallet proposes to account 

 for this unequal radial contraction. For, if the subjacent rocks up 

 to that period still continued fluid, as it is supposed they did, the 

 thin crust would have become corrugated in wrinkles of small dimen- 

 sions, and not in wide depressions and elevations*. But if inequality 

 of contraction be supposed to have produced the difference of eleva- 

 tion as between the ocean-bed and the continental surface, then, 

 taking the coefficient of cubical contraction at 0-00002, which is 

 what Mr. Mallet informs me is the mean, and supposing the crust to 

 have cooled from 4000° E. to 0°E., we shall find that a thickness of 

 thirty-eight miles will give us one mile contraction in the radial 

 direction. Call the thickness forty miles : supposing, then, that from 



* I have proved, in a paper read before the Cambridge Philosophical Society 

 in February last, that a flexible crust of small thickness, resting on a liquid, when 

 compressed horizontally would assume a corrugated form, of which a section 

 across the corrugations would exhibit a series of equal circular arcs, arranged in 

 a festoon like manner as in the lower strong line of the annexed figure. The 

 radii of these arcs would depend only upon the relative densities (p) of the 

 crust and (<r) of the liquid and the thickness (c) of the crust., and would each be 



equal to 2-c, 



Diagram showing the approximate Form of a Section of a Flexible Crust 

 horizontally compressed and resting on a Liquid. 



(The curves bounding the upper and lower surfaces are circles whose centres 

 are O, O, O. The densities of the crust and liquid are supposed nearly equal • 

 and therefore OB = 20 A.) 



o o 



In the case of the cooled crust of the earth, the crust can be only imperfectly 

 flexible, and, the densities being nearly the same, the radii of the lower curves 

 become each nearly 2c. Consequently, if the curves have any appreciable length, 

 the crust cannot be thin in the mathematical sense (that is in comparison to the 

 other magnitudes in question). The above result can therefore be only taken as 

 very approximately true. Nevertheless it seems a sufficient guide to what the 

 general character of the corrugations would be to support the assertion made in 

 the text. 



