THE STRENGTH OF THE EARTH'S CRUST 



JOSEPH BARRELL 



New Haven, Connecticut 



PART VI. RELATIONS OF ISOSTATIC MOVEMENTS TO 

 A SPHERE OF WEAKNESS— THE ASTHENOSPHERE.^ 



Introduction and Summary 655 



Stress-Differences between Contiguous Columns of the Crust 659 



Stresses under Conditions of Isostatic Equilibrium 



Modifications of Stresses Produced by Base-Leveling 



Relief of Stress Accompanying Restoration of Isostasy 

 Relations of Undertow to the Zone of Compensation 



Present Status of the Problem 



Objections against Undertow in the Zone of Compensation 



659 

 666 

 670 

 672 

 672 

 677 

 Undertow Restricted to a Sphere of Weakness — the Asthenosphere 680 



INTRODUCTION AND SUMMARY 



In studies on the nature of isostasy it is necessary to distinguish 

 between, first, the existence of isostasy; second, the limits of 

 isostatic equihbrium; and third, the mode of maintenance of this 

 equihbrium. 



The first has long been known, the knowledge of the existence 

 of some relation of density counterbalancing elevation having been 

 gradually developed since the middle of the nineteenth century 

 through the determination of the local deviations of the vertical 

 as shown by the comparison of the astronomic and geodetic latitudes 

 for the same station. This was a problem which arose in both 

 astronomy and geodesy. It was found, when the attractive effect 

 of the mountain regions was computed, that they did not deflect 

 the vertical at adjacent stations as much as was to be expected 

 from their visible masses. The phenomenon was first pointed out 



' An abstract of Parts V, VI, and VII of this series was given at the April, 19 14, 

 meeting of the American Philosophical Society at Philadelphia under the title, 

 "Relations of Isostasy to a Zone of Weakness — the Asthenosphere." See Science, 

 XXXIX, 842. 



6ss 



