INFLUENCE OF EARTH SHRINKAGE 507 



question whether the acceleration may not have produced a slight heaping 

 of waters toward the equator, sufficient to affect the distribution of the 

 continental seas — seas that have often been so shallow that a change of 

 level of 100 feet would markedly alter their limits. 



If the residual stresses which could remain in the body of the earth 

 after an epoch of shrinkage were small in comparison with those stresses 

 resulting from the acceleration of the earth's rotation due to the shrink- 

 age, then an adjustment of figure to this new speed of rotation would 

 occur as a part of the movement, an adjustment which would involve the 

 interior of the earth and would not be expressed by an equatorial heaping 

 of ocean waters. As the slight equatorial bulging would not modify ap- 

 preciably the character of the general deformation, there would be no 

 visible evidence of the accompanying adjustment to a new figure in rota- 

 tional equilibrium. 



An equatorial heaping of waters accompanying earth shrinkage would 

 therefore require an ability in the earth to retain residual stresses large in 

 comparison with the small bodily stresses resulting from the slightly in- 

 creased speed of rotation. Such a stress would operate through the whole 

 body of the earth. It is readily seen, however, that the change in the 

 earth's shape, due to the acceleration, must be but a small fraction of that 

 involved in the shrinkage, and it is quite possible, therefore, that the 

 undischarged centripetal stresses remaining after the shrinkage are still 

 much larger than the superimposed stresses due to slightly increased rota- 

 tion. 



On this assumption it was sought to find to what extent a given shrink- 

 age of the earth would cause an equatorial heaping of waters. For this 

 purpose were employed the tables on pages 59 and 67 of "The tidal and 

 other problems," by Chamberlin et at., which permit a simple statement of 

 the relations, with an error probably not greater than 5 per cent. 



As the amounts of earth shrinkage involved in epochs of diastrophism 

 are not even approximately known, any greater refinement in treating of 

 the results would be useless. It is seen from these tables that a decrease 

 of earth radius from 4,060 miles to 3,960, maintaining the La Placian 

 law of density, would result in a shortening of the day by 4,419 seconds 

 (page 59). A shortening of the day by 14,990 seconds involves the rela- 

 tive changes in radius given in the first two lines of the table, page 67. 

 From these figures it may be readily computed that a general shrinkage 

 of the earth to the extent of 1 mile in mean radius will result in an 

 increase of equatorial over polar radius of about 95 feet; a shrinkage of 

 10 miles will result in a relative increase of about 950 feet. The results 

 will be somewhat different according to whether the shrinkage is equa- 



