ESTIMATES AND CAUSES OF CRUSTAL SHORTENING 5 5 



rapidly than at present, at one time possibly as fast as once in 

 five and one-half hours. During this time of changing rotation, 

 assuming that the geoid has accommodated itself to its period of 

 rotation in the past as at present, Peirce states that there was a 

 "diminution of oblateness arising from the diminished velocity of 

 rotation upon the axis." He concludes on the hypothesis of 

 homogeneity, when the earth rotated 4.236 times as fast as at 

 present, that the equatorial radius would have been about 2^ 

 per cent, greater than at present. 



Taylor 1 later calculated that "when the day measured but 

 six of our hours, the equatorial radius (assuming a true ellip- 

 soid of revolution, and neglecting the small amount of contrac- 

 tion by loss of heat) would have been about one-tenth greater 

 than it now is, or 4359 miles, and polar radius about one-sixth 

 less, or 3291 miles. In other words, the poles would have been 

 about 658 miles nearer the center of the earth than they are at 

 present, and the equatorial protuberance about 396 miles higher 

 than at present." 



The discrepancy between these two results is so great that I 

 referred the problem, for re-solution, to Professor C. S. Slichter, 

 whose paper on this and other points immediately follows (pp. 

 65-78). I further asked that he obtain the amount of surficial 

 contraction which would result from the change of oblateness. 

 Upon the hypothesis of homogeneity, and with a period of rota- 

 tion of five and one-half hours, he obtains a result which is prac- 

 tically the same as that of Peirce's. He finds that the earth, 

 instead of having a mean radius of about 3959 miles, would have 

 a polar radius of about 3736 miles, and an equatorial radius of 

 about 4076 miles. This change from the past oblate spheroid 

 to the present oblate spheroid would involve a contraction of 

 the surface of the earth of about 210,000 square miles. 



Change of pressure. — It further occurred to me that when the 

 earth rotated more rapidly, the centrifugal force was greater 

 than at present. When the rotation was four time as rapid as at 



1 On the crumpling of the earth's crust, by W. B. Taylor : Am. Jour. Sci., Vol. 

 XXX, 1895, p. 257. 



