32 JOSEPH BARRELL 



2,600 and 3,000 km. A mean value of 2,800 km. (1,740 miles) will 

 be chosen. From the breadth of half a wave-length it appears that 

 0.0034 dyne of anomaly may be taken as equivalent to 100 feet of 

 rock. This gives the crest and trough as 625 feet (190 m.) from 

 the mean plane, a total amplitude of 1,250 feet (380 m.). The 

 stress-differences which this wave-series throws upon an earth 

 elastically competent throughout to bear the stresses are shown 

 by curve C, Fig. 18. Hehnert has published an extensive paper 

 dealing with the force of gravity and the distribution of mass in the 

 crust of the earth,^ to which the writer's attention has been called 

 recently by Professor Pierpont, of the mathematical department 

 of Yale University. In this paper Helmert adopts the hypothesis of 

 regional isostasy and finds his results confirmatory of it, but not 

 in accord with the hypothesis of close and local isostatic adjustment. 

 His work is especially valuable as confirmatory of the present con- 

 clusions, since it deals with regions outside of the United States. As 

 he does not, however, compute the corrections due to the distant 

 large irregularities of topography, his figures cannot be directly 

 compared with Hayford's New Method anomalies. Neverthe- 

 less his conclusions as to the existence of broad regional excesses 

 or defects of mass are comparable to those here reached. Under 

 the section on the horizontal displacement of compensation and 

 extended excesses and defects of mass^ he sums up part of the 

 evidence in the following statement: ''We have then to deal with a 

 continuous region of positive total gravity disturbance in Europe 

 1,000 km. broad and also with a region of negative disturbance 

 in Asia of at least 500 km. breadth, both possessing great linear 

 extension." 



RELATIONS OF ACTUAL STRESSES TO THE SUM OF HARMONIC WAVES 



Both Darwin and Love point out that the actual stress- 

 differences imposed by the superposition of different harmonic 

 waves is not in general the. sum of the individual stress-differences. 

 Darwin, however, states the special conditions under which the 



' "Die Schwerkraft und die Massenverteilung der Erde," Ency. Math, Wissen- 

 schaft, Band VI, i, B, Heft 2 (1910), pp. 85-177. 

 ^Op. «■/., pp. 152-54. 



