no W. D. MacMILLAN 



Hayford and Bowie on the extremely delicate question 1 of the 

 "areas of compensation" is not altogether trustworthy, and the 

 sizes of these areas must be regarded as unknown. 



From the fact that the hypothesis of isostasy reduced the sum 

 of the residuals from 65,434 to 8,013, or by approximately 90 per 

 cent, and from the fact that the average elevation of the United 

 States is about 2,500 feet Hayford concluded that the average 

 departure from complete isostasy in the United States is equal to 

 about 250 feet of rocks. It is not easy to see how Hayford drew 

 this conclusion. It certainly has no mathematical justification, 

 for even if the theory were perfect and the isostasy complete, the 

 sum of the squares of the residuals would not be zero, since the 

 imperfections of the observations would still give us a very respect- 

 able, but quite unknown, sum. How then can we form a quanti- 



1 If the separate anomalies in the United States be compared, it is found that 

 in 16 cases out of 41 the anomaly with local compensation assumed is smaller than 

 with regional compensation assumed uniformly distributed to zone K (18.8 kilo- 

 meters), and only 13 cases in which it is larger. Similarly, there are 20 cases out of 

 41 in which the anomaly with local compensation is smaller than with regional com- 

 pensation extending to zone M (58.8 kilometers), and only 15 cases in which it is 

 larger. There are 26 cases out of 41 in which the anomaly with local compensation 

 assumed is smaller than with regional compensation assumed to extend to zone 

 O (166.7 kilometers), and only 12 cases in which it is larger. In all other cases the 

 two anomalies compared are identical to the last decimal place used, the third. 



The evidence either for or against local compensation in comparison with such 

 regional compensation distributed uniformly over these moderate distances is neces- 

 sarily slight and possibly inconclusive. For, as shown in the table, the difference 

 between computed effects of compensation in the two cases compared is very small 

 upon an average. The whole evidence is furnished by these very small differences, 

 which frequently are less than the errors of observation and computation. As shown 

 by the table, there is but one station among the 41 — namely, No. 43, Pike's Peak — 

 at which the difference between the computed effect of local compensation and the 

 computed effect of regional compensation uniformly distributed to zone K exceeds 

 0.004. Such a difference tends to become greater as the distance over which the 

 regional compensation is supposed to be uniformly distributed is increased, but 

 columns 7 and 8 of the table show that even when the regional compensation is assumed 

 to extend to zone 0, a distance of 166. 7 kilometers, from the station, there is only one 

 station among the 41 — namely, station no. 54, San Francisco — at which the computed 

 effect of local compensation and the computed effect of regional compensation exceeds 

 0.017 dyne. 



Nevertheless the evidence, slight as it necessarily is, indicates that the assump- 

 tion of local compensation is nearer the truth than the assumption of regional com- 

 pensation uniformly distributed to zone K (18.8 kilometers). The evidence is still 

 stronger in the same direction when the comparison is made between local compensa- 

 tion and regional compensation extending uniformly to the greater distances, 58.8 

 and 166.7 kilometers, represented by zones M and O. — Hayford and Bowie, The 

 Effects of Topography and Isostatic Compensation upon the Intensity of Gravity, p. 101. 



