THE DOCTRINE OF ISOSTATIC COMPENSATION 699 



Preponderant effect of near masses due to law of inverse squares. — 

 It is a direct consequence of the law of inverse squares that bodies 

 relatively near the station exert a preponderant influence upon 

 the intensity of gravity, and a relatively small mass of high density 

 within a few miles of the station may thus be responsible for the 

 major portion of the anomaly in the direction or intensity of gravity. 

 To employ an illustration from the field about a magnetic needle: 

 the local variation in the pointing of the needle may be explained 

 either, upon the one hand, by the location of the station with refer- 

 ence to the magnetic poles of the earth, or, upon the other, by the 

 propinquity of excessively magnetic masses — such, for example, as 

 a deposit of magnetic iron ore. Within the Mississippi plain we 

 find generally "normal" conditions explainable by the position of 

 stations with reference to magnetic poles; whereas in many areas 

 of the northern peninsula of Michigan the notable magnetic 

 "anomaly" is explainable almost entirely by local conditions. 



It has sometimes been claimed that the extension of Clairaut's 

 theorem by Stokes makes the value of Ag. independent of local 

 (that is, near-by) variations in density, which maybe both large and 

 abrupt. This, however, is not the case. The non-permissibility 

 of such variations for the application of the theorem was recognized 

 by Stokes 1 , as it has been by Rudzki. 2 Clairaut in fact developed 

 the theorem to apply to an earth supposed to have a liquid interior. 



Hay ford's explanation of anomalies found in systematic regularity 

 as contrasted with local irregularity in distribution of mass. — Hay- 

 ford's studies of the deflection of the vertical and of gravity irregu- 

 larities within the United States have been carried out upon the 

 assumption that they are explainable by general, as contrasted with 

 local, conditions; and his method of reducing residuals falls in 

 with the explanation of magnetic variation within the Mississippi 

 plain. A solution of the problem of anomalies in the intensity of 

 terrestrial magnetism in northern Michigan which caused these 

 residuals to disappear through a process of general averaging 

 would constitute a proof, not of the certitude of the hypothesis 

 assumed, but rather of its falsity. 



1 Mathematical and Physical Papers, II, 164. 



2 Physik der Erde, pp. 35-36. 



