BAUER: ORIGIN OF THE EARTH's MAGNETIC FIELD 5 



force within the sphere is constant in amount and in direction, 

 parallel to axis of rotation in the present instance), /x (u) = 

 fz{u) = i Tfx = constant throughout the Earth, ix being the equi- 

 valent intensity of magnetization per unit of volume. The 

 observed values of the characteristic functions as derived with the 

 aid of (1) are given in Ihe third and fourth columns of the table. 

 It is seen that not only are the two functions not equal to each 

 other for the same parallel, but, what is more important, in both 

 instances the values increase systematically towards the equator. 

 The equivalent value of /x is found to be, in C. G. S. units, about 

 0.070 for parallel 60° and 0.082 for the equator, showing an 

 increase of about 17 per cent — certainly an appreciable quantity. 

 The law of increase in the values of the characteristic functions 

 furnishes a definite criterion for testing the validity or sufficiency 

 of theories of the Earth's magnetism; when applied, it is found 

 that none of the theories thus far advanced account for the equa- 

 torial increase in intensity of magnetization, some in fact giving 

 instead a decrease. The hypothesis that the increased magneti- 

 zation may be due to increased strength of that which produces 

 the primary field — be it increased actual magnetization or 

 increased strength of electric current or of rotating charges — at 

 once occurs to one's mind, and a first examination shows that 

 it is an effect similar to that probably to be expected if attribut- 

 able to the Earth's centrifugal force. ^ 



It is not possible here to give all the mathematical steps involved, • 

 suffice it to say that the analysis at present has been made for 

 possible potential systems both below and above the Earth's 

 surface, which by their combination may be considered to pro- 

 duce the magnetic field observed on the Earth's surface. Instead 

 of supposing a spherical distribution of the two opposite body 

 charges, as did Sutherland, we have taken a spheroidal distribu- 

 tion owing to the supposed action of the Earth's centrifugal 

 force. The expansion has been carried thus far to include the 

 fifth degree zonal harmonic. The differences between the 

 observed values of the rectangular components and of the 

 characteristic functions and the computed values, resulting from 

 the analysis, will be found in the above table. 



8 Terr. Mag. 17: 138. 1912. 



