June 19, 1921 swann: earth's size and magnetization 277 





1 2£. 1 



To fix our ideas, suppose that the permanent magnetization is 

 practically destroyed in a time short compared with ira^/Sp, which, for 

 copper, and for a equal to the radius of the Earth, amounts to 10^^ 

 seconds. Then 8p/ra-a is a small quantity, and we have approxi- 

 mately : 



8pt 



so that, even though the permanent magnetization is destroyed rapidly, 

 the order of magnitude of B will still be So/e after a lapse of 10^^ 

 seconds, or three million years. 



APPLICATION TO THE SECULAR VARIATION 



Such evidence as exists with regard to the secular variation appears 

 to indicate that the magnetic poles describe closed curv'^es about the 

 geographic axis with a period of the order of 500 years. The curv^e 

 is possibly accompanied by smaller loops, which need not concern us 

 here, however. 



Suppose that, as a first approximation, we divide the Earth's mag- 

 netization into two uniform magnetizations, one parallel to and one 

 perpendicular to the geographic axis, and regard the latter as ro- 

 tating, with regard to the earth itself, once in 500 years. We do not 

 know the mechanism of the process; but, it is interesting to inquire 

 as to what would follow by considering it merely as a rotation of a 

 state of permanent magnetization in the above manner. We shall 

 find that the induced currents play a very important part, both as 

 regards their power to almost cancel the effect of the rotating perma- 

 nent magnetization, and also as regards their influence in producing a 

 lag of the resultant magnetization behind the permanent magnetization. 



If Do refers to the permanent component of magnetization perpen- 

 dicular to the geographic axis, then, on considering the case of^ me- 

 ridian circle, we shall have an equation similar to (4), but with Boe~°' 

 replaced by Do cos 2x^/7, where 2Trt/T represents the angle between 

 the direction of Do and the perpendicular to the plane of the me- 

 ridian circle in question. As regards order of magnitude we thus have : 



1 B = — Do cos — - 



dt tto^ ira^ T 



The complementary function may be neglected after a sufi&ciently 

 long time, and we shall be left with the particular solution : 



