276 JOURNAL OF THE WASHINGTON ACADEMY OF SCIENCES VOL. 11, NO. 12 



regards order of magnitude: 



^+ 5£b=o 



dt ira^ 

 leading to : 



Putting p = 1.6X10"^ ohm/cm.^ =1.6X10^ e. m. u, for copper, and 

 (2 = 6.5X10^ cm., as corresponding to the radius of the earth, we read- 

 ily find that 7raV8p = 10^'* seconds; so that, for B/Bo=l/e, we have 

 t = 10^* seconds, that is, 3X10^ years, which, in view of the approxima- 

 tions involved, is in sufficiently good agreement with Lamb's result. 



Case of the destruction of a state of permanent magnetization. — It is 

 usually maintained that the Earth cannot be a permanent magnet on 

 account of the high temperature of its interior. It is interesting to 

 observe, however, that if it had been a permanent magnet originally, the 

 destruction of this magnetization would set up induced currents which 

 would tend to perpetuate the field; and, as will appear, the net result 

 would be that, for a body of the Earth's size, and with the conductivity 

 of copper, about three million years would elapse before the field had 

 sunk to a value 1/e of that prevailing before the magnetization was 

 destroyed. 



Suppose that B represents the average induction through a great cir- 

 cle of the order of magnitude of the radius of the sphere. Then 

 equation (1) applies as before. Now if B is the induction due to the 

 permanent magnetization, then for a sphere of unit permeability, 

 which it will suffice to consider, i is of the order of magnitude obtained 

 by replacing Bhy B — B in equation (2), that is, 



B - B = 0.25Wa 

 so that, using (1), we have, as regards order of magnitude, 



7ra2— +8piB-B)=0 (3) 



at 



Suppose now that the permanent magnetization B decreases according 



to the law: 



5 = ^oe~"' 



Then, from (3), 



dB 8p 8p- , 



— + —,B = -^Boe-'" 4) 



dt Ta^ ira^ 



The solution of this equation, subject to B =Bo when f = 0, is: 



