638 



SCIENCE. 



[N. S. Vol. XX. No. 515. 



The question now is, whether this appar- 

 ent loss is in any way wholly or partially 

 compensated for by a possible increase in 

 magnetic energy of the portion of the 

 earth's magnetism represented by the re- 

 maining terms of the Gaussian potential, 

 i. e., by the portion which can not be re- 



ment of surface. As a check I have made 

 some of the calculations with both forms 

 and have gotten, of course, identical results. 

 The following table gives the values of 

 the magnetic energy as derived for the 

 various epochs and as dependent upon the 

 best of the analyses thus far made : 



Table I. Values of the Earth's Total Magnetic Energy in C. G. S. Units (Ergs). 

 (The tabular numbers are to be multiplied by the cube of the Earth's mean radius. ) 



ferred to a uniform magnetization about 

 some diameter? If mutual compensation 

 does not take place, what is the annual loss 

 of the earth's total magnetization? 



To answer this query, I have made use 

 of the well-known function in physics giv- 

 ing the energy W, of a distribution of 

 forces in terms of the field intensity, F, 

 viz. : 



W= 



= ^Sl^^'^^ 



= ^////'(^'+ Y^+Z')dxcly,lz, 



where /i is the magnetic permeability and 

 cLt is the element of volume and X, Y, Z 

 are the rectangular components of F. The 

 integral is confined to the space outside of 

 earth, so that we may take /x as a constant 

 and set it equal to 1. We may also give 

 the expression the following form : 



W= 



■ 5- / rzds. 



Here V is the magnetic potential and Z 

 the vertical force on the earth's surface, 

 B the earth's mean radius and ds the ele- 



Hence we have for 



1838 

 1884 



Earth's Total Magnetic Energy. 

 0.03635 R^ Ergs 

 0.03532 iS= Ergs 



or a loss of 0.00103 B\ or 2.88 per cent, 

 or about one thirty-fifth part in forty-six 

 years. This result is a startling one, for, 

 if true and if the loss in the earth's 

 magnetization continued at the same rate 

 as prevailed during the period 1842-1885, 

 it would imply that the earth will have 

 lost its magnetic energy in about 1,600 

 years; hence extreme caution should be 

 employed before reaching a definite con- 

 clusion. I have made some attempt to 

 ascertain whether this loss can be accounted 

 for by the difference in the material used 

 in the construction of the various charts, 

 and while it would appear that the loss is 

 greater than the effect due to the difference 

 of material, I am unwilling at present to 

 announce a definite conclusion, -but think 

 it best to leave this question, at present, 

 open. 



Allusion was made above to the possible 



