636 



SCIENCE. 



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



spherical harmonic terms to the fourth 

 order, was Gauss, from whose time a new 

 era in magnetic science was ushered in. 

 As the result of his mathematical analysis, 

 it was definitely proved that by far the 

 greatest portion of the earth's permanent 

 magnetism is to be referred to a system of 

 forces inside the earth and, furthermore, 

 that this system possesses a potential. 

 There were thus deduced two great funda- 

 mental facts of nature that outweigh in 

 importance all of the speculative theories 

 concerning the 'how and whence' of the 

 earth's magnetism. 



Gauss's calculations have been repeated 

 several times with the aid of more com- 

 plete material by several analysts, one of 

 them being the noted astronomer and 

 mathematician, John Couch Adams; 

 Gauss's deductions have been verified by 

 all of them. 



The most elaborate analysis and attempt 

 at perfection of the theory embodied in the 

 Gaussian analysis was that for 1885 by 

 Professor Adolf Schmidt, at present in 

 charge of the Potsdam Magnetic Observa- 

 tory in succession to the late and lamented 

 Professor Eschenhagen. Schmidt made 

 provision in his equations: (a) For the 

 effect of the spheroidal figure of the earth. 

 Gauss having taken a spherical figure, 

 (&) for a possible effect due to forces 

 whose seat was outside the earth, and (c) 

 for a possible effect not to be referred to 

 an inside or outside potential, but to a 

 system of vertical electric currents passing 

 through the earth's surface, whether from 

 inside or outside. 



Schmidt found that about 95 per cent, 

 of the total magnetization of the earth was 

 to be referred to an inside potential and 

 that the remainder was due to a small out- 

 side potential and an electric current sys- 

 tem traversing the earth perpendicularly 

 to its surface. [The writer has since found 

 that the principal term of the outside po- 



tential is displaced about one hundred de- 

 grees (100°) to the west with reference to 

 the principal term of the inside potential.] 



Fritsche in the main verified Schmidt's 

 work, though he did not introduce the re- 

 finement due to taking into account the 

 spheroidal figure of the earth, but retained 

 the simpler equations based on the spherical 

 figure. 



The writer has recently made a critical 

 comparison of the results thus far obtained 

 by the various analysts, and has derived 

 the differences between the elements as com- 

 puted upon the basis of the theory and the 

 observed or chart quantities, his purpose 

 being to ascertain wherein further improve- 

 ment of the theory is needed and what 

 direction promises the best success. The 

 residuals exceed many times the errors of 

 observation. 



It would appear that at the present stage 

 very little increased accuracy has been 

 gained by taking into account the spher- 

 oidal figure of the earth and that the theory 

 must receive elaboration in other funda- 

 mental directions. Thus, for example, sup- 

 pose the principal portion of the earth's 

 magnetic system to be situated at some 

 considerable depth below the surface— a 

 condition of which we in fact have indica- 

 tions — then the question must be considered 

 as to the effect arising from the magnetic 

 permeabilities of the strata intervening be- 

 tween the seat of the system and the place 

 of measurement of the forces. Instead of 

 having the simple Laplacian equation and, 

 as the result of which, a strictly harmonic 

 distribution of the forces, we may have 

 instead the more generalized equation: 



and in consequence a quasi-harmonic dis- 

 tribution. So that the Gaussian potential 

 expression, based on the simple Laplacian 

 equation, may represent only a first ap- 

 proximation to the truth. 



