April 27, 1900.] 



SCIENCE. 



653 



on ' Electric Waves,' to the question 

 " Wiiat is Maxwell's electro-magnetic the- 

 ory of light?" Herz's reply was, " Max- 

 well's theory Is that which is contained 

 in his equations defining the electro- mag- 

 netic field," and so might I reply if I 

 were hard pressed, that " Gauss's theory is 

 that which is contained in his equations 

 consisting of spherical harmonic terms defin- 

 ing the earth's permanent magnetic field." 

 But what do his equations imply? His 

 equations involve the following theoretical 

 assumptions : That all of the earth's per- 

 manent magnetic field is due to causes re- 

 siding within the earth's crust which are 

 01 a character that can be referred to a po- 

 tential, so that, knowing the value of the 

 potential, all the component parts, namely, 

 that directed north and south along the 

 meridan, that directed east and west 

 along a parallel of latitude, and that di- 

 rected vertically downward can be readily 

 computed. If now, these theoretical equa- 

 tions, when applied to the actual observa- 

 tions of the earth's magnetic force in vari- 

 ous parts of the globe, are satisfied within 

 the errors of observation, then the assump- 

 tions underlying the equations have been 

 proved, and that is what Gauss did, and 

 therein, I should say, consists his theory. 

 The equations then represent a definite 

 physical fact. 



Now, Dr. Schmidt, in view of the fact 

 that, since the days of Gauss, observations 

 have been greatly multiplied, decided to 

 test the Gaussian hypothesis anew, and so 

 in his analysis he does not begin by assum- 

 ing the existence of an inner potential func- 

 tion governing the entire magnetic force, 

 but, instead, makes a separate adjustment 

 of each of the three rectangular components 

 and so obtains three spherical harmonic 

 expressions instead of one as Gauss did. 

 He carries his expressions to terms of the 

 sixth order, Gauss stopping at the fourth. 

 The agreement or disagreement in the co- 



efficients of the harmonic terms in the three 

 separate expressions would test the Gauss- 

 ian hypothesis, and Schmidt obtains 4ihe 

 following conclusions : 



The earth's magnetic force consists of 

 three parts : 



1. The greatest part. — This is to be re- 

 ferred to causes within the earth's crust and 

 possesses a potential. 



2. The smallest part about -^-^ of the entire 

 force. — This is due to causes outside the 

 earth's crust and likewise possesses a po- 

 tential. 



3. A somewhat larger part than the preced- 

 ing. — This does not possess a potential, 

 and, in consequence, points to the existence 

 of vertical earth air electrical currents. 

 The currents amount, on the average, for 

 the entire earth's surface, to ^ of an ampere 

 per square millimeter. 



Parenthetically, I may remark that Dr, 

 Schmidt is somewhat skeptical about the 

 proof of the existence of the third portion, 

 believing that errors of observation may 

 have produced such a result. I simply wish 

 to emphasize that, in the main, Gauss's 

 theory (and I may now use this expression — 

 having explained what I mean) has been 

 verified. 



This indefatigable worker. Dr. Schmidt, 

 has, within a few months, made another 

 notable contribution, namely, on the ' Cause 

 of Magnetic Storms.' 



If we compare the photographic traces, 

 obtained at magnetic observatories, show- 

 ing the variation in magnetic declination or 

 in horizontal intensity during a magnetic 

 storm at two neighboring points, a striking 

 agreement at once appears to the ej^e. Ex- 

 amine these curves closer and you will find 

 that the agreement consists principally in 

 the number and position of the individual 

 waves or peaks composing the curves, 

 whereas the magnitudes of the correspond- 

 ing peaks or hollows show distinct differ- 

 ences, so that at times a peak of one curve 



