234 C. F. GAUSS ON THE GENERAL THEORY OF 



41. 



Sufficient data for the investigation above alluded to will pro- 

 bably long be wanting. But it is Avorthy of notice, that the 

 variations of the magnetic force, which manifest themselves 

 simultaneously at different points of the earth's surface, are sus- 

 ceptible of a perfectly similar treatment. This is the case both 

 with the regular changes corresponding to the periods of the 

 day and of the year, and with the irregular changes. Perhaps 

 in this way, the necessary materials may be much earlier collected. 

 It may be well to subjoin some general remarks concerning these 

 future researches. 



After bringing the observed simultaneous changes for each 

 place into the form of alterations of the components of the mag- 

 netic force AX, AY", AZ, it must first be examined whether the 

 alterations of the two horizontal components comport themselves 

 in correspondence with our theory, according to which AX and 

 sin M . A Y, must be values of the partial differential quotients of 

 a function of u and \, according to these variables. If this is 

 found to be the case, the conclusion will be, that the causes 

 either are actual galvanic currents, or at least act in the same 

 manner as such currents, or as separated magnetic fluids. In 

 the opposite case, it would be proved that the causes cannot be 

 galvanic currents. 



We see that highly important conclusions may be derived 

 even from the knowledge of the changes in the horizontal force 

 'only, supposing the determinations sufficiently accurate, nu- 

 merous, and extensive. But if we add thereto the simultaneous 

 changes in the vertical force, then, supposing the first case, the 

 method in the preceding article will inform us whether the 

 causes are situated above or below the surface of the earth ; and 

 further, as they are probably situated in a stratum of small 

 thickness compared to the whole body of the earth, it may be 

 possible to determine the mode of their propagation, at least ap- 

 proximatively. 



As regards the second case spoken of above as possible, it 

 certainly appears to me but little probable as concerns the re- 

 gular changes in the terrestrial magnetic force depending on the 

 time of the year or of the day. In regard to the irregular changes 

 occurring in short intervals, I should hardly venture to pronounce 

 a conjecture at present. If these irregular changes arise from 



