ON THE GAUSSIAX CONSTANTS FOR THE YEAR 1829. 3 



other had wanted empirical supplemeuting *; and we, in consequence thereof 

 undertaking the recomputation now iinished with all available observations, 

 resolved once more to confine ourselves to the determination of the same 

 24 constants solely. Indeed the material on which we have founded this new 

 and definitive calculation is by its geographical completeness far superior 

 to that of both the former ones; but many of its modern accessions do not 

 exceed, nor even attain the exactitude of the observations mentioned above. 



According to what we have stated in the beginning, the Gaussian constants 

 must to the same extent be either dependent on or indexiendent of time as are 

 the phenomena of terrestrial magnetism. Now very old and indubitable 

 experience has proved that each of these phenomena undergoes not only 

 the various short-period changes, from which the observer can easily, 

 and is always supposed to free them, but also the so-called secular 

 variations of by far a larger amount. The Gaussian constants being then 

 likewise variable as to time, it appears that they can be determined each 

 time but for one given epoch, and then out of observations which either have 

 been all made at this epoch, or reduced to what they would have given if 

 made at the same. 



The aim of our present calculations was to determine with all attainable 

 exactitude the Gaussian constants for the year 1829, in order that the results 

 of the newly founded theory might be directly comparable as well with those 

 of their first evaluation, relating nearly to the same epoch, as with the most 

 careful measurements made by Hansteen and Erman between 1828 and 

 1830. liut, as for carrying this out we had to make an equal use of all ob- 

 servations to be relied upon, and originating whether in the selected epoch 

 or at any interval whatsoever before or after this time, our work was 

 divided into two independent parts : — 



1. Formulse were to be constructed and employed for reducing each of the 



magnetic results which, at widely differing times, had been ob- 

 tained by observations all over the earth's surface, to what they 

 would have been in 1829 ; and 



2. Out of these reduced values, twenty-four numbers were to be com- 



puted which, when taken for our twenty-four Gaussian constants, 

 responded as nearly as possible to all empirical data observed in, 

 or reduced to, the e])och 1829. 



I. Reduction of Ohserved Values to the Year 1829. 



Without the existence of the Gaussian theory, the only means to execute 

 such reductions would have been, for every kind of magnetic phenomena 

 at any place, to gaess what changes they had undergone, according to 

 the changes which had been observed for the same phenomena at certain 

 other places. Such rude attempts have indeed been made for the purpose of 

 ascertaining the changes of declination at places where they had never been 

 observed. They could perhaps have been extended, though with much less 

 foundation on experience, to inclination-changes ; whereas for the secular 

 variations of intensity not even this appearance of a means existed, owing 

 to an almost total want of data. But the problem of our reductions has now 



* As, for instance, according to tlie comparison made by A. Erman, between (be results 

 of both systems of constants and the magnetic observations at some places in India, by 

 Mr. K. Koppe, who was commissioned to do so in the Total-Eclipse Expedition of 18C8, 

 as published in the ' Astrouomischo Nachricliten,' vol. Ixxv, p. 242 ct sen. 



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