8 



REPORT 1872. 



The coefficients a,h. . . Ji ot the primary equations have been calculated 

 with d and i as nearly given for 1811 by a mean between the indications of 

 both isogenic and of both isoclinal maps, and with w as sufficiently known 

 since 1829. 



B. On the Equations for annual Increments of Constants durhifj the 



yearlMZ-5. 



"We have already mentioned that our second determination of a set of 

 annual increments a,^, a.^. . . .a^ of the first eight Gaussian constants M\as 

 intended to give these quantities for the date 1843-5. This date follows 

 indeed from being the middle of the period 1829-58, during which 

 had happened those changes of phenomena on which we first founded our 

 conditional or primary equations. These were the values of a or increments 

 of declination that we obtained by a comparison between the normal or 

 theoretically interpolated declinations for 1829, as given in the 'Magnetischo 

 Atlas' by Gauss and Weber, and the corresponding ones for 1858, as re- 

 presented by the isogonic lines in Berghaus's Chart of the World. 



These increments result as follows for thirty-six of the before-mentioned 

 points : — 



Values of a or increments of Dedination from 1829-58. 



As no sufficient data exist for a similar collection of the changes which 

 inclination has undergone during the same period, we have completed our 

 material by the following results of researches on secular variation of 

 magnetic elements. If I generally denotes the annual increment of any 

 element /or the date 1843-5, and/ the total magnetic intensity, there were 

 put X=/ . cos i . cos d, Y=/ . cos i . sin d, Z=/ . sin i, as well as p for the 

 so-called tveight or measure of jirohahiUty ; and then the following numbers 

 were ascertained, in order to be afterwards combined into conditional equa- 

 tions with the sought-for a^, a^. . . .a^, or annual increments of constants. 



