222 Prof, Erman — Magnetic Elements at Berlin. [April 28, 



error than the other declinations, in combining the two reduced values 

 with those obtained in the open air, I have given to the two first only 

 a fourth of the weight of the others. A similar allowance for larger pro- 

 bable errors should perhaps have been made in employing the four state- 

 ments of former observers ; but, for want of particulars about the operations 

 they are founded upon, it was more safe to neglect the difference between 

 their weight and that of the others, than to fix it by an arbitrary as- 

 sumption. 



If, for the moment of ohsefvation, there were marked by 1800 + ^, as 

 before, the tropical years elapsed since the Gregorian epoch, m the positive 

 excess of t over the next integer, x the horary angle of mean Sun^ each 

 observed west declination d' had to be brought under the form 



d'=:D+/(t)-^(l>(m,x), 

 D denoting a constant, and / and two functions, the first of which was 

 to be determined here. 



In order to form J'— x)=d out of each d', I put 

 (j)(m, x) = a-\-a . cos.r-t-y . cos 2x + e . cosSa?, 

 H-/3 . sin x-\-^ . sin 2^-|- 4" • sin 



taking the values of «, a, /3, , ^ by interpolation according to 



m, from the following Table, derived from observations in the Russian 

 observatories at St. Petersburg, Catherinbourg, and Barnaoul in the year 

 1837 and 1838, and well agreeing with my own determinations of <^(m, x) 

 for the years 1828 to 1830, and at eight places between latitude 50° and 

 62° North. 



m. 



a. 



a. 



)8. 



7- 





6. 





0042 



+ 15 



+ 54 



+ 15 



-27 



+ 70 



+ 1 



+ 5 



0-123 



- 62 



+ 61 



+ 46 



-28 



+104 



+33 



+12 



0-204 



- 43 



+ 54 



+135 



+11 



+173 



+22 



+62 



0-288 



-108 



+ 64 



+256 



+14 



+199 



+21 



+82 



0-372 



- 88 



+104 



+264 



+65 



+182 



+42 



+42 



0-455 



+ 14 



+107 



+290 

 +275 



+71 

 +76 



+184 



+64 



+45 



0-538 



+ 77 



+ 82 



+175 



+72 



+43 



0-623 



+ 60 



+ 85 



+221 



+79 



+187 



+69 



+60 



0-707 



+ 72 



+ 91 



+139 



+51 



+156 



+57 



+34 



0-790 



-H 63 



+ 75 



+ 69 



+ 2 



+137 



+29 



+ 9 



0-884 



— 4 



+ 64 



- 10 



-12 



+ 76 



+36 



- 1 



0-959 



+ 5 



+ 82 



- 18 



-20 



+ 68 



+14 



-11 



1-042 



+ 15 



+ 54 



+ 15 



-27 



+ 70 



+ 1 



+ 5 



When I supposed in this way that the parameters a, a, . . . ., ^ of 

 the function ^{m, x), or ^ as I will call it for abbreviation, are the same for 

 all moments alike situated in different years, I was well aware that this 

 assumption is but approximative, and that all sufficiently extended and 

 direct investigations of 0, as chiefly those of General Sabine, have shown 

 a periodicity of about 9 '5 years in the total values of this function. But 

 as the laws of such dependence between T and each of the seven para- 



