224 



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



which furnishes the above calculated numbers ; and by their comparison 

 with the observed ones, the probable errors are — 



in the absolute term of d + r*94 ; 

 in the coefficient t'm d +0'*2932 ; 

 in the coefficient of f in c?±0'-030669. 



If, now, instead of employing the variations ^) (m, x), or (p according to 

 observations in the years 1837 and 1838, we assume (1) that the periodi- 

 cal dependence between this function and the date t consists in always 

 changing each parameter proportionally to its mean or primitive value, 

 and then (2) that, as General Sabine has proved, the whole function has 

 nearly reached a maximum in all moments marked by if=48+7i . 9*5, 

 n being an integer^ and (3) that, according to the same philosopher, the 

 least and the largest amount of corresponding variations are approximately 

 as 1 : 1*4, then, $ marking the function of ^, m, x which in each case 

 must be substituted for ^, and C a function of M and X, we shall have 



$=c|l-20 + 0-20 . sin (2f-45-625)]J | 



and 



^=c 1 1-20-0-20 . sin (8-125) | =1-35811 



To each of the preceding values of d must therefore be added 

 0_O=,^|o-1163-O-1472.sinj^^ (^-45-625)J |. 



By executing this operation, I found that the reduced observations are 

 best represented by 



(C*) ^?=18° 8 •434-0-26831 . ^-0-070652 . 



and that, though scarcely differing from (IV.), this expression is preferable, 

 because the probable error of each of its terms is by nearly of its former 

 value smaller than the corresponding one in (IV.) 



As the expression (C*) is identical with 



(C) <?=18° 8'-68-0'-070C52{jf-l-899p, 



we see that, according to my observations, the west declination at the 

 place in question arrived in 1801-899 at a maximum of 18° 8'-68. 



Putting off for a further article some more general observations on 

 the secular changes of terrestrial magnetism, I briefly resume, as results 

 of my nearly forty years' observations, that for 



latitude =52° 31' 55" North, 



longitude =13° 23' 20" E. from Greenwich, 



