220 Prof. Hansteen on the Decrease of the 



But as the horizontal part of the magnetic intensity here in 

 Christiania is very nearly constant, and the dip decreases, it 

 follows, that the whole intensity is decreasing. Denoting the 

 whole intensity by F, its horizontal part by f, the dip by ?", 

 the time of a certain number of vibrations of the horizontal 

 needle by T, and upon another place of the surface of the 

 earth the same quantities by F',y, i', and T', it is evident, that 



/ 

 f-=. F cos. i, accordingly F = — ,• . 

 J ° J cos. l 



Now, as i is decreasing, cos. i is increasing, and consequently 

 F. decreasing. Further, 



f:f — (T') 2 : T 2 = F cos. i : F' cos. i' 3 and FT 2 cos. i 5= F'(T') 2 cos.»'; 

 that is, F T 2 cos. i is for the same magnetical needle a con- 

 stant quantity over the whole surface of the earth, and also in 

 the same place at different times. Calling this constant = C, 

 we have, 



I. FT 2 cos. * = C, or F = =-^ .. 



1/ COS. I 



"Where C can be found when upon a single place F, T, and 



i are observed. Differentiating the equation, No. I., you will 



find, (C being constant,) 



dF 2dT 

 II. — - -\ — — - — Tang, i di = O, (where di may be expressed 

 F T 



in parts of the radius.) 



As in Europe di is negative, the last member, Tang. i. di, 

 changes its sign, and consequently the whole sum cannot be — 



0, unless —-, or -~-5 or both of them, are negative ; that 

 F T 



is, unless the variation of intensity dF, or of the time of vi- 

 brations dT, are negative. In Christiania 1 have found, by 

 a great number of observations, 



In 1820, - - £ = 72°42'6 



1825, - - ?=72°26'4 



Decrease in five years, = — 16'2 



Yearly di = - — 3'24. 



By the observations of Mr Arago at Paris, (where the 

 whole intensity, according to Humboldt's Observations, is 

 supposed = 1.3482,) with one of my cylinders, I have found 



