7-2 



Royal Society. 



Erman's results, I at once decided on taking up my work afresh. I 

 have made use of ail the data I could procure, and have thus been 

 able to determine the component Z at above HOO places, including 

 a series of observations which I had myself made from 1847 to 1849 

 in Liefland, Esthonia, Finland, Norway, and on the route from Arch- 

 angel to Petersburg. I have as far as possible reduced all determi- 

 nations to the epoch of 1830. A calculation of the several observa- 

 tions by the method of least squares would have required an entire 

 life ; I therefore preferred following the same path as Gauss ; in doing 

 this, however, I soon discovered that the 5th order could not be 

 neglected ; and I then obtained the following values : — 



^0^ 6-4 



^.o=_5r8 

 ff*fi=-Syz 



5rU= 89-8 

 ^2,1 _ __ J40'6 



^.1= ii2'3 

 ^.1=. — I03'2 



^.ic= —115-1 



2-5 

 -86-9 

 -41-3 

 -96-5 



A2.2=_37.3 



A8.2=-I7'2 



A^.2= 43-4 

 A&.2=-io*o 



ff*^= i8-8 A4.3= 1 8-6 



^,3= 2*3 ^8.3= _ i'6 



5^'^ = 3*9 



flf5,5= -o 



A^.''=4-3 



AM = 2-8 



A comparison will show you that these quantities agree much, 

 better with Gauss's than Erman's do; and this is also true in respect 

 to the agreement with the observations, especially in the high souths 

 latitudes. Thus there was found — ■ 



Latitude. 



-69 54 

 -69 52 



Means —69 53 



Longitude. 



179 55 



180 04 



180 



Inclination. 



Force. 



-84 30 1999 



-83 34 1994 



-84 02 



1996-5 



Z=-1985-8 for —70° and 180°; Gauss found —2193-5; Erman? 

 '^—1781*1 ; my calculation givt^s —2009*3. My constants also still 

 ^*^quire a small correction. I do not however mean to examine 

 this at present, but propose first to consider the horizontal compo- 

 nent, in order to satisfy myself previously whether both components 

 depend upon the same constants or not. The probable error of a ■ 

 single determination is nearly 1 9 ; and to show the degree of agree- ; ; 

 ment, I subjoin the following table. As in forming it I merely took i ' 

 from my larsje table every 10th observation i.. the order of succes- 

 sion, you will not be surprised at finding unimportant places, whilst 

 others of greater note in their vicinity are omitted: it may suflSce 

 however for the present purpose. The quantities given are the dif- 

 ferences between the observed and calculated vertical intensity. , 



