4.6 



same work in hand, I left mine unfinished. I did not then possess 

 the Reports of the British Association, as it was not until this last 

 summer (1850) that they were obtained here, and when I had seen 

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

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

 able to determine the component Z at above MOO 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 : — 



^1,0 = 



927-9 



pU = 



89-8 



^2,0 = 



- 6-4 



^2.1 = 



— 140*6 



^3,0 = 



-51-8 



g^A = 



II2-3 





-83-2 



g^.l = 



— I03"2 



g5.0=. 



H'3 



^,1 = 



-115-1 



^1,1 = 



-163-7 



9''' = 



2*5 



^2,2 = 



-37'3 





- 14-1 



gS,2 = 



-86-9 



^3,2 = 



-17-2 





48-5 



54.2 = 



-41-3 



M2 = 



43 '4 





- i8-2 





-96-5 



A5.2 = 



— lO'O 





72-8 











1,3 = 



1,3 — 



4'4 



^3,3= — 2^' J 



5-4,4=3.9 



^4.4=4.3 



i8-8 



A4.3= 1 8-6 





AM = 2-8 



3*3 



A5,3=_ 













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 south 

 latitudes. Thus there was found — 



Latitude. 



-69 54 

 -69 52 



Means —69 53 



Longitude. 



179 55 



180 04 



180 



Inclination. 



-84 30 

 -83 34 



-84 02 



Force, 



1999 

 1994 



1996-5 



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

 — 1781*1 ; my calculation gives — 2009*3. My constants also still 

 require 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 19; and to show the degree of agree- 

 ment, 1 subjoin the following table. As in forming it I merely took 

 from my large table every 10th observation in 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 suffice 

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

 ferences between the observed and calculated vertical intensity. 



