194 C. F. GAUSS ON THE GENERAL THEORY OF 



It is obvious that in this equation the units of intensity and 

 of distance are arbitrary. 



10. 

 As an example, we will apply the formula to the magnetic ele- 

 ments of 



Gottingen 8° ^ jg" 38' i^ = 67° 56' 



go = 18° 38 

 Milan 8' = 18 33 i' = 63 



Paris 8" = 22 04 i" = 67 



whence it follows that a)° = 0-50980 

 w' = 0-57094 

 to" = 0*51804. 



Taking the geographical position of 



49 

 24 



->|rO = 1-357 

 ^|r' = 1-294 

 ■f " = 1-348 



Substituting these values in our equation, and those given above 

 for B°, B', S", we have 



= 17556 ftjO + 2774 o)' - 20377 «", 



or, co" = 0-86158 ca^ + 0-13613 to'. 



Hence we deduce from the observed horizontal intensities at 

 Gottingen and Milan, that at Paris w" = 0*51696, agreeing al- 

 most exactly with the observed value 0-51804. 



It is easily seen that if we permit ourselves to take the di- 

 stances P°, P", &.C. instead of their sines, the above formula 

 can be expressed immediately by the geographical longitudes 

 and latitudes of the places. 



11. 



The line on the earth's surface, in all points of which V has 

 the same value = V^, divides generally speaking the parts of the 

 surface in which the value of V is greater than V°, from those in 



