Page:Scientific Memoirs, Vol. 2 (1841).djvu/206

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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 elements of

Göttingen
Milan
Paris

whence it follows that



Taking the geographical position of

Göttingen 51° 32′ latitude 58′ longitude from Greenwich
Milan 45 28 9 09
Paris 48 52 2 21

and performing the calculation for a spherical surface only, we find

(01) = 11′ 31″ = 5′ 20″
(10) = 184 35 35
(12) = 128 47 31 = 5 41 06
(21) = 303 48 01
(20) = 238 20 20 = 5 32 04
(02) = 64 10 12

Substituting these values in our equation, and those given above for , , , we have



Hence we deduce from the observed horizontal intensities at Göttingen and Milan, that at Paris , agreeing almost exactly with the observed value .

It is easily seen that if we permit ourselves to take the distances , , &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 has the same value , divides generally speaking the parts of the surface in which the value of is greater than , from those in