in the Magnetic Forces of the Earth. 37 



From the fundamental principles which I have stated, I de- 

 duced, in the memoir referred to, three simple formulas; one, for 

 the horizontal component of the directive force of the needle, or 

 the horizontal magnetic intensity of the place ; a second, for the 

 vertical intensity ; and a third, making known the declination. 

 These formulae were afterwards tested by numerous comparisons 

 with the results of observations made in every variety of locality 

 in the northern hemisphere of the earth. The agreement was 

 found to be very close — the differences amounting only to a few 

 hundredths for the horizontal and vertical forces, and less than 

 2° 40', and in most cases less than 1° for the declination. The 

 positions of the magnetic poles, the pole of maximum intensity, 

 and the magnetic equator were also theoretically deduced, and 

 shown to correspond very closely with their observed positions. 

 In view of the whole discussion the following great truths were 

 supposed to have been established. 



1. All the magnetic elements of any place on the earth may be 

 deduced from the thermal elements of the same ; and all the 

 great features of the distribution of the earth's magnetism may 

 be theoretically derived from certain prominent features in the 

 distribution of its heat. 



2. Of the magnetic elements, the horizontal intensity is nearly 

 proportional to the mean temperature, as measured by a Fahren- 

 heit's thermometer; the vertical intensity is nearly proportional 

 to the difference between the mean temperatures at two points 

 situated at equal distances north and south of the place, in a di- 

 rection perpendicular to the isogeothermal line (that is, a line 

 conceived to be traced through all points at which the mean tem- 

 perature of the matter of the earth, near its surface, is the same 

 as at the station of the needle): and, in general, the direction 

 of the needle is nearly at right angles to the isogeothermal line, 

 while the precise course of the inflected line to which it is per- 

 pendicular may be deduced from Brewster's formula for the 

 temperature, by differentiating and putting the differential equal 

 to zero. 



3. As a consequence, the laws of the terrestrial distribution of 

 the physical principles of magnetism and heat must be the same, 

 or nearly the same ; and these principles themselves must be 

 physically connected in the most intimate manner. 



4. The principle of Terrestrial Magnetism, in so far as the 

 phenomena of the magnetic needle are concerned, must be con- 

 fined to the earth's surface, or to a comparatively thin stratum of 

 the mass of the earth. 



which has 

 features. 



5. The mechanical theory of terrestrial magnetism 

 been under discussion, must be true in all its essential 



6 - We may derive the magnetic elements by very simple for- 

 mulae, and with an accuracy equal to that of Gauss's formulas, 



