2^6 C. F. GAUSS ON THE GENERAL THEORY OF 



considering the earth as an actual magnet, we should prefer to 

 ascribe ten-estrial magnetism simply to constant galvanic cur- 

 rents in the earth. But if we consider the earth as an actual 

 magnet, we are obliged to ascribe to each of its portions, of the 

 size of the eighth of a cubic metre, on an average, at least* as 

 great a foi'ce of magnetism as that contained in one of the above- 

 mentioned bars. Such a result will be an unexpected one to phi- 

 losophers. 



32. 



The manner of the actual distribution of the magnetic fluids 

 in the earth necessarily remains undetermined. In fact, accord- 

 ing to a general theorem which has been already mentioned in the 

 2nd article of the Intensitas, and will be treated of in greater detail 

 at a future opportunity, we may substitute for any supposed 

 distribution of the magnetic fluids in the interior of a body oc- 

 cupying space, a distribution on the surface of the same space, 

 which shall leave the effect on every point of external space pre- 

 cisely the same. It may be easily concluded from hence, that one 

 and the same action on all external space may be deduced from 

 an infinite number of different distributions of the magnetic fluids 

 in the interior. 



We are enabled to assign on the other hand that fictitious 

 distribution on the surface of the earth, which shall be perfectly 

 equivalent to the actual distribution in the interior, as regards 

 the external resultant of the forces ; and the spherical form of the 

 earth allows us to do so in a very simple manner. 



We may express the density of the magnetic fluid in each 

 point of the earth's surface, i. e. the quantum of the fliud which 

 corresponds to the unit of surface, by the formula 



i^.d — > 



or by - -^ (3 P'+ 5 P"+ 7 P'", + 9 P^^ &c.) 



The result of this formula will be hereafter exhibited by a 

 graphical representation. We shall only notice here that it is 

 negative in the northern and positive in the southern parts of 

 the earth, but in such manner that the dividing line cuts the 



* In as far as we are not prepared to assume the magnetic axes of all the 

 magnetized particles of the earth to be everywhere parallel to each other, — the 

 more imperfect this parallelism, the greater must be the average force of mag- 

 netism in the parts to produce the same total magnetic moment. 



