196 C. F. GAUSS ON THE GENERAL THEORY OF 



filled, by a precise definition being given of what should be 

 understood by a magnetic pole. We intend to apply this de- 

 nomination to each point of the earth's surface where the hori- 

 zontal intensity = : where therefore, speaking generally, the 

 dip = 90 ; but including the singular case, did it exist, where 

 the total intensity = 0. If we were to give the name of magnetic 

 poles to those places where the total intensity is a maximum 

 (i. e. greater than anywhere in the surrounding vicinity), it must 

 not be forgotten that this is something quite different from the 

 above definition; that neither the situation nor the number of these 

 last-named points have any necessary connexion with those of 

 the points first spoken of; and that it tends to confusion when 

 dissimilar things are called by the same name. If we look 

 aA^ ay from the actual condition of the earth and take the ques- 

 tion in its generality, there may certainly exist more than two 

 magnetic poles ; but it does not appear to have been noticed 

 that if, for example, two north poles exist, there must necessarily 

 be between them yet a third point, which is likewise a magnetic 

 pole, but is properly neither a north nor a south pole, or is both 

 if that expression be preferred. A consideration of our system 

 of lines will best serve to elucidate this subject. If the function 

 V have at a point of the earth's surface P* a maximum value F*, 

 and all ai'ound smaller values, then a series of progressively de- 

 creasing values will correspond to a system of rings, each of which 

 will inclose all the preceding ones, together with the point P*, 

 and on each of these rings the direction of the horizontal magnetic 

 force, or that of the north pole of the magnetic needle, will be 

 inwards-\. 



This is the characteristic mark of a magnetic north J pole. 



It is clear that the rings may be made so small, or the cor- 

 responding values of the function V may differ so little from F"*, 

 that any other point may be excluded. 



We will designate by S the space included by all the points 

 on the surface of the earth at which the value of V is greater 



f These rings, themselves assumed as infinitely small, are not necessarily cir- 

 cular, but generally speaking oval, so that the normal direction of the mag- 

 netic needle in reference to them only coincides with the direction towards 

 P* at four points of each ring. Great error may be involved, therefore, if with- 

 out further precaution, the intersection of the prolongations of two compass di- 

 rections at considerable distances is assumed to be P*. 



X We conform here to the mode of speaking in common usage, according to 

 which the point established by Captain James Ross is so designated, although pro- 

 perly speaking it is a south pole, when the earth itself is considered as a magnet. 



