410 MAGNETIC CONDITION OF THE GLOBE. 



By making the potential vary continuously from V l to V 2 , we 

 shall find a value V for which the two curves, previously separated, 

 come in contact, and merge into a single one S ; the junction may 

 take place either by a single point of intersection, as in Fig. 93, or 

 by a greater number of points of intersection or of contact. Let O 

 be one of these points. It is first of all clear that the horizontal 

 component there is null, and that therefore the point corresponds to 

 the ordinary definition of poles ; it is, however, to be observed that 

 as we move in certain directions we get increasing, and in other 

 directions decreasing, potentials ; for the former directions the point 

 O would act like a south pole, and for the second as a north pole. 

 This is what we may call a false pole. 



There cannot thus be two distinct poles in the same hemisphere 

 without there being at the same time at least one false pole. But 

 observations give nothing of this kind, and it is only an inexact 

 interpretation of phenomena which has sometimes led to the con- 

 clusion, that observations indicate the existence of two poles in the 

 northern hemisphere. 



Near a pole, in fact, the magnetic parallels have an elliptical 

 shape ; their perpendiculars that is to say, the magnetic meridians 

 do not coincide in the same point, but the points of convergence, 1 

 which they show more or less clearly, are the centres of curvature, 

 and have clearly no relation with the poles. 



. Observation leads then to this consequence, that, apart from 

 purely accidental and local circumstances, there are only two mag- 

 netic poles on the surface of the Earth a negative pole in the 

 northern and a positive pole in the southern hemisphere. 



It is important to add, also, that terrestrial magnetic poles, such 

 as we have defined them, have nothing in common with magnetic 

 poles, properly so called, considered as centres of gravity of positive 

 and negative magnetic masses. The magnetic axis of the Earth is 

 the right line along which the sum of the projections of the mag- 

 netic moments of the various elements is a maximum (297). 



437. PROPERTIES OF A CLOSED POLYGON. We know that if we 

 move a magnetic mass equal to unity from a point Pj where the 

 potential is V 15 to a point P 2 where it is V 2 , and if we denote by F 

 the force, by ds the element of the path described by the mass, and 

 by e the angle of the force with the element, the magnetic work is 

 expressed by the equation 



Yds cos e. 



