912 



— it' H,j is negative — be roughly speaking analogous with those 

 of a ferro-magnetic body with hysteresis. If on the contrary we 

 And a |)Ositive value for H,j, we have to do with a body without 

 hysteressis that can only be magnetised up to saturation by a strong 

 field //,/. With a weaker exterior field the magnetic atoms will not 

 remain totally directed and consequently M will decrease. We shall 

 deduce for that case the connection between the intensity H and 

 magnetisation, in other words: the permeability. 



In orde!' to find from H,^ the coërcitive force He, we must bear 

 in mind that the latter is defined as the negative m^<?r/(jr field required 

 to make the magnetisation change its sign. This interioi- field will 

 always l>e found by adding the field //,<„i, which is caused by the 

 magnetised body itself, to the exterior field He- The field H^on must 

 be calculated on the supposition, that the body has a continnons 

 space-magnetisation. 

 So we have 



H = He -\- Hcoti and especially He ^ — Hg — /^con- 

 Here — Heon is the so-called demagnetising force. By this defini- 

 tion Hr will become independent of the form of the body considered, 

 which consequently is not the case for H^. In the preceding para- 

 graph we must consequently read for //^ everywhere H,, -f- Heon- 

 In our calculation we shall always take the limit spherical. Then 



Heon is — V. M. 



It is easy to demonstrate that H,, becomes :=:0 when we impose 

 on the turning of the atoms the limitation discussed above that their 

 axes always remain parallel. F^or this purpose we only have to sum 

 up the reciprocal energy of two dipoles over the whole lattice. From 

 considerations of symmetry we then find that this sum is zero. ^) 



We shall give another proof of the theorem mentioned, the principle 

 of which can also be useful for our further calculation. 



We choose a system of axes parallel with the edge of the lattice 



and take the origin in one of its points. We imagine in all the 



points of the lattice except in the origin, Northpoles of unity 



strength, and we imagine the lattice linuted by a very large sphere 



about 0. Let \\{x,i/,z) represent the potential in a point x,y,z. The 



OF, 

 potential of dipoles with moment /; in de .c-direction is p—r-, 



Ox 



Ö' V d" V d' V 

 the intensity in is consequently /> ^ — * , p — — -^ , p — — ^ respectively 



Ox'' ot/ox dzoc 



in the a,-, y and ^r-direction. The potential energy of a dipole 

 1) H. A. LoRENTZ. Theory of Electrons. Note 55. p. 208. 



