918 

 with moment p' in O will consequent!}' be pp' — — -, when this di- 



O.l'* 



pols was also directed along the u;-axis, whilst it amounts to — 



pp' , when the last dispoie is directed along the axis of y. 



oi/o.r 



When we place in all corners equally directed dipoles, we can 



dissolve these in dipoles according to the direction of the axes in 



components with moments px, py, pr- And so the potential energy 



of the dipole in the origin is: 



+ 2p,p, -— + 2p,py — ~ .. 

 OxOz OzOy ) 



On account of the symmetiy the three mixed differential-quotients aie 



Ö' V, d' r„ d^ F. 

 zero, and we have further =: — — =z — — . Consequently these 



d.J'' 0?/' 02-' 



differential-quotients are also zero because V^ fulfills the equation of 

 Laplack. In consequence therefore the interior energy of the lattice 

 is zero, independent of the direction of the dipoles (provided all 

 dipoles are parallel). So a very weak exterior field will be sufficient 

 to let all dipoles assume the dii-ections of this field, in other words : 

 H,/ is zero. 



The same result holds good for the two other Bravais cubic 

 arrangements: the centred cubic and the plane-centred cubic lattice. 

 The limitation used thus yields a coercitive force which is equal 

 to one third of the magnetisation of saturation. For steel the coer- 

 citive force is at least 80 times smaller. 



2. In what follows we shall want the potential F of a rectangular 

 lattice with unequal edges a, h, and c for the case that every corner 

 carries a pole of unity strength; this potential depends upon the form 

 of the boundary even if we imagine it at great distance. We shall 

 avoid the difficulties of the boundary by the following artifice. 

 Besides the point-charges 1 in the corners we give the body a 

 homogeneous space-charge of — 1 per volume a, b, c. In total the 

 body is thus uncharged and the parts at a great distance of the particle 

 considered have a vanishing influence. So we are able to calculate 

 the potential V' for this case of a lattice infinitely extended in all 

 directions. From this we shall then find V for the case of a sphere 

 by adding the potential in a homogeneous sphere with a charge- 



