CONTEMPORARY ADVANCES IN PHYSICS 239 



observed. To state two points of difference among many: the "per- 

 mitted" directions for the super-atoms depend upon the crystal struc- 

 ture, those for the atoms depend upon the field-direction and the 

 angular momentum of the atom; and if one applies a field to a single 

 crystal in any direction oblique to all of the cubic axes, the super-atoms 

 will consent to point in that direction, provided the field strength is 

 rather high. 



Now I must explain what these super-atoms are, since our under- 

 standing of them is one of the most satisfactory features in our, as a 

 whole very imperfect, theory of ferromagnetism. They are groups — 

 commonly called domains — of adjacent individual atoms; the member- 

 atoms of each domain are behaving like the atoms of a paramagnetic 

 solid. A diagram of a ferromagnetic solid might be drawn as an 

 assemblage of large arrows, each representing the magnetic moment 

 of a single domain; then, around and beside each of these large arrows 

 might be drawn a lot of small arrows representing the magnetic mo- 

 ments of the individual atoms constituting the group; the big arrow 

 would be the resultant of all the little ones. It would not be practic- 

 able to do this accurately, for there would have to be millions, or 

 millions of millions, of little arrows to each of the big ones ; but even a 

 few suffice to show the idea. It may, however, be recalled that I 

 have lately said that the atoms of a paramagnetic body have an ir- 

 restible urge to be in a state of random orientation whenever there is 

 no applied field acting upon them. The resultant of all the little 

 arrows of a domain should then be zero. How can it have a magnitude 

 which is not merely different from zero, but (on the scale customary 

 for such things) very considerable, and independent of the field 

 strength which is applied to the iron.'' 



The answer to this question is given, and very well given, by that 

 extra field or "Weiss field" within the group, which I first mentioned 

 in connection with the constant 6 which paramagnetic solids exhibit. 

 It will be remembered how this constant is explained by assuming that 

 the torque, which acts on any one of the atomic magnets, is due not 

 entirely to the applied field // but to the resultant of that and an extra 

 field .4/ which is proportional to the magnetization / of the body. We 

 have already had the equation (10) which links / and H when this 

 extra field is present. Now striking H altogether out of that equation, 

 we arrive at this one : 



I ^ Nfi tanhiiJiAI/kT) (12) 



which refers to a situation in which there is no applied field at all. 

 This may be regarded as an equation for /, fixing the value or values 



