240 BELL SYSTEM TECHNICAL JOURNAL 



of / which can exist in this situation. Now everything which I have 

 said so far encourages the reader to suppose that the only possible 

 value of / in the situation is zero ; and as a matter of fact, zero is always 

 a solution of this equation. But suppose that there should be another 

 solution, different from zero. The equation would then assert, that 

 if somehow that value of magnetization should arise in the substance, 

 then the extra field would also arise, and in just the right magnitude 

 to maintain that magnetization perpetually, without any aid in the 

 form of a field applied from t' '^ outside. 



Well, the equation is not exactly easy to solve for /, but it can b 

 mastered— most conveniently by a graphical way — and the striking re- 

 sult is reached, that if T is greater than d there is no other solution 

 than 7 = 0, but if T is less than B there is a second solution. I will 

 denote this other by Iw Consider, then, the situation when there is 

 no applied field : if the temperature is higher than 6, I repeat what I 

 have been saying all along, that random orientation of the atomic 

 magnets is inevitable; but when the temperature is lower than 6, then 

 there is another possibility: there is a stable alignment of the atomic 

 magnets entailing this value Iw of the magnetization, which can 

 maintain itself indefinitely if it should ever come into being. Do not 

 leap to the other extreme, and suppose that this is a perfect alignment 

 of the atomic magnets and hence a perfect saturation of the domain. 

 Such a situation could exist (according to the theory) only at absolute 

 zero. The equation gives us Iw as function of T, and this function 

 declines smoothly from the value Njx (for a domain of unit volume!) 

 at absolute zero, to the value zero at T = 6. The curve between these 

 two points is completely determined by the values of n and 6, which 

 are derived in such ways as I have indicated from the magnetic prop- 

 erties of the substance at the higher temperatures well above 6. 



And now, the culmination. The so-called saturation of iron — the 

 ordinate of the I-\s-H curve when it flattens out and becomes sensibly 

 parallel to the axis of abscissae- — is itself (as I mentioned) a function of 

 temperature; it is this same function (Fig. 3). What is usually called 

 "saturation" with ferromagnetic bodies consists in aligning the big 

 arrows of the domains., so that in unison of direction they exhibit that 

 value of magnetization which is dictated by their internal temperature 

 and internal field. "True" saturation — "saturation of saturations" 

 — the alignment of the atoms within each domain superposed on the 

 alignment of the domains with the field — this can be attained only at 

 the absolute zero of temperature. We are able, however, to work at 

 temperatures so close to absolute zero, that the remaining degree of 

 extrapolation is slight; and we are able, therefore, to give with much 



