CONTEMPORARY ADVANCES IN PHYSICS 303 



the function / which describes the magnetization which would produce 

 such a field. The vector / is not uniform throughout the iron, either 

 in direction or in magnitude. Though He is the same everywhere 

 within the metal, / varies from point to point. This result by itself 

 seems to demolish the assumptions. 



The contradiction however is only apparent; it vanishes if we make 

 due allowance for the field produced at every part of the magnet by 

 the other parts, for the effect of the magnet upon itself. Continuing 

 to use the illustration of the short rod in the uniform impressed field: 

 the distribution of elementary magnets which the function / expresses, 

 and which produces at every point outside the iron a calculable 

 field agreeing with the field there observed, should also produce a 

 calculable field at every point within the iron. Considering that we 

 have assumed that the force due to even the innermost volume- 

 element of the magnet is exerted unimpeded everywhere in the outside 

 world, we cannot consistently avoid assuming that its force is exerted 

 unimpeded upon the other volume-elements as well. Thus it is 

 reasonable to suppose that if the value of / at any point in the iron 

 is controlled by the magnetic field there prevailing, then the truly 

 controlling field comprises not only the one {He) due to the external 

 agencies, but also the other {Hi) due to the multitude of little magnets 

 presumed to constitute the piece of iron. The value of / should 

 depend on the resultant // of //« and Hi. In the present case of the 

 short rod inside the solenoid, the vector He is uniform, but the vector 

 Hi varies from point to point, and consequently so does the resultant 

 // of He and Hi, and consequently so does /. More properly, I 

 should not use such a word as "consequently" at all; both / and H 

 vary from pomt to point, either accounting for the other, either 

 being cause and either being effect. 



This, by the way, is one of the reasons why as a rule it is not possible 

 to analyze the magnetization of a magnet by cutting it into little 

 pieces and measuring the moment of each separately. When such a 

 piece is isolated from the rest of the magnet, the field acting upon it 

 is changed even though all the external field-producing agencies 

 remain the same. The other reason for not cutting up a magnet is, 

 that the stresses exerted on the material in the process of cutting are 

 likely to change it into some very different ferromagnetic material — 

 but of this, more later. 



The problem of determining I now assumes its full scope. For 

 every magnet, or let us say for every piece of magnetized iron, there 

 should be a function / describing its magnetization, defined at every 

 point within it and satisfying these conditions: 



