Magnetic Induction in Iron and other Metals. 341 



Example 4.— Take <2?=4, 11=180, and H = x = 45 ; in (12). 

 Then 4 



I=i x 0-444 



7T 



= 0-57. 



Now the value H = ^ = 90 in these numerical examples 

 would, in an actual experiment, be evidently represented by 

 a field-intensity of zero ; whilst H = -r = 45 would be repre- 

 sented by the maximum field-intensity. 



Examples 1 and 2 above show that for x=l the residual 

 magnetism is somewhat smaller in value than the magnetism 

 at the greatest field-intensity. Examples 3 and 4 show that 

 under corresponding circumstances the residual magnetism 

 is the greater. 



This last result is hardly conceivable. I think that the 

 explanation lies in the fact that the form of the graph of (12) 

 for the case of x = is probably different from fig. 5. (See 

 remarks on the values of a, /?, and c on p. 336 ante.) 



I am hopeful that the fuller investigation of such points 

 may lead to a more intimate knowledge of the numerical 

 values of the function of the molecular condition of materials 

 which I have called x. It is possible that the numerical 

 value of x for a material may prove to be as much a property 

 of that material as its specific heat, for instance. 



The treatment on the same lines as the above of the case 

 where a material placed in a magnetic field is subjected to 

 stress, must be left till another opportunity. I will content 

 myself with pointing out that when the effects of changes of 

 stress have become cyclic, we can write 



v= 2)1 A^-^cos (2nx + <f> n ) + B n e~ n2n sin {2nx + <£'J }, (14) 



where v represents the part of I which varies cyclically with 

 periodic changes of stress. 



As H becomes larger and larger the right-hand member 

 of (14) reduces more and more nearly to the form 



Ke~(w) H .cos (^-.x + A 



In other words, for small values of the field-intensity I is 

 represented by a sum of terms whose graph is in general a 

 complex curve. For large field-intensities, the graph reduces 

 more and more nearly to a simple cosine curve. These 

 deductions agree with the experimental facts. (Cf. Ewing, 

 Phil. Trans, pt. ii. 1885, fig. 42, pi. 63.) 

 Gordon's College, Aberdeen, 

 December 1900. 



