treated according to Van der Waals's Equation. 345 



parallel to itself on the other side of the origin. When this 

 is done the line at some point C becomes tangent to the 

 curve, and if there were any further growth of the negative 

 field the line and the curve would part company and there 

 would be no positive value of I which would satisfy both 

 equations ; the magnetic intensity then enters an unstable 

 region. But since I can take negative as well as positive 

 values the curve of equation (1) must be continued sym- 

 metrically in the opposite quadrant, as in the figure, and it is 

 then seen that when the straight line parts company with the 

 curve of positive values of I it is cutting the negative branch 

 of the curve at F', where there is a stable negative value for 

 I. Thus, at the point C, the magnetization becomes unstable 

 and rapidly passes over to the point F' on the negative side, 

 and for increasing negative fields it continues along the 

 stable path F'R'. 



Again, as the field is carried from negative to positive 

 values, the intensity passes from a high negative value 

 through its residual value at D' to the point of instability C\ 

 and then suddenly changes to a positive intensity at F. 



Hence, when the field performs a cyclic change from 

 positive to negative and back to positive values, the magnetic 

 intensity traces out a hysteresis loop. A part of this loop is 



T 

 represented for the reduced temperature 7^- =0*3 in the 



upper part of fig. 4, where the negative field is given on an 

 arbitrary scale. 



4. Expressions can be obtained for (a) the reduced residual 

 magnetic intensity at the point D, (6) the reduced intensity 

 at the point of instability C, and (c) the negative field which 

 gives rise to instability. Let the values of (a), (6), and (V) 

 be put m n m lt , and H M respectively where 



m r = I r /I and t?i„=I m /I . 



If m=I/I equations (1) and (3) are 



m = cothx , (4) 



x 



" ,= ;Jr T *-Hr < 5 > 



(a) When H = m r is at once determined as the inter- 

 section of (4) and (5) for the given temperature T. 

 Phil Mag. S. 6. Vol. 33. No. 196. April 1917. 2 A 



