336 Mr. J. Buchanan on the Theory of 



independent variable : the values of the other quantities 

 which are assumed are : — 



No. 1 a=0'2; h = 2 ; c = l ; x = 2. 



No. 2 a = 0'2; A = 2 ;" c=l ~';~ x = l. 



No. 3 a = 02; h = 2 ; c = l ; #=4. 



No. 4 a = 0'2; A = 0'5 ; c = 0'7 ; a = l, 



For comparison are show a in broken lines in the same 

 figure three of Ewing's curves drawn to the same scale, 

 taking a magnetic intensity of 1700 = unity, since he has 

 found that for iron the saturation- value of I is about 1700. 



Curve A is a copy of fig. 20 in Ewing's ( Magnetic 

 Induction in Iron/ 



Curves B and C are from fig. 14, plate 59, of Ewing's 

 paper in Phil. Trans, part ii. 1885. A and B refer to 

 annealed wrought iron, C to the same wire as B but after 

 having been hardened by stretching. 



The graph No. 4 has been drawn to correspond to the case 

 where the magnetization of iron is carried out at a tem- 

 perature a good deal above the normal (cf. fig. 78 in Ewing's 

 * Magnetic Induction in Iron ') . 



From the course of the investigation given above it will 

 readily be understood that since a priori the values of F(«) 

 in (4) and (6) are completely arbitrary, it is quite probable 

 that a set of values for F(«) different from mine may express 

 the relationship of I to H better than those employed here. 

 All that I have attempted to show here is that (7) gives a set 

 of curves of the same type as those found by experiment. 

 It seems very likely, for instance, that the quantities a, c, and 

 h in (7) are really functions of x and H, in order to cover 

 the case where the temperature of the material is altered 

 considerably. In fig. 1 it will be observed that the values 

 a = 0'2, h = 0*5, <? = 0*7 have been taken in order to get curve 

 No. 4 to cut No. 1 and No. 2 *. 



These considerations recur in connexion with the question 

 of residual magnetism. 



Periodic Variation of H, and Residual Magnetism. 

 Before proceeding to deal with the periodic variation of H, 

 there is one point which needs to be made clear. 



* Since the above was put into type I have found that, within the 

 limits of fig. 1, curve B can be represented extremely well by a graph of 

 (7) if we take 



«=0-2, h=l, c=0-84, .r=l-2. 



This value of c would appear to show that the highest part of fig. 144 

 in Ewing's * Magnetic Induction in Iron ' exhibits better the form of that 

 portion of the graph of F(«) than does fig. 2 above. 



