428 Dr. Silvantts Thompson on 



It will be seen that the values of the sine terms beyond A h 

 are negligible, and are not greater than the errors due to the 

 approximate nature of the method. The cosine terms are all 

 negative and of decreasing values for the successive orders. 

 In the Plate the wave-curve has been given for comparison, 

 and on it the components A v A 3 , B u B z , and B 5 have been 

 plotted in dotted wave-curves. For comparison with the 

 hysteresis loop its chief components have also been drawn in 

 dotted lines : the ellipse corresponding to A x ; the trilobate 

 curve of A 2 ; the oblique straight line of B h and the curves 

 for B 3 and Z? 5 . 



Example II. fig. 15, PL VI., Ewing's loop for annealed 

 iron wire, being fig. 5 of plate lviii. of Phil. Trans. 1885. 



The analysis gives : — 



A x =3-98 



B x =-7-38 



A 3 =214 



B 3 =-4-74 



A 5 =1-36 



B 5 =-2-04 



A 7 =0-88 



B 7 =-3-78 



A 9 =0-16 



J9 9 =-2-14 



A n = 0'U 



jB u =-1-90 



The ellipse and the straight line, corresponding respectively 

 to A x and _B l5 have been added in dotted lines in the figure. 



Example III. fig. 16, PL VL, Ewing's loop for annealed 

 iron wire, being fig. 6, plate lviii. of the same memoir. 



The analysis gives :-— 



A x =4-2 



B x =-35-4 



A, =1-8 



B s = -25-5 



A 5 =0-7 



B 5 =-17-9 



A 7 =0-2 



B 7 =- 6-7 



A % =0-3 



B 9 = - 4 5 



A n = 0-2 



B u =- 0-5 



Example IV. fig. 17, is taken from Lord Rayleigh's 

 paper in the Phil. Mag. xxiii. pp. 225-245, 1887, or 

 (Scientific Papers, ii. p. 593, and is the loop obtained with 

 very small magnetizing forces on a specimen of " rather 

 hard Swedish iron." 



The analysis gives : — 



A x =0-553 



B,= -1-022 



A 3 =0-038 



B 3 =-0-094 



A 5 =0-006 



B, =-0-046 



A 7 =0-002 



^ 7 = -0-025 



A Q =0-005 



B 9 = -0-023 



A n = 0-000 



B n = -0-012 



