Magnetic Hysteresis loss in Straight Iron Strips. 273 

 or sectional strip is closely given by the expression : — 



B 



(lo» n 0, 



and hence for a given frequency and thickness the eddy- 

 current loss per pound of iron is very quickly found from a 

 simple parabolic curve representing B 2 in terms of B. 



In all the above observations with the iron strip used, 

 which was 12 mils thick, this correction has been applied, 

 and it is sufficient for this purpose to take as B in the above 

 formula the value B, of the effective induction. 



The eddy-current loss varies from point to point in the bar, 

 being always proportional to the square of the maximum 

 value of the induction density. Hence, properly speaking, 

 the mean value of the eddy-current loss should be obtained 

 by taking the mean square value of the induction all along 

 the half-length of the bar, and using the mean-square value 

 instead of the B 2 in the formula above. 



We have, however, found that the point on the half-length 

 of the bar at which the actual induction has a value equal to 

 the root-mean-square value, or to the square root of the mean 

 of the squares of the distributed induction, is always very close 

 to the point at which the l'6th root of the mean of the l'6th 

 powers of the distributed induction is found. In other words, 

 the induction at the effective point is the induction corre- 

 sponding to the mean eddy-current loss as well as to the mean 

 hysteresis loss. This is shown by the curves given in figs. 4 

 and 5, Plate V., in which the curve marked B is the curve of 

 variation of the maximum value of the induction-density 

 along the half-length of a bundle of iron strips, and the curves 

 marked B 1 6 and B 2 represent (to different scales) the variation 

 of these powers of B. In a bar 5 centim. long (see fig. 5, 

 Plate V.) the points where the actual induction had a value 



equal to Vm . B 2 and to \/m. B 1 6 were only separated by 

 a fraction of a millimetre. Hence by another curious coinci- 

 dence we are enabled to apply the proper correction for the 

 eddy-current loss by taking the square of the effective induction 

 B x and putting its value into the expression 



B^nH 2 



10 16 ' 



where n is the frequency and t the thickness of the strip in 

 mils. 



