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PROCEEDINGS OF THE AMERICAN ACADEMY. 



of B which correspond to these as determined from the HB diagram 

 for the iron, are 2995, 2S95, 2810, 2635, 2460, 2310, 2150, 2005, 1870, 

 1745, 1620, 1505. If 2895 be multiplied by the thickness of the ring 

 at a distance of 6.1 cms. from the axis (OY), 2810 by the thickness at 

 a distance of 6.2 cms. from OY, etc., a curve of the form KNQ shown 

 in Figure 1 will be obtained. This curve was actually laid down on a 

 large scale by the help of a needle point on a sheet of good coordinate 



Figure 1. 



paper, and the area under it was determined to be 6816, though the 

 last significant figure is not determined. This divided by ■n-a'^ gives 

 21 70 as the mean value {B') of B in the ring. The mean value of // in 

 the ring is 1.0052 and the value {B") of B which corresponds to this is 

 2176. Although these results have been obtained with great care, they 

 cannot of course be assumed to be quite correct ; but it appears to be 

 true that the error in this case is not very large. 



The corresponding process in the case of a ring with rectangular 

 cross section is much simpler and the results are more trustworthy, for 

 the ring has a uniform thickness and the curve which bounds the nearly 

 trapezoidal area to be measured often has so slight a curvature that 



