PEIRCE. — MAGNETIC TESTS UPON IRON AND STEEL RINGS. 91 



the application of some form of Simpson's Rule may be made to yield a 

 result much more accurate than a planimeter can be expected to furnish. 

 In the case of such a ring, as appears from the last two columns of 

 Tables III, IV, and V, B' is usually a trifle larger than //', for very 

 small values of the mean //in the iron, but is equal to it for a single 

 somewhat larger value. Then, with increasing values of //, B' is a trifle 



Figure 2. 



smaller than B" ; but the ratio B'/B" soon approaches unity from the 

 under side, and, for high excitations, is sensibly equal to one. It is 

 evident, however, that the form of B'/B" as a function of the average 

 value of // in the ring must depend upon the dimensions of the latter 

 as well as upon the magnetic properties of the material of which the 

 ring is made. 



If a ring of rectangular cross section, of the same inner and outer 

 diameters as the toroid just described, be made of the Norway iron, 

 and if the excitation be made such that the average value of the mag- 

 netic field in the metal at the centre (C) of the cross section is unity, 

 the values of H and B already found may be used to draw the curve 

 PQ, Figure 2. The area under this curve as computed by Simpson's 



