54 PROCEEDINGS OF THE AMERICAN ACADEMY. 



If two of the semiaxes (b, c) were equal, and if the third axis had the 

 direction of the outside field, H, which had been chosen also for the 

 direction of the a; axis, the field in the ellipsoid would agree with H in 

 direction, and we might write, 



where e 2 = (a 2 -6 2 )/a 2 = (a?-c?)/a 2 . The ratio of the intensity of the 

 field, H', within the ellipsoid to that of the exciting field, H, would be 



1 



(l+2irabckK ) ^ 



Table I shows the numerical values of a 3 ivo and of 1 + 2TabckKo 

 for several different values of the ratio m = a/b. 



Even though it be not possible to realize these conditions exactly 

 in practice, and a relatively slight departure from a truly ellipsoidal 

 form in the testpiece may alter the conclusions appreciably, yet the 

 measurements of several observers who have used such nearly ellip- 

 soidal rods as they were able to procure, show a fairly close agreement 

 with this theory, and we shall find it instructive to examine the numeri- 

 cal results obtained by applying it in the cases of one or two kinds of 

 soft iron and steel to be bought in the market. 



Some time ago, Mr. J. Coulson and I examined with great care a 

 long rod of soft Bessemer steel in a uniformly wound solenoid of 20904 

 turns, 4.85 meters long, as well as shorter specimens of the same 

 material between the poles of a massive soft iron yoke. Table II 

 gives very approximately for this steel and for various values of H, 

 the values of the susceptibility; of the fractional increase in the 



