514 PROCEEDINGS OF THE AMERICAN ACADEMY. 



= 2 -*S \ ( y> e -v*, (i6) 



a *Hn p - J x (n, a) v J 



' n t ■ J x (n p a) 

 p 



dJ (nr) . 



and, since - — -= = — n • J x {nr), 



+i#V J i( n J> r ) -of i / 17 x 



2 ir a ^4 J x 



(n p a) 

 p 



In the case here treated the diameter of the core is 25 centimeters 

 (a — 12.5), and for the kind of iron used, at room temperatures, we may 

 write 



g*= 5 - 12 <"">' ■ (18) 



The negative of the time rate of change of the total flux of induction 

 through a cylindrical surface of radius r coaxial with the core and 

 lying within it, is at every instant proportional to the expression for q 

 given above. The values of ,T (x) and J 1 (x) for every hundredth of a 

 unit between x = and x = 15.50 are given in Meissel's Tables 8 to 

 twelve decimal places, and after the proper value of /x has been intro- 

 duced into (18) and the value for r chosen, it is not very difficult, except 

 in the case of small values of t, to compute the value of the series (S) in 

 (17) for different epochs. If, for example, /x is 40, and if we consider 

 a point at the boundary of the core, S has the values given in the next 

 table. The time is of course measured in seconds. 



TABLE II. 

 t S t s 



0.25 1.3120 3.00 0.1085 



0.50 0.8413 4.00 0.0518 



0.75 0.6285 5.00 0.0247 



1.00 0.4974 6.00 0.0118 



2.00 0.2227 8.00 0.0026 



Figure 5 shows four curves in which $ is plotted against t for r = a 

 and fx = 20, 40, 80, and 160 respectively. If the circuit of a few turns 

 of fine insulated wire wound directly on the core were closed through an 

 oscillograph, and if jx were independent of H and there were no time lag 

 in its magnetization, the records should show curves like these. For large 



8 Meissel, Tafel der TCessel'chen Functionen, Berliner Abhandlungen, 1888 ; 

 Gray and Mathews, Treatise on Bessel's Functions, pp. 247-266. 



