PEIRCE. — BEHAVIOR OF THE CORE OF AN ELECTROMAGNET. 173 



The first ten roots are as follows : 



TABLE VII. 



From these numbers the /3's can be found, and then from (63) the flux 

 in the core after any interval. When the time is short, the series con- 

 verges very slowly, and the computation is long and troublesome, but 

 for relatively large values of t the work is not difficult. 



The next table shows the fractional part (ft) of the original flux re- 

 maining in a core, the cross-section of which is a circle of 20 centi- 

 meters diameter, and in which p is 2< )< ) ; 1 second, 4 seconds, and 8 

 seconds after the breaking of the exciting circuit : the corresponding 

 fraction for a core of square cross-section (20 cms. X 20 cms.) is given 

 for comparison. The actual value of the original flux is of course a 

 little larger in the second case because the area of the cross-section is 



greater. 



TABLE VIII. 



After 16 seconds ft for the round core would be 0.016. In the case 

 of a round core of exactly the same cross-section area as the square 

 solid core, and the same original flux, the fractional part remaining 

 after one second would be 0.630. 



If the square core of the solenoid — the area of the cross-section of 

 which is A square centimeters — be made of a bundle of infinitely long, 



