PEIRCE. — BEHAVIOR OF THE CORE OF AN ELECTROMAGNET. 171 



f = 



64 • fi • H 



(t^e-gW+W ^ e-^k+iy-t 



TT 



^(2i+l) 2 ^"(2 



A- + l) s 



(60) 



In these equations absolute electromagnetic units are to be used, and 

 for good soft iron we may assume that 7rp/4 is very approximately equal 

 to 8000. It is evident that for different values of c when /u is given, 

 e~ KH will have the same numerical value for values of t proportional to 

 c 2 ; for instance, if c = 20, t = 10, e— KH will have the same value as it 

 would if c were 1 and t, 1/40. If c is fixed, e~ KH will have the same 

 value for values of t proportional to //.. 



It is possible to show that if c = 1 and /* = 200, — to take a special 

 case, — the series 



s =Hk^-^- (61) 



lc-0 



',k+ l) 2 



has at different times the approximate values given in the following 

 table : 



TABLE V. 



From the numbers in this table it is easy to compute, for cores of 

 square cross-section, the fractional part of the original induction flux 

 through the core which remains after the circuit of the exciting coil has 

 been broken for a given time. For a solid core, .the area of the square 

 section of which is 100 square centimeters, the results are given in the 

 next table, when ^ is 200. 



If the core were built up compactly of varnished square rods of one 

 square centimeter in cross-section, the times in the table should be 



