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



^ 



Ufi-Ho- c''^^e-<^^y+^y-' ^'^ e-^'i'^+m 



TT 



2^(-2j+ir 2^'(2 k + If 



j—l k—l 



(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 fi. is given, 

 e~^'^ will have the same numerical value for values of t proportional to 

 c"; for instance, if c = 20, ^ = 10, e"^'' will have the same value as it 

 would if c were 1 and t, 1/40. If c is fixed, e"^'' will have the same 

 value for values of t proportional to /x. 



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

 case, — the series 



«=Xw^^' («i) 



k=0 



'k+ ly 



has at different times the approximate values given in the following 

 table : 



TABLE Y. 



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 fi 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 



