PEIRCE. — BEHAVIOR OF THE CORE OF AN ELECTROMAGNET. 177 



absohms at the room temperature (Fleming and Dewar), 2irJV 2 p/w 

 will be equal to tV, and the equation for m takes the form 



J« (»*) = £)(«•») • A («*) = x ' yi ( " ,4) - (81) 



But" , = V 2X^L_ 



■^ (A - + m-lj-) J (ml>) 



and hence 



° = ^hS ,J7 trfl? , < (83) 



TO 



The whole flux of magnetic induction through the iron of the core is 

 then /j.71 2 times the integral of w taken over the circle of radius b in 

 which gt is defined ; that is 



4> = 4 ^XlI n-bS ( ^T'^t) i\ i ( 84 ) 



*mi m (A- + nrb') J (mb) 



+ = 4 ^///^ ffl2( ^' M ^ • (85) 



Since A = 1 0//? 2 , the coefficient of the series may be written 400 ir/*J5r o /» a , 

 and we may assume that //. = 100. 



The time rate of change of the total induction flux through the turns 

 of the solenoid, per centimeter of its length, is 



9950 -lO 4 -//^ e-F' 



ri z 



°2,;?+rfp- (86) 



If the square core is built up of 100 circular rods, each 1 centi- 

 meter in diameter, ri* = 100, A = 1/10, and the m's are defined by the 

 equation 



J (mb) = 10 mb • J x (mb) (87) 



in which b = 1/2. 



It is not difficult to show by trial and error from Meissel's tables 17 

 that the first five roots of this equation have values approximately 

 equal to those given in the following table : 



16 Byerly, Treatise on Fourier's Series, etc., p. 229. 



17 Meissel, Tafel der Bessels'schen Functionen, Berliner Abhandlungen, 1888; 

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

 Willson, Bulletin of the American Mathematical Society, 1897. 



vol. xliii. — 12 



