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



absohms at the room temperature (Fleming and Dewar), 2ttN^p/iv 

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



But 16 1 = K ^ ^ • -^n (^^0 



-4' (A^ + ,,^^6^) To (;«/.)' ^^-^ 



and hence nr = 2 AZTo V-^^^^^^A(^ (gg) 



m 



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

 then jxn^ times the integral of zs taken over the circle of radius b in 

 which 57 is defined ; that is 



^ = i.^XHyiS~f^^4f}^„ (84) 



Since A = 10/w^, the coefficient of the series may be written 400 TrfxH^/n-, 

 and we may assume that jx = 100. 



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

 of the solenoid, per centimeter of its length, is 



9950 • 10^ -^^-^^ e-^'' , , 

 1 Z^ vis •"2 - (86) 



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

 meter in diameter, »^ = 100, A = 1/10, and the ms are defined by the 

 equation 



J^ {mb) = 10 mb • Ji (mb) (87) 



in which b = 1/2. 



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

 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. 



" 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 



