172 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



divided by 100, and if the core were made up of 10,000 slender fila- 

 ments, the flux would sensibly disappear during the first thousandth of 

 a second. It is easy to get similar results for any other value of /u. 



TABLE VI. 



If the cross-section of the core were a circle of radius a, and if, after 

 a uniform magnetic field of strength Ho had been established in the 

 core the exciting circuit were suddenly broken, the intensity of the 

 field at any time, at any point distant r centimeters from the axis 

 would be given by the expression ^^ 



2H, 

 a 



2 





(62) 



where /8^ = p«'-^/4 tt/a and the whole flux through the core would be 



Hrdr or 4 ^M^o^. ^ ' (63) 



In these equations Hija is the /th root in order of magnitude of the 

 Bessel's Equation 



J,(?Ki) = 0. (64) 



^5 Heaviside, Electrical Papers, 1, xxviii. Peirce, These Proceedings, 41, 1906. 

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



