102 PROCEEDINGS OP Tin: AMERICAN ACADEMY. 



section (2 a x 2a) built up uniformly (Figures .">!> and fio) of a Urge 

 number of varnished filaments of square cross-section (c X c), or else 

 consisting of a bundle of infinitely long straight wires. The axis of 

 the prism shall be the z axis, and the ./• and // axes shall be parallel 

 to taces of the prisin. The electric resistance of the solenoid per centi- 

 meter of its length shall be ir, the constant applied electromotive force 

 per centimeter of the length of the prism shall be h\ and the intensity 

 of the current in the coil shall be C. Within the core, the magn< 

 field i // will have the direction of the z axis, and if q is the current 

 flux at any place 



4*9 = 00x117, <--'T 



or 4 wq x — -Q-, 4 -q„ = - ^ . 4 irq B = 0. 



Within any filament of iron in the core, // satisfies the equation 



cH_ P (&H </, 



where p is the specific resistance of the iron and p is its permeability, 

 which for the present purpose shall be regarded as having a fixed 

 value. 



When there are no Foucault currents in the core, the intensity i // t 

 the magnetic field within has at every point the boundary value //. 

 or 4 7T.Y7', but if positively directed eddy currents exist, // may be 

 greater at inside points than at the surface. We need not distinguish 

 between the flux p through the turns of the coil per centimeter of its 



length, and N times the induction flax p J j Hdxdy through the 

 core, so that we may write 



or by virtue of (28), 



_ wffs p4>NCC(&R r-1J\ 1 , . . 



^=T^ + ^JJ{^ + wr r '-" (30) 



where the integration extends over a cross-section of the core. 



The vector // is always perpendicular to its curl, and the intensity 

 of the component of the current at any point in the iron, in any direc- 



