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PEIRCE. — MAGNETIZATION IN IRON. 133 



but which is hnked with the primary circuit by the mutual inductance, 

 M. The branch AQB or (1), which is directly coupled with the 

 primary, has a resistance Ri, a total self inductance Ni, and carries a 

 current I\. The branches KB, CD, or (2), (3), contain condensers 

 of capacities A^ and A's respectively. Their resistances are E^ and i?3, 

 their self inductances, iVo and N^ and they carry currents I2 and I^. 

 The branches (4) and (5) have no condensers. Their resistances are 

 Ri and R„, their self inductances, Na, Nr„ and their currents, h and /s- 

 The current in DB, which has a negligible resistance, is, of course, li. 

 If accents are used to denote differentiations with respect to the 

 time, an easy application of Kirchhoif's Laws to these two circuits 

 leads to the equations:^ 



T' - L-r - MI\ = RI, 



- M-r - N,-I^ - Ni-I,' - N,- h' 



= R^-h + R,-h + R,- h, 



- M ■ r - iVi (/o' + iz + h') - ^\ ■ u - Q2/K2 



= Ri (h + /3 + h) + R2 • I2, 



-M -r -N,{h' + U + h')-N,{h' + h')-N,-h' -Q,/K, 

 = Ri{h + h + h) + RAih+h) + Rs'h, 



h = L+U = 1. + h+ h, 

 or 



{L-r -\-R-I) + M ■ u + M • u + M ■ h' = r, 



+ iNrh'-^N4-h'-\-X,-h' + Ri-h + RA-h + R,-h)=^0, 



M ■ I" + (xVi • I./' + A'2 • h" + Ri • I2' + R2 ■ Li + I2/K0) 

 + (iVi • h" + R,h') + (Xy • h" + Ri • U) = 0, 



M-I"+ {Nr • h" + i?i • h') + (iVi • h" + ^-4 • 73" + Ns • h" 

 +/?, • U + R, • U + i?3 ■ h' + /3/A3) 

 + {N, • h" + N, • h" + Ri ■ U + Ra ■ h') = 0. 



If, for I we write 7o + V/R, the second number of the first equation 

 becomes zero, while all the equations remain otherwise unchanged in 

 form, and it follows that every one of the currents satisfies a single 

 linear differential equation of the sixth order with constant coefficients 



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