198 Mr. 0. Heaviside on the 



tively simple manner. [In passing, I may mention that on 

 comparing the measured with the calculated value of the 

 inductance of a long solenoid according to Maxwell's formula 

 (vol. ii. art. 678, equations (21) and (23)) in the first edition 

 of his treatise, I found a far greater difference than could be 

 accounted for by any reasonable error in the ohm (reputed) 

 or in the capacity of the condenser, and therefore recalculated 

 the formula. The result was to correct it, and reduce the 

 difference to a reasonable one. On reference to the second 

 edition (not published at the time referred to) I find that the 

 formula has been corrected. I will therefore only give my 

 extension of it. Let M be the mutual inductance of two long 

 coaxial solenoids of length Z, outer diameter c 2 , inner c l3 

 having 7i x and n 2 turns per unit length. Then 



M = A7r 2 n 1 n 2 c 2 \l-2c 1 ), (46c) 



where, if p — Ci/c 2 , 



»-^H( 1 +S( 1+ S( 1+ 3P( l+ *+ •- W 



When 



Cl = c 2 , 2a = l-*149 = -851. 



As regards Maxwell's previous formula (22), art. 678, how- 

 ever, there is disagreement still.] 



References to authors who have written on the subject of 

 induction of currents in cores other than, and unknown to, 

 and less comprehensively than, myself, are contained in Lord 

 Rayleigh's recent paper*. So far as the effect on an induction- 

 balance is concerned, when oscillatory currents are employed, 

 it is to be found, as he remarks, by calculating the reaction of 

 the core on the coil-current. This I have fully done in my 

 article on the subject. Another method is to calculate the 

 heat in the core, to obtain the increased resistance. This I 

 have also done. When the diffusion effect is small, its in- 

 fluence on the amplitude and phase of the coil-current is the 

 same as if the resistance of the coil- circuit were increased 

 from the steady value R to t 



= R + 2l7rk(7rT$c 2 fJ,n)* = B+R 1 say J ' ' (48 ^ 



Many phenomena which may be experimentally observed when 

 rods are inserted in coils may be usefully explained in this 

 manner. Here /jl and k are the inductivity and conductivity 



* Phil. Mag. December 1886. 



t ' Electrician,' May 31, 1884, p. 55. 



