502 Transactions. — Miscellaneous. 



It will be observed that for the soft-iron wire 0222in. in 

 diameter the resistance of the wire is 125 times its resistance 

 for steady currents. 



The wire 0145in. in diameter is seventy times its ordinary 

 resistance, and wire 0-039in. about eight times. 



The general result of this investigation supports the theory 

 of increase of resistance of conductors as the rapidity of the 

 oscillations is increased. 



The experiments here recorded receive additional confirma- 

 tion from later investigations on the circular magnetization 

 of iron. 



It will be observed that the wire OOllin. in diameter does 

 not double its ordinary resistance for a frequency of 3,500,000, 

 and the resistances increase more rapidly for increase of 

 diameter than ordinary theory would lead us to expect. 



Lord Eayleigh has shown that the resistance of a wire of 

 permeability /x for rapidly-alternating fields is ^/^jxplB,, where 

 R = resistance for steady currents. 



Now, for wire of diameter 0-222in., 



i/foplB, = 4 ; 



and substituting p = 2-1 x 10 7 , 



I — 377 



E = 0-032 ohm, 

 we get an equation for fx, and it will be found that in this 

 case jx = 121 ; and, if we thus determine jx for the different 

 soft-iron wires, we get the following table : — 



Diameter. Calculated 



-Permeability. 

 0-011in. ... ... ... 5-8 



0039in. ... ... ... 18 



0-145in. . . ... ... 87 



0-222in. ... . ... 121 



It will be observed that the apparent permeability of the 

 wire increases proportionately to the radius. Where the 

 radius of wire is increased twenty times, permeability is 

 increased twenty times, and so on. 



I am not aware that anything definite on this subject has 

 been hitherto done ; but the following approximate calcula- 

 tion possibly gives the true explanation : — 



Consider a condenser charged with a quantity Q of elec- 

 tricity. 



The maximum current of discharge J=jjQ , assuming no 

 decrease in amplitude. 



Now, if this current be confined to a surface-skin of the 

 conductor, the magnetic force, at a distance r from the centre, 

 is given by 9T 



H = — . 



