3:^9 



7. We shall now consider a special case. Let us imagine a 

 s^'stem of two currents, one passing through a vertical cylindrical 

 iron bar, the other through a vertical solenoid which is concentric 

 with the iron bar. We suppose the iron bar, whose length is assu- 

 med to be large with respect to tlie diameter, to be in the middle 

 part of the solenoid, and that the latter on both sides projects far 

 beyond tiie bar. For the present we assume for simplicity's sake 

 that the permeability of the iron has a constant value. 



The tirst current /, gives rise to a circular magnetisation in the 

 iron, the second I., to a longitudinal magnetisation. If ƒ, and ƒ, 

 are in I'ighthand cyclical order the corresponding strengths of the 

 field .^1° and •C'," are so too. 



The resistances of the conductors are called ]\\ and IT,. 



We can now twist the iron bar, l^ being =^ I and /^ = ; in 

 consequence of this three main directions will arise in the iron with 

 different permeability, which will also cause a longitudinal magneti- 

 sation in the bar, which is accompanied with an impulse of current 

 in the second conductor. Ijikewise we may twist the bar when 

 7j = and ƒ, =: I, which gives rise to a circular magnetisation of 

 the bar, and accompanying this an impulse of current in the first 

 conductor. We shall compute for both cases the quantities of elec- 

 tricity which pass through every section in consequence of the 

 impulses of current. 



If the radius of the iron bar is /?, then 



holds for the intensity of te field Jp°i inside the iron at the distance 

 r from the axis of the cylinder. 



If the solenoid has m windings per unity of length, the intensity 

 of the field in the middle part in which the iron bar is found, is: 



c 



We shall as.snnie the bar, which has a length /, to be twisted 

 over an angle ((• = /.«, and this in sucii a way that while one 

 e.xtremity, where the current l^ enters, is held fast, the other extre- 

 mity is twisted over an angle ^ in the sense of the current ƒ,. In 

 consc(|uence of this an originally square surface element with sides 

 of a length one of a cylinder surface concentric with the axis of 

 the bar, with radius r, will assume a rhombic shape. 



In this the angle which the sides of the rhomb, which were 

 originally parallel to the axis, form with the direction of the axis, 



