m 



in which lf'^„, is the resistance of the linear part of the circuit. 

 From this we get : 



ty2w,.-w. 



R\/ — ^ '-^ (23) 



When Tr„, is small compared with T'F,, r will differ little from 

 R. As a I'lile, however, the reverse will be the case, from which 

 ensues that r approaches the value ^R [/2. We can calculate the 

 current through the central part of the bar by means of the relation 

 (13). For this we get: 



VKf /c i 



.('■■) : 



1 -\- ■ ■ • (24) 



32o'^( IV, 



When W^ — W„^ is small with respect to W^ this quantity of 

 electricity will become much larger than t^,; it can become arbitrarily 

 large with respect to i\ when IF, — Tr„, is made small enough 

 with respect to ]I\. On the other hand when W„^ was small with 

 respect to ir,, e^'^■'''> would differ oidy little from e,. 



Let us now suppose that a current I^ runs in the fust conductor, a 

 current 7, in the second. We assume that then the state of equilibrium 

 is characterized by this that the bar is twisted over an angle tt per unity 

 of length. The torsion couple amounting to /v/^\ «, the elastic energy 

 of the bar is ^KR'^ . a' . I in the twisted state. We make this state 

 undergo an infinitesimal change so that « increases by the amount 

 da. Then the elastic energy increases by the amount KR* a I dn, 

 the work of the ponderomotive forces being found from (20) for the 

 considered change, which formula, after introduction of '?3?a and W,,, 

 produces 



dA = i A' . ,l(t fr . .(■>," .rp," . JS = — mlk 7, /^R^ . da. 

 J ' Se- 



in case of equilibrium this work must be equal to the increase 

 of the elastic energy, from which we find for the angle « : 



krul,!^ 



8c°-KR' ^ ' 



The whole torsion becomes : 



kmlJ , /, 



'KR' 



(25') 



If /■ is positive, then with the given current directions of J, and 

 7j the bar will be twisted .so that when the extremit}- where 7, 

 enters, is kept in fixed position, the other extremity is rotated in 

 the sense of the current I^, hence counter clockwise, when we 



