144 Dr. F. Auerbach on the Passage of 



magnetizing force, is much greater than the direction-force. 

 Now, as long as the rotations are infinitesimal, the force varies 

 in inverse proportion to the angle of rotation; therefore the 

 work of the current remains constant ; but when the longitu- 

 dinally magnetizing force is considerable, and therefore the 

 rotations into the axial position cannot be regarded as infini- 

 tesimal, the work to be done by the current increases, although 

 the circular turning produced by it is less. If, to demonstrate 

 this, we denote by I) the direction-force, by H the directing 

 force of the principal current, we get (first, apart from a lon- 

 gitudinal magnetizing), for the work to be done for any one 

 molecule in rotating it the angle ty: — 



A = i D s'niTJrdyjr. 

 Jo 



Now, if the direction of D for this molecule makes with the 

 axis of the wire the angle <p, then -^r is determined by the 

 equation 



D sin yjr = M cos (<£ + yfr), 



from which follows 



, H cos 6 



tan yjr = -^ — ^ . • 



Inserting this value in the equation 



A = D(l-cos^), 

 we find 



D + Hsin<^ 



— Vt ( ~\ _. D + Hsiik/ a 



where W denotes the quantity + V D 2 + 2HD sin <p + H 2 . 



If now we would describe rigorously the phenomena of the 

 extra currents, we have to solve the following problems: — 



(1) What is the mean value of A for all the molecules of 

 the wire? 



(2) What is the amount of the corresponding work for one 

 molecule, on which, beside the forces T> and H, the force M 

 acts perpendicular to H ? 



(3) What is the mean value of this work for all the mole- 

 cules ? 



I have prosecuted this calculation under the following 

 assumptions : — (a) In the unmagnetic state, all the values of 



IT 



<£ between and x are represented with equal frequency ; 



77" 



values between ^ and tt appeared to me, on account of the 



At 



