132 Prof. R. Clausius on the 



of the current, this must of course be taken into account in 

 determining the magnetization which occurs with weak cur- 

 rents. It would be difficult to say how this should be done 

 in order to attain the greatest accuracy; nor does it concern 

 us for the present purpose, for we may content ourselves 

 with an approximation. This will be as follows: — Let jj, be 

 the moment of the remanent magnetism, assumed to be small; 

 we will first define the value of i, for which the above ex- 

 pression for M has the value p. Thus, if i± is the correspond- 

 ing value of i y we must put 





from which follows 



1 + aii 



From this determination we will settle that for all values of 

 i, which are smaller than i± the equation 



shall be applied for determining the magnetic moment M; 

 and for all values of i which are greater than %i the equation 



M: M 



1 + ai 



We thus arrive at a method which is to be applied during 

 the starting of the machine. At the outset we must consider 

 the magnet as a magneto-electrical machine, the fixed magnet 

 of which has the small value /x. Such a machine acts as a 

 current-producer even with small velocities of rotation, and 

 the current increases with an increase in the velocity of rota- 

 tion; but from the smallness of//, this increase can only be 

 very slow. But when the velocity of rotation has become so 

 great that the strength of the current has become i l} the 

 machine acts as dynamo-electrical machine in which the 

 fixed electromagnet has then also the moment //,, and gives a 

 current of the same strength; and from this period we apply 

 the principal equation, II. a, deduced for the dynamo machine, 

 in order to determine the current-strength. 



The question now arises, what is that velocity of rotation, in 

 which the machine gives as dynamo machine the same current 

 as the magneto-electrical machine, that is the current of 

 strength i v In determining this value of v, which may be 

 called v l9 we have to put i x (40) in place of i. We will at 

 the same time denote the values of w and «/, corresponding 



