VARIOUS TYPES OF MACHINES. 701 



2nd. In magnetic machines the induction is produced by the 

 motion of a circuit in an invariable magnetic field, like that of a 

 system of permanent magnets. The work W x is then proportional 

 to the current, which gives 



3rd. In magneto-electrical machines, the inductor and the induced 

 body are coils containing soft iron or electromagnets, the two systems 

 of wires being traversed by the same current, or by given fractions 

 of the same current. The work W x comprises : ist, a term of the 

 form CI 2 , due to the action of the two systems of wires; 2nd, 

 a term CjMI, due to the action of the magnetised iron of each 

 of the systems on the wires of the other, and proportional to the 

 magnetism M ; 3rd, finally, a term C 2 M 2 , due to the action of 

 the two systems of magnets. 



If the currents are weak, the magnetism M of the armatures 

 is sensibly proportional to the current, and we may write 



W^C + Q + C,)! 2 , <(!) = (C + C 1 + C 2 )I. 



As the current increases, the intensity of the magnetisation of 

 the iron tends towards a maximum ; the products CjM and C 2 M 2 

 tend to become constants C' and C", which gives 



4th. We may, lastly, call those machines mixed in which the 

 inductor is a constant magnetic field due to an external agency, 

 and the induced body is an electromagnet. 



The work W x is then made up of two terms Al-f A X M, which 

 correspond to the action of the field on the wire and on the mag- 

 netised iron of the induced body. 



For weak currents we have still 



and, when the currents can produce the maximum magnetisation 



A + . 



