Theory of Dynamo-electrical Machines. 47 



that it has been attempted to express by mathematical for- 

 mulae the processes which take place in them. The formulae 

 hitherto applied do not seem to me quite to fulfil this object: 

 either they rest on a theoretically imperfect basis, or they are 

 too incomplete to account for all the circumstances which are 

 to be taken into consideration. In what follows I venture to 

 give a somewhat more complete theoretical explanation. 



§ 1. Essential parts of Dynamo-electrical Machines. 



The dynamo machines which have hitherto been constructed 

 are very different in their external forms, but in principle 

 they vary little from each other; and I think, that of the 

 machines for direct currents, those of Gramme and Siemens 

 may be regarded as typical. These also are so similar to each 

 other in their action, that in so far as concerns the develop- 

 ment of the fundamental formulae they need not be treated 

 separately, but may be comprised in one common treatment. 



To the essential parts belong, first of all, a fixed electro- 

 magnet with large pole-pieces, or a combination of several 

 fixed electromagnets whose like poles are joined by pieces of 

 iron, and are thereby provided with common pole-pieces. In 

 considering the question, it is not necessary to discriminate 

 between the cases in which the magnets have only one, from 

 those in which they have several electromagnets; and wherever 

 one fixed electromagnet is spoken of in the sequel, we under- 

 stand that it also applies to a combination of several fixed 

 electromagnets. 



In the space between the poles of the fixed electromagnet 

 is the rotating electromagnet. In Gramme's machine this 

 has the form of the ring originally devised by Pacinotti, and 

 consists either of a solid iron ring, or, what is now usual, one 

 formed of iron wire, round which the insulated conducting 

 wire is coiled in a spiral. In Siemens' machine it consists of 

 an iron drum, on the surface only of which the conducting 

 wire is coiled. We will consider separately the two parts, the 

 wire coiled and the iron core. It is essential for the former 

 that it shall rotate, and we shall speak of it as the rotating coil 

 (drehbare Umioickelung) ; and the latter, which need not rotate 

 with the coil (which is better so far as the action is concerned, 

 though more difficult to effect in practice), we shall speak of 

 as the iron core of the rotating coil. 



The rotating coil is divided into several portions in conduct- 

 ing communication with each other, which is effected by con- 

 necting the end of one and the beginning of the next division 

 with a metal strip. These metal strips are so placed near each 

 other that, without being in metallic contact, they form together 



