Magnetic Circuit of Dynamo Machines. 501 



the accompanying figure for various values of /3. The curve 

 B, fig. 1, is that given by Mr. Bidwell in his paper (Proc. 

 Royal Society, No. 245, 1886). The curve Hi has been 

 obtained from Dr. Hop kin son's experiments on wrought iron 

 in the Philosophical Transactions, 1885, plate 47. We wish 

 that Dr. Hopkinson had in this paper given his experimental 

 numbers, instead of plotting them in curves to such scales 

 that one feels very great uneasiness in making measure- 

 ments. We have determined the curve H x by taking a 

 medium curve between Dr. Hopkinsoir's curves for rising and 

 falling magnetizations. It is quite probable that, in view of 

 the great differences in the behaviour of the same and 

 different kinds of iron, under different circumstances, Dr. 

 Hopkinson did not feel that he was justified in drawing his 

 curves on paper too finely divided. It will be observed that 

 from /3 = 10000 to /3= 16300 we may take p= 5221-0-3071/3. 

 Unfortunately for easy methods of calculation in many 

 machines much larger values of ft than 16300 are often used. 



Curve H 3 is computed from Dr. Hopkinson's results for 

 cast iron, and it shows how very important it is, when cast 

 iron is used in the magnetic circuit of a machine, to have its 

 section much greater than that of the wrought iron portions 

 of the circuit, if throttling the induction is to be avoided. 



Curves K b K 2 , and K 3 are computed from the formulas 

 given in Mr. Kapp's paper for the wrought iron used in the 

 armature, field-magnets, and yoke respectively of a dynamo 

 machine. 



The differences among these curves throw great light upon 

 the fact that it is really impossible to predetermine the 

 " characteristic " of a dynamo machine. Mr. Kapp gets over 

 discrepances by calculating a value of his leakage-resistance 

 which suits the actual observations made on an already con- 

 structed dynamo machine ; and Dr. Hopkinson's curves, al- 

 though calculated on the basis of actual measurements of the 

 leakage made on an already constructed dynamo, and although 

 only computed lor a very small portion of that part of the 

 characteristic where the iron magnetic resistance is important 

 (the only portion about which there is any difficulty), repre- 

 sent this small portion very indifferently indeed. Methods 

 of calculating the leakage which have been put forward we 

 can in no way believe in, for reasons given by one of us in 

 the discussion on Mr. Kapp's paper at the Society of Tele- 

 graph Engineers. We are not in any way detracting from 

 the merits of Dr. Hopkinson's beautiful theory. We are too 

 well aware of the great services he has done us and of the 



Phil. Mag. S. 5. Vol. 25. No. 157. June 1888, 2 L 



