1886.] 



Dynamo-Electric Machines. 



327 



p. 397, and Maxwell, "Treatise on Electricity and Magnetism," 

 vol. ii, p. 24) be represented by the equation » = /(a), then the 

 characteristic curve is — 



If the relation between a. and a be given in the form of a curve, this 

 formula indicates at once a perfectly simple graphical construction 

 for the characteristic. Taking the curve of magnetisation determined 

 by one of us for wrought iron, and constructing a characteristic in 

 this way, we have obtained a theoretical curve which agrees over a 

 long range with the actual results of observation on a dynamo 

 machine more closely than any empirical formula with which we are 

 acquainted. 



To determine v, a wire was taken once round the middle of one 

 magnet and connected to a ballistic galvanometer, a known current 

 was then either suddenly passed round the magnets or short circuited, 

 the elongation of the galvanometer being noted. A similar observa- 

 tion was made with the same current, the galvanometer being con- 

 nected to a single convolution of the armature in the plane of commu- 

 tation. The ratio of the two elongations is the value of v. 



The distribution of the waste field {y — 1) I was roughly ascertained 

 in a similar manner. 



The currents in the fixed coils round the magnets are not the only 

 magnetising forces applied in a dynamo machine. The currents in 

 the moving coils of the armature have also their effect upon the 

 resultant field. Id well-constructed machines the effect of the latter 

 is reduced to a minimum, but it can be by no means neglected. This 

 introduces a second independent variable, viz., C, the current in the 

 armature. The effect of the current in the armature depends upon 

 the lead given to the brushes. Denote this by X, which we may also 

 regard as an independent variable, as it is subject to arbitrary 

 adjustment. 



If I=F(47mc) be the characteristic curve when no current passes 

 through the armature, then 



v h \ v / 



where m is the number of convolutions in the armature. Here we 

 omit the comparatively unimportant portion of the magnetic force in 

 the core of the armature and the pole pieces. From this formula it 

 is not difficult to deduce a geometrical construction for the character- 

 istic surface (vide " Practical Applications of Electricity," Lectures 

 delivered at the Institute of Civil Engineers, 1882-83, p. 98). The 



