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IX. Dynamo-Electric Machinery. 
By J. Hopkinson, M.A., D.Sc., F.R.S., and E. Hopkinson, M.A., D.Sc. 
Received April 19,—Read May 6, 1886. 
[Plates 16-20.*] 
Theoretical Construction of Characteristic Curve. 
Omitting the inductive effects of the current in the armature itself, all the properties 
of a dynamo machine are most conveniently deduced from a statement of the relation 
between the magnetic field and the magnetising force required to produce that field, 
or, which comes to the same thing but more frequently used in practice, the relation 
between the electromotive force of the machine at a stated speed and the current 
around the magnets. This relation given, it is easy to deduce what the result will be 
in all employments of the machine whether as a motor or to produce a current through 
resistance, through an electric arc, or in charging accumulators ; also the result of 
varying the winding of the machine whether in the armature or magnets. The proper 
independent variable to choose for discussing the effect of a dynamo machine is the 
current around the magnets, and the primary relation it is necessary to know concern¬ 
ing the machine is the relation of the electromotive force of the armature to the 
magnet current. This primary relation may be expressed by a curve (Hopkinson, 
Meehan. Engin. Instit. Proc., 1879, pp. 246 et seq., 1880, p. 266), now called 
the characteristic of the machine, and all consequences deduced therefrom graphically; 
or it may be expressed by stating the E.M.F. as an empirical function of the 
magnetising current. Many such empirical formulas have been proposed; as an 
instance we may mention that known as Frohlich’s, according to whom, if c be the 
etc 
current in the magnets, E the resulting E.M.F., E=— —. For some machines 
this formula is said to express observed results fairly accurately, but in our experience 
it does not sufficiently approximate to a straight line in the part of the curve 
near the origin. The character of the error in Frohlich’s formula is apparent 
by reference to Sheet I. (Plate 16), which gives a series of observations on a dynamo 
machine, and for comparison therewith a hyperbola F, drawn as favourably as possible 
* Plates 19, 20 added Aug. 17. 
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