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Drs. J. Hopkinson and E. Hopkinsou. [Apr. 15, 



II. " Dynamo-Electric Machines. — Preliminary Notice." By 

 John Hopkinson, D.Sc, F.R.S., and Edward Hopkinson, 

 D.Sc. Received April 3, 1886. 



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. This relation 

 given, it is easy to deduce what the result will be in all employments 

 of the machine, also the result of varying the winding of the machine 

 in armature or magnets. The magnetic field may be expressed 

 algebraically as a function of the magnetising force, or more conve- 

 niently by a curve (" Proceedings of the Institution of Mechanical 

 Engineers," April, 1879, p. 246). Amongst the empirical formula? 

 which have been proposed to express the electromotive force of 

 dynamo machines in terms of the currents around the magnets, we 



may mention that known as Frohlich's, where E = ac , E being 



1 + oc 



the electromotive force of the machine at a given speed, c the exciting 

 current, and a and b constants. For some machines this hyperbola is 

 said to express observed results fairly accurately. In our experience 

 it does not sufficiently approximate to a straight line in the part of 

 the curve near the origin, and gives too high results for large 

 values of c. 



One purpose of the present investigation is to give an approximately 

 complete construction of the characteristic curve of a dynamo of given 

 form from the ordinary laws of electromagnetism and the known 

 properties of iron. Let n be the number of convolutions on the 

 magnets, c the current round the magnets, l x the mean length of the 

 lines of force in the iron of the armature, A x the area of section of 

 iron in the armature, Z 2 the distance from iron of armature to iron of 

 pole pieces, A 2 the area of the magnetic field in which the wires move 

 corrected for its extension round the edge of the pole pieces, Z 3 the 

 total length of the magnet cores, A 3 the area of the magnet cores, Z 4 

 the mean length of lines of force in the yoke connecting the magnet 

 limbs in machines of the type on which we have principally experi- 

 mented, A 4 the area of section of the yoke, l 6 the mean length of the 

 lines of force in each pole piece, A 5 the mean area of section of pole 

 piece, I the total induction through the armature, when no current 

 passes in the armature, and vl the total induction in the magnet 

 cores ; and finally let the relation between the magnetic force (a) 

 and induction (a) {vide Thomson, "Electrostatics and Magnetism," 



