550 KEPOET— 1886- 



15. On Maijnetic Hysteresis. By Professor G. Forbes, M.A. 



Professor Ewing^ has made a contribution to the science of magnetism, which 

 has only lately come into the hands of scientific men, but which is certain to lead 

 to an extension of our powers in dealing with applications as well as with the theory 

 of magnetism. Lord Rayleigh has already drawn deductions from it in a paper 

 communicated to the ' Philosophical Magazine ' for August 1886. 



The consequences which 1 wish to draw from it have reference partly to prac- 

 tical applications, and specially to secondary generators or transformers, and partly 

 to Weber's molecular theory of magnetism. 



If a coil of wire carrying an electric cun-ent encloses an iron core whose length 

 is at least 400 times its diameter, or which is of a ring shape, the magnetic induc- 

 tion produced at the middle of the bar, or at any part of the ring, is due altogether 

 to the direct action of the electric current, since there is no free magnetism. In 

 this case the magnetic force is proportional to the electric current. 



A curve may be drawn in which abscissae denote electric current or magnetic 

 force, and ordinates represent magnetic induction. As the magnetic force is 

 increased a curve is traced ; but this curve is not retraced as the magnetic force 

 decreases. If the magnetic force reach alternately a positive and a negative maxi- 

 mum a closed curve is traced, the area of which indicates the work done upon the 

 iron core in a cycle of these operations, just as the area of the curve traced by th© 

 steam engine indicator measures the work done by the engine in a complete cycle 

 of the movements of the piston-rod. 



The nature of this curve shows that we cannot express the magnetic induction 

 in terms of the magnetic force alone. It is also a function of the history of the 

 iron in the immediate past. This phenomenon is called magnetic hysteresis. 



Fig. 1 (taken from Ewing) shows the increase of magnetic induction from zero 

 to a maximum, with increase of magnetic force and the subsequent cycle produced. 

 The arrows indicate the direction in which the curve is traced. 



If the iron be subjected, during the process of magnetisation, to mechanical 

 shocks, these peculiarities disappear, and the induction becomes a pure function of 

 the magnetic force. It is generally supposed that the tremors of a dynamo machine 

 prevent the effects of magnetic hysteresis from showing themselves. This may 

 sometimes be the case. It is not always so. In the first model non-commutating 

 dynamo constructed by me the electromotive force did not diminish ten per cent, 

 after the exciting current was reduced to zero. That model consisted of a long 

 cylindrical electromagnet, rotating about its axis, its poles being connected by a 

 soft iron cylinder with closed ends. In secondary generators hysteresis must play 

 an important part. In this case the magnetising force is due to the sum of the two 

 currents in the primary- and secondary coils. Now the maximum value of the 

 current in the primary is reached earlier than the maximum of the sum of the two 

 currents, and the maximum of the secondary current later. This fact introduces 

 intere^ing modifications in the form of the magnetic indicator diagrams of the two 

 circuits, to which I wish to draw attention. I will suppose that the maximum of 

 magnetic induction is coincident in time with the maximum of the algebraical sum 

 of the primary and secondary currents. 



The phase of the primary current may precede, and the phase of the secondary 



T 

 cuiTent may follow, that of the magnetic induction by a value varying from to — 



when T is the period of a complete cycle. The currents are taken as harmonic 

 functions of the time. 



To transform Ewing's cyclic curve of hysteresis into the corresponding diagram 

 for the primary or secondary circuit whose phase is +a or —a in advance of the 

 phase of induction. Let the maximum abscissa represent the magnetic force due to 

 the maximum current in that circuit, and describe a circle with this abscissa as 

 radius, and the zero of co-ordinates as centre. Take any point P on Ewing's 

 curve ; draw its ordinate PM. Let this line, produced if necessary, cut the 

 circle in Q Qj. This line cuts Ewing's curve in two points P P^. If P be the 



> Phil. Trans. 1885, Part II. 



