8 HIE MAGNETIC CIRCUIT [ART. 1 



analogy is purely formal, the two sets of phenomena being entirely 

 different. An equation similar to (1) can be written for the flow 

 of heat, of water, etc. It merely expresses the experimental fact 

 that, for a certain class of phenomena, the effect is proportional 

 to the cause. 



If the space within the coil be filled with practically any known 

 substance, solid, liquid, or gaseous, the reluctance (R remains 

 within less than 1 per cent of the value which obtains with air. 

 The notable exceptions are iron, cobalt, nickel, manganese, chro- 

 mium, and some of their oxides and alloys. 1 When the circuit 

 includes one of these so-called " ferro-magnetic " substances, a 

 much larger flux is produced with the same m.m.f., that is, the 

 reluctance of the circuit is apparently reduced to a considerable 

 extent. Moreover, this reluctance is no longer constant, but 

 depends upon the value of the flux. The behavior of iron and 

 steel in a magnetic circuit is of great practical importance, and is 

 treated in detail in Chapters II and III. 



The definition of the unit of reluctance follows directly from 

 eq. (1). A magnetic circuit has a unit reluctance when a magneto- 

 motive force of one ampere-turn produces in it a flux of one 

 maxwell. 2 No name has been given to this unit so far. The author 

 ventures to suggest the name rel, and he uses it provisionally in this 

 book. Granting that reluctance is a useful quantity in magnetic 

 calculations, one must admit that it should be measured in some 

 units of its own ; unless one chooses to use the cumbersome nota- 

 tion " ampere-turns per maxwell." The name rel is simply the 

 beginning of the word reluctance. Thus, a magnetic circuit has 

 a reluctance of one rel when one ampere-turn produces one 

 maxwell of flux in it. The unit rel is analogous to the ohm in the 

 electric circuit, and to the daraf in the electrostatic circuit. 



Prob. 4. What is the reluctance of the magnetic circuit in Fig. 1 

 if 47,600 ampere-turns produce a flux of 2.3 kilo-maxwells? 



Ans. 47,600/2300 = 20.7 rels. 



Prob. 5. How many ampere-turns are required to establish a flux 

 of 1.7 megalines through a reluctance of 0.0054 rel? Ans. 9180. 



Prob. 6. A wooden ring is temporarily wound with 330 turns of 

 wire; when a current of 25 amperes is flowing through the winding the 



'See Dr. C.P. Steinmetz, Magnetic Properties of Materials, Electrical 

 World, Vol. 55 (1910), p. 1209. 



2 See Appendix I at the end of the book. 



