204, 205] DIELECTRICS AND MAGNETIZABLE BODIES. 397 



205. Hysteresis couple. In the examples of 192198, 

 it is evident that a sphere or cylinder turned about an axis of 

 symmetry in the field would experience no resisting couple, for no 

 work would be done against the forces of the field. In like manner 

 an ellipsoid would require on the whole no work to rotate it about 

 an axis, for the forces hindering the motion in one part of the 

 revolution would have corresponding forces helping the motion in 

 another part of the revolution. If hysteresis exists, however, the 

 case is quite different. Then the ellipsoid in a position in 

 which its long axis makes a diminishing acute angle with the 

 direction of the field experiences a mechanical couple tending to 

 accelerate its motion. The magnetic force parallel to the long 

 axis is then increasing, so that when the force has reached the 

 same value in the symmetrical position in which the axis 

 makes the same angle with the direction of the field, but on 

 the other side, F being then on the decreasing branch of the 

 hysteresis-loop, the value of the magnetization is greater, so 

 that the mechanical force, which now retards the motion, is 

 greater. Accordingly the motion is on the whole retarded*, and 

 it is easy to see that- the mean retarding couple is proportional to 

 the mean difference of the ordinates on the upper and lower 

 branches of the loop, that is to the area of the loop. Upon this 

 principle is based Ewing's Hysteresis indicator^, in which a long 

 sample of iron is rapidly revolved between the poles of a magnet, 

 and the mean couple between them measured by the pull on the 

 magnet. The couple is, as seen above, independent of the time of 

 revolution. 



* An effect of this sort was observed in diamagnetic and very slightly magnetic 

 bodies by Mr. A. P. Wills, in the physical laboratory of Clark University, in the fall 

 of 1895, and was discovered independently by Mr. Wm. Duane, in the physical 

 laboratory of the University of Berlin. Wied. Ann. Bd. 58, p. 517, 1896. 



t Ewing, Journ. Inst. Elec. Eng. 24, p. 398, 1895. 



OF THF 



UNIVERSITY 



