ACOUSTICS AND GRAVITATION. 145 



The following data were obtained for the fringe displacement AJV, showing 

 the permanent effect of reversing current. 



3 amperes, AN = ? 10 amperes, AN = 0.00031 20 amperes AN = 0.00065 



Below 3 amperes I was unable to observe a displacement. For larger currents 

 the twist increases proportionally to the current passing the tube. It is prob- 

 able that here, as in similar cases in magnetization, fields below a certain 

 small value are ineffective, as though there were static friction. 



A further observation is to be made. If a certain magnetic set is produced by 

 a stronger current (say 20 amperes), then a weaker current (say 10 amperes) 

 is unable to modify it, provided both currents are in the same direction. If 

 this weaker current is reversed, the change of twist corresponding to the cur- 

 rent will appear. The absolute value of the set thus depends upon the past 

 history of the iron, however varied this may have been, with the understanding 

 that the set produced by the maximum current in either direction is character- 

 istic of the strength of that current. Differential values, in other words, re- 

 main the same. 



112. Data. Finally, the numerical equivalents of the observations made 

 may be stated. The elastic torsional coefficient for a tube of the dimensions 

 given may be computed with the usual equation, using the differential form 

 dT/dr = 2Trr 3 d/l with the mean radius r and length / and taking the rigidity 

 n as 8.2Xio n . If T is the torque corresponding to the twist of 6 radians, 

 the relation was found to be T=io 9 X4-70. 



On the interferometer, if the breadth of ray parallelogram is b = 10 cm. and 

 A9 is the rotation of the mirror mm' around a vertical axis corresponding to 

 the displacement of mirror AN (the mirror being at 2 = 45 to the rays) the 

 relation will be A0 = 0.071 AN, since A6 = AN cos i/b. Hence, if we assume 

 that the resistance to magnetic set is the same as the elastic resistance for the 

 same twist Ad, the above values of AN will correspond to the following data : 



Current. AJVXio 5 Torque Xio~ 6 Energy. E/vo\. 

 10 amperes 31 cm 1.03 1.13 ergs o.io 



20 amperes 65 2.16 4.97 0.43 



The energy E potentialized by the magnetic set is computed as TAB/ 2 . From 

 the volume of iron in the tube, 11.5 cm 3 ., the data of the last column follow. 

 My conception of this phenomenon is that of two concentric circular fields 

 in opposite directions, one within, the other on the outside of the tube, intro- 

 ducing a rather intense vortex sheet in the thin walls of the tube, in which the 

 circular fields terminate. 



113. Longitudinal field. The longitudinal strain produced by a longi- 

 tudinal field is well known. The question may be asked whether, in this case, 

 in a free iron bar there is any corresponding torsion. This was easily answered 

 by slipping a helix over the steel tube. Feeding it with I amperes, the micro- 

 meter displacement AN was successively 



