becomes equal to r a, so long as the second and higher powers of 

 a are neglected. The diagonals of the rhomb become resp. : 



j/2 (1 + 1 r «) and l/2 (1 — ^ r a), 



hence the ratio between this and the original length resp. 



1 + 4 >• « and 1 — h r a. 



We call the direction of the strength of llie lield 'f?\ x, that of the 

 strength of the fielj .f)\ y. 



In consequence of the twisting the considered surface element has 

 obtained two main directions, which coincide with the diagonals of 

 the rhomb'). We call the direction of the diagonal which fails between 

 the positive ^.-direction and the positive //-direction, (/, that of the 

 other diagonal v. In the direction ii the iron is elongated, in the 

 direction v compressed. The elongation resp. compression amounts 

 to ^rn per unity of length. Let /■. P. be the increase of the permeability 

 in a certain direction, when the elongation per unity of length 

 amounts to ). in that direction, the compression per unity of length 

 normal to that direction being of the same value. Then 

 f(„ = ft + 2 ^ '■ " M'- =^ f* — \k r a. 



We assume /• to be independent of the strength of the tield. 



If we further assume the angles which the directions n and r 



form with .r and ?/ to amount to 45°, which is permissible so long 



as we confine ourselves to quantities of the first order in «, weget: 



^-)„ = i 1/2 (^,. + S?,j) 



S?, = { 1/2 (- ^, 4- ^,), 



and further, as : 



®M = f«« • •% ^v = Ho • ^?l; 



^„ = I »/2 (.fp. + .<>,;) + i /• r « 1/2 (.^... + .%) 



^y>,. = 1 1/2 (- .!:■>, + ..>,/) +ikra[/2{- .n, + ^^), 



from which follows : 



J5ar =: ft -^x + ^Icra ^y 

 55,, =1.1-% + kkra.r:)x. 

 We see that here the relation f«i2=^F3i holding universally for 

 anisotropic media with three mutually normal main directions is 

 satisfied. 



In the twisted bar JX has everywhere the same value at a certain 

 distance from the axis, when we move along a circle normal to 

 the axis, as there is radial symmetry with respect to this axis. The 



1) The third radially directed main direction may be left out of consideration, 

 as no change takes place in lliat direction. 



