STEEL, NICKEL, AND COBALT TUBES IN THE MAGNETIC FIELD. 



475 



These broad results are deduced from the numbers contained chiefly in Tables II. 

 and VII. To facilitate somewhat the comparison between iron and nickel I have drawn 

 up the following table giving for the Tubes B V. (iron and nickel) the dilatations in chosen 

 fields at the inner and outer surfaces, thus indicating the ellipsoidal form into which an 

 originally spherical element is changed under the action of magnetic force. The chosen 

 fields are the fields of maximum elongation and of zero elongation in the Iron Tube 

 B V., and the greatest field reached in the experiments. The ratios A, m, v are one 

 millionfold the elongations of three mutually perpendicular unit lines, which when added 

 to unity give the principal semi-axes of the ellipsoid into which the unit sphere is changed. 



Principal Elongations in Iron and Nickel Tubes B V., expressed in Millionths (10~' ; ). 





Field = 190. 



Fa-Id = 310. 



Field = 500. 





Iron. 



Nickel. 



Iron. 



Nickel. 



Iron. 



Nickel. 



A 



V 



+ 21 

 -1-5 

 - -4 



-16-2 

 + 4-2 

 + 12-0 





 -•4 

 + •6 



-2L8 

 + 6-7 

 + 15-7 



-2T8 

 + -8 

 + 1-57 



- 24-8 

 + 6-9 

 + 17-9 



V 



+ 2-1 

 -L25 

 - "65 



-16-2 

 + 6-5 

 + 9-7 





 -•1 



+ •3 



-2L8 



+ 8-4 

 + 13-4 



-2T8 

 + 1-01 

 + 1-26 



-24-8 

 + 9-6 

 + 15-2 



We have no right to assume that these values hold for every point along the 

 inner and outer surfaces of the tube. Being calculated from observed total 

 changes of length and volume for the whole tube, they are, at best, only average 

 values ; and it is highly probable that they vary as we pass from points at the middle 

 to points near the ends. Nevertheless, since much longer tubes give very similar 

 results, these average values must be fair approximations to the true values at most 

 parts of the tube. 



It is also a fair presumption that elements in the heart of the metal suffer strains 

 intermediate in character to those belonging to the surface elements. 



Taking, then, the mean of the two strains in each case just given, let us calculate the 

 stresses associated with these strains, assumed for the moment to be elastic. 



Let P, Q, R be the principal stresses corresponding to the elongations A, v, v. Then 

 P is of the form MS + NA ; and the corresponding expressions for Q and R are obtained 

 by cyclical permutation of A, p., v. 



Expressed in terms of Young's modulus E and the rigidity n, the stresses become 



= »( 



E-2/i 



3w-E 



, S + 2A 



),Q = 



= etc., R = etc. 



