MAGNETIC STRESS AND MAGNETIC DEFORMATION IN NICKEL. 
191 
It can also be shown that if a tension 8P per unit area be ajiplied to a long uniform 
wire of the material and produce a small increase SI in the magnetisation, then 
E SI k' 
H SP ~ 1 + 29 
Between (1) and (2) the quantity ^ + k'j can he eliminated, and the result¬ 
ing ecjuation is 
81 ^ ^ I J 1 IT 
I ~~ 3E ■ 1 + 2^ 2E(1 + 2^) ^ ^ 8P 
(3). 
In order to compare this result with experiment a long cylindrical specimen should 
first be used to determine I and 8I/SP for several constant field-strengths. Then the 
specimen should be turned down to the form of an ellipsoid of revolution and the 
magnetic elongation a"* measured with the specimen in the same magnetic state as 
that in which I and SI/SP were determined. 
At first it was intended to do this, hut afterwards it was thought sufficient to use 
a wire of the material (of length very great in comparison with its thickness) in both 
parts of the experiment, thus assuming that the elongation of a long thin wire is the 
same as that of an ellipsoid of revolution having the same dimensional ratio.! The 
general agreement between the results of different experimenters, who in measuring 
magnetic elongation have used wires, strips and ellipsoids of various shapes and 
degrees of purity, shows that this is at least approximately the case. 
It can also be proved independently that in a uniformly magnetised wire the 
81 
term ^IT which is generally by far the greatest on the right-hand side of (3), 
represents the elongation due to those stresses which arise in consequence of the fact 
that magnetisation depends upon strain. For the potential energy, which unit 
volume has in consequence of the magnetisation, is — iHl-t Hence, if the body 
has dilatations e, f, cj, parallel to the axes of x, y, z, respectively, the part of the 
Lagrangian Function depending on magnetisation and strain coordinates is (supposing 
the quantities to vary infinitely slowly) 
L = JHI - (e +/+</)<=- in {e'i + - 2 <y - ifij - 2 </e).§ 
* The symbol a, is here used for the observed elongation of the specimen, i.e. the ratio of the observed 
increase of lens’th to the whole lenerth. 
t A change in the state of the surface of the specimen would be caused by the turning down, which 
would make that process inadvisable. 
X Maxwell, “Electricity and Magnetism,” vol. 2, § 632. 
§ J. J. Thomson, loc. cit. 
