326 
MR, J. J. THOMSON ON SOME APPLICATIONS OF 
but if E be the elongation of the bar produced when the bar is magnetised so that the 
intensity of magnetisation is I, equation (46) shows that 
dl 2 2 d¥ de \ BJ 
(52) 
so that by equation (51) 
1 _ dk 
de 
by equation (50) 
81 = 
(53) 
Now, since the elongation increases with the intensity of magnetisation—at any 
rate when the latter is strong—c/E/c/P is positive, so that from equation (53) Se and 
81 will have the opposite sign, so that if the strain of a strongly magnetised soft non 
bar be increased the intensity of its magnetisation will be diminished. The experi- 
ments of Villari and Sir William Thomson confirm this result, but each of these 
physicists found that if the intensity of magnetisation was below a certain critical 
value, an increase in the strain was accompanied by an increase in the intensity of 
magnetisation ; equation (53) shows that when this is the case c/E/c/P must be 
negative, so that a soft iron bar will contract on magnetisation when the magnetising 
force is small. I have not been able to find any experiments on the extension of soft 
iron bars under the action of small magnetising forces. Sir William Thomson found 
that the critical force was about thirty times the earth’s vertical force at Glasgow, so 
that to test this point the magnetising force ought to be less than this value. The 
critical value of the magnetisation, i.e., the intensity of magnetisation when it is not 
altered by slightly straining the bar, is given by the equation 
d d^_ P 
de dV B — 0 
(54) 
Sir William Thomson’s experiments show that this value of I depends upon the 
state of strain of the bar; hence we see that equation (54) must involve e, so that if 
1/B be expanded in powers of e it must contain powers of e about the first, but if l/B 
involves the square of e there will be a-term in the expression for the kinetic energy 
of the form APe 3 , and as the coefficients of elasticity depend upon the coefficients of 
e 2 in the expressions for the kinetic and potential energies, we see that in this case the 
elasticity of a soft iron wire will be altered by magnetisation. Many experiments 
have been made to detect this effect, but with negative results; an investigation 
similar to that on page 313 will show however that the effect on the critical value of 
magnetisation will be more easily detected than the effect on the elasticity. Since 
