338 
MR. C. CHREE ON THE EFFECTS OF PRESSURE 
If then, through a small increase in the stress, there be increases Se, hf, Zg in the 
strains, we must have 
hg = hf=—cT^e . . . ■.(3). 
If be the consequent increase in the magnetisation, the field remaining constant, 
and so by (l) and (3) 
Thus from (2) 
83 = 'f s<; + ^| 8 /+^j 83 , 
df 
da 
83 = 8e('f-2.| 
k4=C('i-^ 
d3/ he 
W; 
where S3 and Se denote the small increments in the magnetisation and longitudinal 
strain which follow a small chanofe in the longitudinal stress. 
If (4) were a complete representation of the state of matters, then dejd'^ and S3/Se 
should always have the same sign, and should vanish for the same value of the 
magnetisation. 
It should be carefully noticed that in employing (4) we tacitly assume the changes 
in the strains to be very small, and thus the value of 83/Se should be obtained by 
experiments in which the change in the longitudinal stress is very small. 
Thus, in particular, the magnetisation at which S3/Se vanishes is the Villari point, 
as determined by experiments in which the difference between the two assigned states 
of stress is very small. And thus, in accordance with the experiments of Sir 
W. Thomson and Professor Ewing, this theoretical Villari point may well be very 
much higher than those hitherto found by experiment. 
It may also be as well to point out that the magnetisation answering to the vanish¬ 
ing of c/e/c/3 is not the critical magnetisation observed by Mr. Shelford Bid well 
where the rod resumes its original length, but the much lower magnetisation where the 
rod, if iron, has its greatest extension, if cobalt, its greatest shortening. 
Comparison of Theory and Experiment. 
§ 14. The experiments already recorded sufficiently show that in iron, there is in 
weak fields, and again, in very strong fields, an agreement in sign between c/e/c/3 
83/Se, both expressions changing from positive to negative as the strength of the field 
is raised. It will be noticed, however, that the magnetisations obtained experimentally 
for the Villari point are much lower than those obtained for the point of maximum 
lengthening of the rod. This difference is certainly in some measure accounted for 
