296 Proceedings of the Royal Society of Edinburgh. [Sess. 
lower half of the hemisphere the opposite relationship will hold. Further, 
on the above assumption, the rotation of the S. molecules in the upper 
and lower halves of the hemisphere will have the same effect as 
the rotation of the N. molecules in the lower and upper halves of the 
hemisphere respectively. A little consideration will also show that if 
the hemisphere — as in the present case — be bounded by the plane con- 
taining ab and H H, the positive and negative vertical changes of position 
of. the N. molecules in the upper and lower halves of the hemisphere as 
above defined, expresses fully what is occurring in the whole sphere 
irrespective of the polarity of the molecules. For the future, therefore, 
N. molecules only need be considered. 
In iron which has been demagnetised by heat, the position of the 
molecules in the upper and lower halves of the hemisphere is, by 
hypothesis, each the reflection of the other, and after rotation by the 
field the opposite changes of the vertical components of the molecular 
magnetic moments will neutralise each other. Such iron experiences no 
transverse induction change when magnetised. 
On the other hand, in the case of iron demagnetised by reversals, unless 
ab coincides with, or is at right angles to, H H the position or stability or 
both of the molecules in zones will not be symmetrical in the upper and 
lower halves of the hemisphere, and after rotation by the field the changes 
of the vertical components of the molecular magnetic moments will not 
neutralise each other. It is this which constitutes, on the molecular theory, 
transverse induction changes in iron previously demagnetised by decreasing 
reversals. 
If it now be assumed that a definite law connects the initial and final 
angular positions of a molecule with the field strength, the transverse 
vertical change due to each molecule can be calculated. The law (arbitrary) 
upon which the present calculations are based is, for those molecules lying 
equatorially in reference to the magnetising field, that the cotangent of 
the polar distance is equal to the strength of the field. Thus (full line 
curve of fig. 2), when the deflecting field is unity, the polar distance of 
the molecules will be 45°, finally approximating to 0° for high values of 
the field measured as abscissae. For molecules lying at other angles than 
90° the law is given by the various curves of fig. 2, which are so drawn 
that they reach the asymptote at higher values of the magnetising field 
the greater the initial polar distance of each molecule. These vertical 
ordinates have double values, and the (initially) ascending or descending 
curves must be taken according as the angles are greater or less than 90°. 
If the transverse vertical components of induction, due to the rotations 
