28 
MR. S. W. J. SMITH ON THE THERMOMAGNETIC ANALYSIS OF 
It is well known that for pure iron and for many iron alloys the values of p and H 
in weak fields are connected by a linear relation of the form 
/x = «+&H, 
where a and b are constants. 
Assuming that this relation may hold in the present case and calculating from the 
numbers just given, by the method of least squares, the most probable values of a 
and b, we find 
p = 99-5 + 55-2H. 
The following table shows how far the values of /x calculated from this equation 
agree with those actually found. 
Observed. 
Calculated. 
103-2 
104-4 
110-3 
109-1 
113-7 
113-9 
118-8 
118-5 
It will be seen that the agreement between corresponding numbers is within about 
1 per cent. 
§ 3. The values of p and H given above were deduced from the observations in the 
ordinary way by assuming that the intensity of the field in the ring (for a given 
current in the primary) was uniform and equal to that at the mean radius. 
The assumption that /x is constant throughout the cross-section of the ring, and 
that H has the value corresponding to the field intensity at the mean radius is, of 
course, very nearly true when the radial width of the ring is small compared with the 
mean radius. But if this latter condition is not fulfilled, or if the permeability varies 
rapidly with the field, the error introduced by this method of calculation may be 
considerable. 
Although the dimensions of the ring were such that the intensity of the magnetising 
field for a given current in the primary coil would be more than 20 per cent, greater 
at the inner than at the outer surface of the ring, it was thought, having regard to 
the nature of the material examined, that the ordinary method of calculation would 
probably be as appropriate as any other, and that the degree of concordance of the 
numbers already given was sufficient for the purpose in view. Nevertheless, it is of 
interest to notice that, if the relation p = a + bH is approximately true, a close 
approximation to strictly corresponding values of /x and H can be easily obtained, 
even when the ratio of the radial width to the mean radius is considerable, or when 
the variation of /x with H is large. The inductive effect per turn of the ring- 
secondary is | B ds = j pH d.s, where ds represents an element of the cross-section 
of the ring, H is the intensity of the field at this element, and p is the value of the 
