METEORIC AND ARTIFICIAL NICKEL-IRON ALLOYS. 
29 
permeability corresponding to H. Hence, assuming the linear relation between p and 
H, stated above, we get 
| pH ds = a | H ds + b j H 2 ds, 
from which it follows at once that f pH dsj\ H ds, being equal to a + b\ II 2 c/.s/[H ds, 
represents the permeability of the material for a field of intensity JH 2 ds/fH ds. 
The value of JpHcZs is determined directly by experiment, and the values of 
jH 2 ds and of JHds can be calculated from the constants, geometrical and electrical, 
of the ring. 
In the present case, the ring being nearly rectangular in cross-section, it was found 
that if p m and H m represent strictly corresponding values of permeability and field, 
while p, and H represent approximately corresponding values as calculated in the 
ordinary way, then 
fx m = *996p. and H m = 1'006H. 
That is, values of p, and H calculated in the ordinary way would require to be 
reduced 0'4 per cent, and increased 0‘6 per cent., respectively, in order to give the 
true corresponding values of permeability and field intensity. 
The cross-section of the ring is frequently a rectangle terminated by semicircles, and 
we can then suppose the ring to be made up of a circular and a rectangular part. To 
complete the calculation in this case, according to the method just described, it is 
necessary to find the expressions for p, and H in the case of a ring of circular cross- 
section. 
This is easily accomplished, since, as will be seen, in this case 
[h * = 4n-Ni {r 2 — vV^T 2 } 
and 
[h 2 A = 8^NV{(r 2 /y^?)-l}, 
where is the radius of the circular cross-section, r 2 is the mean radius of the ring, 
and N and i are the number of turns and the current, respectively, in the ring 
primary. 
It may be noticed that the method of calculating corresponding values of p. and H, 
just described, would probably always give more accurate values than the ordinary 
method, even if the relation between p, and H, over a considerable range, were only 
expressible in the form 
p, = a -(- 6H -f- cH 2 +..., 
for in many cases the assumption, that within the limits of H experienced in the ring 
a linear relation between p, and H is fulfilled, would not lead to appreciable error. 
All the values of permeability given later have been calculated according to this 
method. 
