RESEARCHES IN MAGNETISM 
579 
The limits are oq and a 2 as above, and cos 6= 1 — 
Hence, 
This applies from X=p to X=oo. For values of X below p, 3 — 0- * is of 
course the magnetism of saturation. The following values of 3 are calculated from 
this equation :— 
X 
3 
p 
0 
1-25 p 
0‘360 mn 
1-5 p 
0'556 mn 
2 P 
Off 50 mn 
Sp 
0'889 mn 
4 P 
0'937 mn 
bp 
0'960 mn 
10 p 
0'990 mn 
100 p 
0'999 mn 
By supposing that p is different for different molecules we can avoid the discon¬ 
tinuity which occurs at X=p ; and the relation of 3 to X deduced from the formula 
agrees fairly well with actual curves of 3 and <§ in specimens of soft annealed iron. 
Removal of X would of course give a straight line (3 = constant), and application of 
X with sign reversed would give a rapid fall as soon as the value of the reversed force 
exceeded p. The results correspond so nearly with those found in soft annealed iron 
that it may be concluded that this extreme supposition (namely, that D is an insignifi¬ 
cantly small quantity, and that retentiveness is due to p), although doubtless not very 
exact, does represent fairly well the behaviour of this material. No such simple theory 
will answer in dealing with hard iron or steel. 
When we subject soft iron to vibration during the application ana removal of the 
magnetising force, we cause p to vanish more or less completely, and the action which 
we observe agrees fairly well with the original theory of Weber as developed by 
Maxwell ( loc . cit., equations 5-8), and shows that I), though finite, is a very small 
quantity. 
§ 68. Numerical Values of the Maximum of p and k. —The following table shows 
in a collected form, and in round numbers, the maximum values (deduced from these 
experiments) of p and k during initial magnetisation, and the value of <§ at which they 
were found. 
