578 
PROFESSOR J. A. EWING ON EXPERIMENTAL 
produced in iron by changes of magnetising force (and, as I shall show later, by other 
things besides magnetising force) do occur in ways which are not only extremely 
suggestive of the movement of solid bodies against frictional resistance, but are exactly 
analogous to such movements in some of their effects. 
§ 67. In the molecular theory of magnetisation, as developed by Weber and Max¬ 
well, the equation expressing the equilibrium of a magnetic molecule when deflected 
by a magnetising force, X, is 
X sin 9= D sin (a — 6), 
where a is the original inclination of the molecule’s axis to the line of action of X, 6 is 
its inclination to the same line when deflected, and D is an assumed directive force 
which tends to keep the molecule in its primitive position. 
We may introduce the idea of frictional resistance by writing this— 
X sin 6= D sin (a — 6)-\-p, 
where p is a statical couple due to friction (to be reckoned per unit of magnetic 
moment of the molecule). In this form the equation will apply to cases where the 
deflection of the molecule is being or has just been increased by application of X. 
When the deflection is being diminished by reduction of X the term expressing the 
friction is to have its sign reversed. 
The most easily affected molecules are those whose inclination to the axis of X is —. 
Hence, on beginning to apply magnetising force there is no deflection of any molecule 
until X=p. Again, after magnetisation has been produced and the applied force X 
begins to be removed, no return of the molecules (that is to say, no loss of induced 
magnetism) occurs until the amount by which X is reduced exceeds 2 p. The sub¬ 
sequent loss of magnetism as X is further reduced will depend on the relation of 
D to p. 
Now, in soft iron the retentiveness is so nearly complete that D must be very small. 
We may examine the comparatively simple extreme case which we should find if D 
were equal to zero. Every molecule which is being turned by X must then satisfy 
the equation X sin 0=p, and the action is always limited to those molecules for which 
sin a > sin $ > v- For any given value of X, during the increment of X, the only 
molecules affected are those whose original inclinations lie between the values 
sin -1 ^ and oc. z =tt —cq. Molecules lying outside these limits do not contribute 
to the resultant magnetisation of the piece. 
Using the notation of Maxwell (‘ Electricity and Magnetism,’ vol. ii., § 443), in 
which m is the magnetic moment of a molecule, and n the number of molecules per 
unit of volume, we have 
;5 = 
mn 
cos 6 sin a c/a, 
