88 Mr. R. H. M. Bosanquet on the Magnetic 
expresses the condition of equilibrium ; is the unit angle, so 
that wd is d expressed in degrees. 
If we pass from the consideration of a single molecule to 
that of a molecular arrangement we are confronted with 
problems which, for the most part, must be regarded as 
insoluble. One point, however, is clear. 
If the axes of the molecules are arranged uniformly in all 
directions, the average inclination to any one line is 60°. 
For we may suppose the axes of transmissibility uniformly 
distributed over the surface of each hemisphere, and the hemi- 
sphere is divided into two equal portions by a cone whose 
semi-vertical angle is 60°. 
If therefore we represent the condition of the average 
molecule with respect to inclination by a single molecule, we 
must assume the initial inclination to the axis of magneti- 
zation to be 60°. 
And, in the above expression, when 0=0, op=60° ; so 
that op=60°—w0. And the equation becomes, 
p sind 
It only remains to connect @ with the auxiliary angle 6. 
In the absence of exact knowledge of the molecular arrange- 
ments, the only thing we can do is to assume the simplest 
connection possible. We shall assume 
b=, 
where fis a factor. We thus obtain the system of equations, 
w=A(B,, —33) cos 6, 
ay), 
k 60°— 0 
dm p sin 9 
This system of equations involves only the arbitrary constants 
A, &.,, f, and 4 for 60° cannot be called arbitrary. The 
equations are capable of representing very well the connection 
between » and %. The Fourier’s series are in some respects 
more flexible. But these equations are important as regards 
their physical bearing. As the computations present some 
difficulty, I here give a systematic scheme for adapting these 
equations to the representation of experimental series of values 
of % and yp. 
Given a series of experimental values of % and yw, it is 
required to represent them by the formule 
