174 ~—Prof. Maxwell on the Theory of Molecular Vortices 
Hence the lines of force in a part of space where is uniform, 
and where there are no electric currents, must be such as would 
result from the theory of “imaginary matter” acting at a di- 
stance. The assumptions of that theory are unlike those of ours, 
but the results are identical. 
Let us first take the case of a single magnetic pole, that is, 
one end of a long magnet, so long that its other end is too far 
off to have a per ceptible influence on the part of the field we are 
considering. The conditions then are, that equation (18) must 
be fulfilled at the magnetic pole, and (19) everywhere else. The 
only solution under these conditions is 
m I 
ae ee (20) 
where 7 is the distance from the pole, and m the strength of the 
pole. 
The repulsion at any point on a unit pole of the same kind is 
dp m1 
—=— =. ; : re 
oe (21) 
In the standard medium w~=1 ; so that the repulsion is simply 
= -> in that medium, as has been shown by Coulomb. 
In a medium having a greater value of w (such as oxygen, 
solutions of salts of iron, &c.) the attraction, on our theory, ought 
to be ess than in air, and in diamagnetic media (such as water, 
melted bismuth, &c.) the attraction between the same magnetic 
poles ought to be greater than im air. 
The experiments necessary to demonstrate the difference of 
attraction of two magnets according to the magnetic or dia- 
magnetic character of the medium in which they are placed, 
would require great precision, on account of the limited range 
of magnetic capacity in the fluid media known to us, and the 
small amount of the difference sought for as compared with the 
whole attraction. 
Let us next take the case of an electric current whose quan- 
tity is C, flowing through a cylindrical conductor whose radius 
is R, and whose length is infinite as compared with the size of 
the field of force considered. 
Let the axis of the cylinder be that of z, and the direction of 
the current positive, then within the conductor the quantity of 
current per unit of area is 
iy al dB wi), ; 
nae we dy ae 
L* 
