164 Prof. Maxwell on the Theory of Molecular Vortices 
The necessary relations among these forces have been in- 
vestigated by mathematicians; and it has been shown that the 
most general type of a stress consists of a combination of three 
principal pressures or tensions, in directions at right angles to 
each other. 
When two of the principal pressures are equal, the third be- 
comes an axis of symmetry, either of greatest or least pressure, 
the pressures at right angles to this axis being all equal. 
When the three principal pressures are equal, the pressure is 
equal in every direction, and there results a stress having no 
determinate axis of direction, of which we have an example in 
simple hydrostatic pressure. 
The general type of a stress is not suitable as a representation 
of a magnetic force, because a line of magnetic force has direc- 
tion and intensity, but has no third quality indicating any dif- 
ference between the sides of the line, which would be analogous 
to that observed in the case of polarized light*. 
We must therefore represent the magnetic force at a point by 
a stress having a single axis of greatest or least pressure, and all 
the pressures at right angles to this axis equal. It may be 
objected that it is inconsistent to represent a line of force, which 
is essentially dipolar, by an axis of stress, which is necessarily 
isotropic ; but we know that every phenomenon of action and re- 
action is isotropic in its results, because the effects of the force 
on the bodies between which it acts are equal and opposite, 
while the nature and origin of the force may be dipolar, as in 
the attraction between a north and a south pole. 
Let us next consider the mechanical effect of a state of stress 
symmetrical about an axis. We may resolve it, in all cases, into 
a simple hydrostatic pressure, combined with a simple pressure 
or tension along the axis. When the axis js that of greatest 
pressure, the force along the axis will be a pressure. When the 
axis is that of least pressure, the force along the axis will be a 
tension. 
If we observe the lines of force between two magnets, as in- 
dicated by iron filings, we shall see that whenever the lines of 
force pass from one pole to another, there is attraction between 
those poles; and where the lines of force from the poles avoid 
each other and are dispersed into space, the poles repel each 
other, so that in both cases they are drawn in the direction of 
the resultant of the lines of force. 
It appears therefore that the stress in the axis of a line of 
magnetic force 1s a ¢ension, like that of a rope. 
If we calculate the lines of force in the neighbourhood of two 
gravitating bodies, we shall find them the same in direction as 
* See Faraday’s ‘ Researches,’ 3252. 
