454 OX PHYSICAL LINES OF FORCE. 



consists in general of pressures or tensions different in different directions at 

 th" same point of the medium. 



The necessary relations among these forces have been investigated by mathe- 

 maticians ; and it has been shewn 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 becomes 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 mag- 

 netic force, because a line of magnetic force has direction and intensity, but 

 has no third quality indicating any difference 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 reaction 

 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 is 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 indicated by iron 

 tilings, 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 



* See Faraday's Researches, 3252. 



