ON PHYSICAL LINES OF FORCE. 453 



The mechanical conditions of a medium under magnetic influence have been 

 variously conceived of, as currents, undulations, or states of displacement or 

 strain, or of pressure or stress. 



Currents, issuing from the north pole and entering the south pole of a 

 magnet, or circulating round an electric current, have the advantage of repre- 

 senting correctly the geometrical arrangement of the lines of force, if we could 

 account on mechanical principles for the phenomena of attraction, or for the 

 currents themselves, or explain their continued existence 



Undulations issuing from a centre would, according to the calculations of 

 Professor Challis, produce an effect similar to attraction in the direction of the 

 centre ; but admitting this to be true, we know that two /series of undulations 

 traversing the same space do not combine into one resultant as two attractions 

 do, but produce an effect depending on relations of phase as well as intensity, 

 and if allowed to proceed, they diverge from each other without any mutual 

 action. In fact the mathematical laws of attractions are not analogous in any 

 respect to those of undulations, while they have remarkable analogies with those 

 of currents, of the conduction of heat and electricity, and of elastic bodies. 



In the Cambridge and Dublin Mathematical Journal for January 1847, 

 Professor William Thomson has given a " Mechanical Representation of Electric, 

 Magnetic, and Galvanic Forces," by means of the displacements of the particles of 

 an elastic solid in a state of strain. In this representation we must make the 

 angular displacement at every point of the solid proportional to the magnetic 

 force at the corresponding point of the magnetic field, the direction of the axis 

 of rotation of the displacement corresponding to the direction of the magnetic 

 force. The absolute displacement of any particle will then correspond in magni- 

 tude and direction to that which I have identified with the electrotonic state ; 

 and the relative displacement of any particle, considered with reference to the 

 particle in its immediate neighbourhood, will correspond in magnitude and direc- 

 tion to the quantity of electric current passing through the corresponding point 

 of the magneto-electric field. The author of this method of representation does 

 not attempt to explain the origin of the observed forces by the effects due to 

 these strains in the elastic solid, but makes use of the mathematical analogies 

 of the two problems to assist the imagination in the study of both. 



We come now to consider the magnetic influence as existing in the form of 

 some kind of pressure or tension, or, more generally, of stress in the medium. 



Stress is action and reaction between the consecutive parts of a body, and 



