518 JAMES CLEEK MAXWELL. 



dicular to the direction of the force, is proportional to the 

 magnitude of the force in the neighbourhood, and that the 

 number of lines passing through the unit area of any other 

 surface is proportional to the component of the force at right 

 angles to that surface. Maxwell therefore imagined the 

 positively electrified surfaces from which the lines started to 

 be divided into areas, each containing one unit of electricity, 

 and lines of force to be drawn through every point in each 

 bounding line. These lines therefore divide the whole of 

 space into " unit tubes," whose boundaries are lines of force, 

 and Maxwell showed that, in virtue of " the law of inverse 

 squares," the force at any point in any direction is inversely 

 proportional to the area of the section of the unit tube of 

 force made by a plane perpendicular to that direction. 

 Maxwell further showed that on the negatively electrified 

 surface upon which these tubes terminate, each tube will 

 enclose one, unit of negative electricity, and consequently, if 

 a metallic surface be introduced so as to cut the lines of 

 force, the surface being placed at right angles to the tube, a 

 unit of negative electricity will be induced on each portion 

 of the surface contained within the trace of a tube of force ; 

 and hence, in any isotropic medium, these unit tubes of force 

 are also unit tubes of induction. If, therefore, a system of 

 tubes of force be drawn in connection with any electrified 

 system, and in accordance with this plan, the whole of the 

 space in which the force acts will be divided into tubes each 

 originating from a unit of positive electricity and terminating 

 upon a unit of negative electricity, while the direction of the 

 force at any point will be indicated by that of the tube, and 

 the magnitude of the force will be inversely proportional to 

 the area of the cross section of the tube. Now, if the law 

 of force had been any other than that of the inverse square, 

 and tubes had been drawn starting from an electrified surface 

 as above, and such that the area of any section of a tube is 

 inversely proportional to the force across the section, these 

 tubes would either leave spaces between them as they recede 

 from the surface, or would intersect one another ; so that it 

 is only for the law of inverse squares that the system of 



