Experiments and Inductions. 195 



and that increases in a high inverse ratio of their mutual dis- 

 tance, and produces a proportionally intense longitudinal con- 

 tractile static tension. The mutual distance varies at every point 

 of a line, and responsively so does the transverse repulsive ten- 

 sion and its dependent longitudinal contractile tension. 



Let the disk c (fig. 25) have a magnified representation in 

 fig. 28, and let it be composed of a double film of metal c Y c 2 , the 

 two films being perfectly close together, yet not cohering. We 

 may further imagine these double films to extend all round to 

 form concentric spherical surfaces as before (52). It will be 

 remarked that we have negative or V roots developed on c v 

 and positive or A roots on c%, the lateral repulsive tension 

 acting in the space between these roots on both sides of the 

 duplex film c; but on the side c x it produces a longitudinal 

 strain in one direction, i. .e. towards a; and on the side c 2 it pro- 

 duces an equal longitudinal strain in the reverse direction, i. e. 

 towards d or b. 



Let a, x } b, z (fig. 29) represent four rods jointed at their ex- 

 tremities ; press a and b towards c, this will press x and z from 

 c in opposite directions. A rough notion may thus be obtained 

 of the lateral and longitudinal strain that exists on every part of 

 an electric line — the lateral convergent being the ab pressure, 

 and the longitudinal divellent being the x z. 



The lateral force affects the position of the lines, and thence 

 of their polarized roots on conducting surfaces ; but it is the ' 

 longitudinal strain at the polarized roots that immediately pro- 

 duces the phenomena of motion and discharge. The motor phe- 

 nomena resulting from the strain at the roots sometimes assume 

 the appearance of attraction and sometimes of repulsion in adja- 

 cent bodies, as, from the lateral action of the lines, the roots 

 happen to be distributed more on their near or their opposite 

 sides. 



55. If we examine closer this quantitative relation between the 

 lateral and longitudinal forces, we shall find a certain simplicity 

 that is worth keeping in remembrance. 



Suppose two planes at the infinitesimal distance dr to cut the 

 lines at right angles. The lines intersect these planes in points, 

 each point, as p, fig. 30, being the centre of a certain extent of 

 surface which may be denoted by a, and dr may be viewed as the 

 axis of a cylinder whose area is ocdr. This area is small when 

 the lines are closely packed, and vice versa. What relation does 

 the static intensity of the longitudinal force at p bear to the area 

 of this infinitesimal cylinder ? 



The force, as it has been proved from Harris (51), is as the 

 square of the density of electricity, or as the square of the num- 

 ber of points in a square inch. Thus a being the area of one 



