Page:Proceedings of the Royal Society of London Vol 69.djvu/448

430 The complex inequality which corresponds to the separation of the positive and negative inequalities is one displacement, not two. This fact admits of no question, and might have been recognised long ago had it not been for the general assumption that positive electricity repels positive electricity, the fact being that the apparent repulsion of the positive electricities is the result of their respective efforts to approach their respective negative inequalities. By the assumption it became apparently possible to express the potential v and the elec- tricity q as rational quantities, while, as it now appears, the potential v and the electricity q are respectively

-(-e 2 )*.- 1 and (-e 2 )*, r

which are both irrational. Their product being the rational quantity

which differentiated with respect to the distance is
 * 1) /r t

-e 2 /'/- 2 = K. And the mechanical explanation of these is

and for the effort to revert we have

Then for the electrostatic units we have, since r 1, and E, = 1,

and from the known value of p, the number of grains displaced through unit distance necessary to cause the unit effort is

1-61 5 x 10 45 ,

andr = 6'493 x 10~ 3, from which we have the ratio of the effort to reinstate the normal piling, to the effort of gravitation, from the same number of grains absent in each inequality as are displaced in the complex inequality, the distances being the same

1-2 xlO 15 ;

so that the effort of attraction between two inequalities, the grains absent about each of which are the same as the grains displaced in