1891.] 



by Gratings, $c., of Conducting Material. 



409 



jquipotentials around the infinitely thin bars, that indicated by the 

 shading, for example which I have added to Maxwell's diagram, let 

 c be the distance from the infinitely thin primary bar within it, at 

 which it is cut by the plane of the primary bars. By putting, in the 

 expression for 0(z, x), z = 0, and x = c, we find 



0(0, c) = pa log 



4 sin'' 

 a 



(11) 



the potential at the surface of each of these chosen ovals. Con- 

 struct now each of these ovals in metal, and let the supposed uniform 

 force, 27T/3, be produced by uniform electrification of density />, on a 

 ictal plane, B, at any great distance, 6, on the positive side of the 

 iting. We thus construct a grating of thick bars of oval-shaped 

 3ross section which, when electrified with the same quantity of elec- 

 ricity as that which we gave initially to the infinitely thin bars, and 

 subjected to the influence of the equal quantity of negative electricity 

 :>n B, has 0(z, x) for potential through external space from B (z = fe), 

 infinite distance on the other side of the grating (z = oo), and 

 for potential through all the portions of space within the surfaces 

 the grate-bars the constant value expressed by (11). In this 

 system the potential, for positive values of z great in comparison with 

 i, is, by (4) with mz instead of 



= 4irpz 



(12). 



le difference of potentials between B and the grating is, by (6) 

 ind (5), 



-2 T' 



4sur - 



(13). 



[ence the electrostatic capacity of che mutually insulated system, B, 

 and the grating of oval-shaped bars is equal to the capacity of a pair 

 of parallel planes, B and a plane at a distance beyond the plane of the 

 primitive infinitely thin bars equal to 



47T 



log 



. . , 7TC 



4 sin 2 



(14). 



11. If in (4) we put nz in place of -\-rnD, we have the potential of 

 system in which besides the electricity of the primary bars there is 

 listant electricity such as all in all to give at great enough distances 

 )n the two sides of the primitive bars uniform fields of z-force re- 

 spectively equal to 



