L89L] 



by Gratings^ fyc., of Conducting Material. 



411 



)pposite directions, leads to a complete theory of electrostatic screen- 

 ig by a triangular lattice of metallic wire or ribbon. The funda- 

 lental potential formula for this system obtained by summation of 

 tpressions, each given by an application of (4) to one of the three 

 )ws, is 



= log. 



2 COS mg-f- 



2 COS nr-\- e'"')^ 

 V ---- (19); 



rhere o, 6, c denote the intervals between the successive lines of the 



iree systems ; -aro, pb, <rc, the quantities of electricity per unit 



length of bar in the three systems ; p, q, r, z, special coordinates of the 



)int for which (19) expresses the potential, viz., z, its distance from 



le plane of the primitive bars, and p, g, r its distances from three 



jlanes drawn perpendicular to this plane through a bar of each of 



the three systems; D the value of +z for planes on the two sides of 



le net for which the potential is zero ; and, lastly, 



I = 27r/a,.?, = 25T/6, n = 2w/c 



(20). 



Tor the present, however, we may confine ourselves to the case of 

 two rows of primitive lines dividing a plane into squares and 

 sharged, both rows, with equal quantities, %pa, of electricity per unit 

 ength. The potential formula, a particular case of (19), is 



+2mD] (21). 



3 (e"" 2 COS ntx -j- e""") (e** 2 COS my + e 



15. The consideration of the equi potentials of this surface is very 

 iteresting. The equipoteatial lines in the plane of the primitive 

 are given by the equation 



\ 



J a 



(22). 



16. Considerations quite analogous to those of 6, 7, 8, and 

 iin the other considerations analogous to those of 9 13, are, 



fter the full explanations there given, easily completed so as to 

 formulate a full theory of electrostatic capacity and electrostatic 

 sening for square nets of wire exposed to electric action giving 

 iniform fields of force at distances on each or on one side of the 

 jlane of the net considerable in comparison with a, the side of each 

 luare. 



17. In what follows we shall for brevity call any thin sheet, whether 

 plane or not plane, which answers to the description contained in the 

 title of this paper, a perforated sheet or a perforated surface ; under- 

 standing that its radii of curvature are everywhere large in com- 



