408 



Sir W. Thomson. On Electrostatic Screening [Apr. 



capacity of the conductor I so constituted is equal to that of a plant 

 sheet of thickness 



2alog[2*]/(2*r), or '44 a 



insulated midway between the two earth plates 8, B', at the 

 distance asunder as they had with I between them. 



8. By (4), (5), and (7), we have for the equation of the sui 

 constituting the two sides of I in this critical case, 



= 4 



Taking double the positive value of z which this gives when x = 

 we find 



Salog [(1+ ^/2*f\l(2ir) t or '562a 



as the maximum thickness of I. This is log (l + v / '2)/log2, or 1'S 

 times the amount shown in (8) for the thickness of the plane-side 

 plate of equal electrostatic capacity ; which is just such a relation as ii 

 expected before calculation ! 



9. If 0(z, a;) denote what V becomes when in place of mD we sut 

 stitute mz in (4), we have the potential due to a uniform electric 

 force pam, or 2-a-p, added to the z-component, of the force due to tl 

 grating with its given charge of pa quantity per unit length of each 

 bar; and it is the eqnipotentials and lines of force of this system that 

 are represented in Maxwell's diagram of Plate XIII, reproduced her 



In it the resultant force for infinitely large positive values of z is 

 parallel to OZ, and of constant value 47iy> ; and it is zero for infinitely 

 large negative values of z. The approximation to these values is very 

 close, at only so moderate a distance as a on either side of the 

 grating. 



10. Choosing, in the system of 6, any one of the multiple-oval 



