by Gratings, $-c., of Conducting Material. 413 



greater it is the less is the screening efficiency. We shall therefore 

 call ft, the electric permeability, and fir 1 the electric screening efficiency 

 of the perforated sheet. The sheet is homogeneous as to permeability 

 or screening efficiency if ft has the same value for all parts of it, but we 

 .eed not assume this to be the case ; on the contrary, we shall suppose 

 to be any known function of (a;, y, z). In 5 16 we have the 

 xplanations necessary for determining p in the various cases of 

 gratings and nets there described. For similarly perforated surfaces, 

 the values of fi are as the linear dimensions of a perforation or of the 

 rs or bosses of the structures. 

 22. The equation of electric equilibrium is 



0+/*/> = K (a constant) 



rhen S, being insulated and electrified, is not under the influence 

 any other electrified matter. 

 It is 



K-V .................. (25), 



when S is under the influence of any given electrified bodies pro- 



iucing a given potential, Y, at (x, y, z). 



23. As a first example, going back to (24), let fi be such that 

 lall be constant. This makes, if we denote by A; a constant, 



(26), 



being a constant), which means that the screening efficiency is, in 

 different places of S, inversely proportional to -the electric density at 

 ilarly situated places of a continuous electrified conductor of the 

 .me shape as S. Let, for instance, S be an ellipsoid ; then, if the 

 sizes of the perforations be inversely proportional to the perpendicular 

 from the centre to the tangent plane, (26) is satisfied. Generally, to 

 fulfil this condition, the net must be finer in the more convex and 

 more projecting parts, and coarser in the flatter and less projecting 

 parts. 



24. If any perforated conductor or cage, S, fulfilling the condition 

 of 23, be electrified and insulated away from the disturbing influence 

 of other conductors, or electrified bodies, the charge distributes itself 

 so as to have in every part the same quantity per unit area of the 

 medial, as a smooth continuous metallic surface agreeing with the 

 medial and electrified with the same total quantity. When the medial 

 is a closed surface, the electricity on the perforated surface does not 



nfine itself to the parts of it outside the medial : on the contrary, 

 en the apertures are very wide in compaiison with diameters of 

 cage-bars, bosses, &c., the electricity distributes itself almost equally 

 on the parts of the complex surface inside and outside the medial. 



25. Seeing that the electric density (as defined in 17) is the 



II 



