414 Sir W. Thomson. On Electrostatic Screening [Apr. 9, 



same for a perforated surface fulfilling the condition of 23 as 

 for the medial constructed in continuous metal, we naturally ask 

 the question, what then is the difference between the two cases, 

 if any, besides the fact of the electricity being equally but very 

 unequably distributed over the outer and inner portions of tin- 

 complex surface in one case, and equably over the outside of the 

 smooth medial in the other ': There is a very important and interest- 

 ing difference. The electrostatic capacity of the perforated con- 

 ductor, S, is less, in the ratio of 1 to 1 + k, than that of the medial 

 constructed in continuous metal ; as we see by (23) and (26). 



26. As a sub-example, suppose S to be a spherical surface. 

 homogeneously perforated, it will fulfil the condition of 23 : and 

 its screening efficiency is the same as that of a grating of parall 

 bars (circular cross section of diameter 2r; distance from centre 

 centre a), we have, by (o) of 7, when vc/a is very small, 



Now, S being spherical, if R denotes its radius, we have ( 20) 



= 47rR,> .................... (28) 



Hence, by (26) and (27), 



a . a 1 . a 

 k = ~ log - = v? lo - 

 2rR 5 re N 6 2C 



where N denotes the number of bars in the equatorial belt of the 

 cage of 27 below. 



27. To illustrate a realisation of 26, let a spherical cage be made 

 up of a narrow equatorial belt of approximately straight parallel 

 bars of diameter 2 c, and distance from middle of one bar to middle of 

 next, a ; completed by polar caps (nearly hemispheres) of thin metal 

 perforated so as to have everywhere the same effective electric 

 screening efficiency l{2a log (a/2 ire)}. 



Suppose, for instance, the bars to be of " No. 18 gauge ' 

 (2c = 0'122 cm.) and a = 5 cm. We have 



log (a/2a-c) = log 13 = 2-57. 



Hence, for this case, and any other in which the ratio o/c is the same, 

 we have, by (27) and (29), 



ft. = 5-14 a ..................... (30), 



