18 



891.] by Gratings, fyc., of Conducting Material. 415 



IThus, if a = 5 cm., and R = 50 cm., Tc = 0'0409 = -^ ; and ( 25) 

 e electrostatic capacity of the spherical cage ff of that of a simply 

 continuous spherical surface of the same magnitude. 



128. Let now an electrified metal globe, or globe of insulating 

 aterial uniformly electrified, G, be insulated concentrically within 

 S. It may be of any magnitude, large or small, provided only that 

 the interval between the two surfaces be at least two or three times 

 the diameter of the largest of the perforations of S. Let S be con- 

 nected with the earth, and let Q denote the quantity of (positive) 

 electricity with which G is electrified, and Q' the quantity of the 

 opposite electricity which it induces on S. The potential in the 

 ictal of S due to Q' is, by (23), 



iis, added to Q/R, the potential due to G, must be zero, and there- 

 fore 





(33) ' 



,by(26), Q = Q'(l+4) (34). 



Hence, in the particular case of 27 (31 ), 



Q = Q'(l 



l+ 0-409 .............. (35); 



and when R = 10a, we find Q Q' = ^V Q> an< ^ conclude that the 

 effect of S, earthed, with G electrified and insulated within it, is just 

 per cent, of the effect of G unscreened. 



29. If S is connected with the earth, and supported at a height 

 ve the earth equal to at least six or eight times its diameter, the 

 antity of electricity (positive in fine weather) induced on it will 

 l/(l + k) of that which would be induced on a simply con- 

 nous metal globe of the same size. Hence the potential at any 

 int of the air within S at not less distance inwards than 2 a will be 

 :/(l + k) of the undisturbed atmospheric potential at the same 

 height above the ground, or 5 per cent, in our particular case. This 

 quite in accordance with the imperfectness of the screening effect 

 ainst atmospheric electricity found by Roiti* within earthed wire 

 iges, supported at a considerable height above the ground, by a 

 cket attached to the top of a wall of a building in Florence, 

 ted by a water-dropper with its nozzle inside the cage con- 



* " Osservazioni Continue della Elettricita Atmosferica " (' Pubblicazioni del 

 Istituto di Studi Superior! in Firenze '), Florence, 1884. 



