1891.] by Gratings, fyc.. of Conducting Material. 417 



* - (42), 



or, according to (27), and (29), 





X , or X (43). 



3a a 3 , a 



This result is also applicable to a hemispherical screen of radius R, 

 simply placed on the ground. For the particular proportions of 

 27, it makes the force under the hemispherical cage of the un- 

 disturbed force outside. A cage of ordinary gardener's (anti-rabbit) 

 hexagonal wire-net (of 5^ cm. from parallel to parallel) cannot be 

 very different from this. If, instead of the radius being 50 cm. it be 

 200, bat the cage still of the same net, the force inside would be only 



Iper cent, of the undisturbed force outside. 



32. In every case the force at any distance from the perforated 

 surface, on either side of it, more than the diameter of a perforation, 

 is, as is easily proved by Fourier's methods, very nearly the same as 

 if the electricity were spread equably over the medial surface, with 

 the same quantity per unit area of the medial as the grating has in 

 each part of it. Hence, in the case of 31, the force is uniform 

 throughout the interior of the cage, except within distances from the 

 net of two or three times the aperture. Hence a second screen, 

 similar but slightly smaller, placed inside the first will reduce the 

 force farther in the same ratio ; so that, if eX denote the force inside 

 the single screen, the force inside the inner screen when there are 

 two will be e 2 X, provided the distance between the two is nowhere less 

 than the diameter of the perforation. Thus, with screens such as 

 those in the last particular case of 31, the force inside the inner 

 screen would be only 9/10,000 of the undisturbed force far enough 

 outside the outer. The two screens, if placed close together, so as 

 to narrow the apertures as much as possible, would have little more 

 than double the screening efficiency of either singly, as we may judge 

 from (27) of 26, and from (21) of 14. The principle that, to 

 duplicate a screen with best advantage, the two screens should be 

 placed, not in one surface but in two, with not less distance between 

 them than the diameter of their apertures, is not only theoretically 

 interesting, but is of great practical importance in the screening of 



Jctrometers against disturbing electric force. 

 33. Questions analogous to those of 26 32, but for circular 

 cylindric (mouse-mill) cages of equidistant parallel bars, instead of 

 the spherical or hemispherical cage which we have been considering, 

 readily answered by the simpler work corresponding to that of 



