212 Mr. K. H. M. Bosanquet on 



surface of the sphere in all directions. This is the case close 

 to the surface; and by far the greater portion of the resistance 

 of the divergence arises close to the surface. It is, then, easy 

 to show that the resistance of the divergence from each hemi- 

 sphere is equal to that of a cylindrical air-space having the 

 equatorial section of the sphere for base, and height = half the 

 radius. In fact, if s = 27rr 2 , 



/y/n 



resistance of hemispherical shell = — > 



total resistance = "* = * [-1V- 1, 



a 2irr 2 2ttL r] a 2ira 



a 

 2 



~~ it a 1 ' 



If the sphere be of infinite conductivity, the total resis- 

 tance is twice this, i. e. a cylinder of altitude a. 



Remove the sphere. Then the resistance is that of the 

 cylinder, with divergence from the flat ends. If we take 

 these divergences each to have resistance *6 a of the cylinder, 

 as we know to be the case approximately in the analogous 

 case of the divergence of sound from the end of a pipe*, we 

 have for the whole resistance in this case that due to cylinder 

 + 2 ends, measured by a(2 + 2 x *6) = 3*2a. Comparing 

 this with the resistance of the sphere, w r hich w r as measured 

 by a, we have 3*2 for the permeability of the sphere, which 

 agrees very fairly with what went before. 



There remains the important case of a disk. According to 

 our view the disk will have finite air-resistances around it, 

 and when its thickness becomes small the air-resistances will 

 not be sensibly altered by its removal. The conductivity of 

 the circuit through a thin disk is therefore unity. Accord- 

 ing to the ordinary theory (Maxwell, vol. ii. p. 65), the mag- 

 netization of a disk for which /c=oc is l/(47r). Here we meet 

 again the same difficulty as in the case of the sphere : if we 

 use the ordinary formula //,= 1 +47T&, and assume that the 

 magnetizing force flows through the disk as well as the lines 

 of force that result from the magnetization, then fx — 2. But 

 from our point of view the force is a magnetomotive force ; 

 the induction in the substance takes the place of that in 

 space, and is not additional to it, and fi=l 9 or the state of 

 things is unaffected by the disk. 



Permanent Magnets. 

 The following quotations appear to embody the facts as 

 they are supposed to be : — 



* See Lord Rayleigh on Sound, ii. p. 169. 



