r 



Bending of Electric Waves round a Large Sphere. 157 



We have thus for the plane capillary layer in the case 

 when the law of Cailletet and Mathias applies : 



p-pK + «(T K — T), 

 or : 



The average density of a plane capillary layer is a decreasing 

 linear function of the temperature. 





XIII. On the Bending of Electric Waves round a Large 

 Sphere: II. By J. W. Nicholson, M.A., B.Sc* 



Investigation of the transitional region. 



IN the section immediately preceding, the extent of the 

 region of transition between brightness and shadow, 

 when a radial oscillator is placed close to the surface of a 

 perfectly conducting sphere, was examined. The present 

 section is devoted to a discussion of the nature of this region. 

 On reference to an earlier section this region, being the 

 continuation on one side of that of brightness, will contain 

 a magnetic force which, on this side, may be derived like (44) 

 in the form 



yp = 2r u(l +e 2 ' x ») sin (m0-J») i**'***, (66) 



where 



u = im(2m sin R )l R )ir /7rk' 2 a i )*, 



provided that we neglect points in the immediate vicinity of 

 the oscilLitor, so that is not small, and the use of an 

 asymptotic formula for the zonal harmonic is legitimate. 

 A different type of solution is valid for such points, which 

 must be deferred for the present. 



Again, in the region of brightness, it was shown that the 

 above series could be expressed as the sum of four others of 

 the exponential type, such that two only could have a 

 vanishing derivate of an exponent. This property will con- 

 tinue to hold in the initial part of the transitional region. 

 Since x n is not of an order capable of causing oscillation in 

 an exponent involving it, the exponents of the four series 

 may be regarded as 0» — 0» r ±w*^, whose derivates when x 

 is not too nearly equal to unity are, with respect to m, or z x, 



sin" 1 a— sin -1 cx± 6. 



Only the lower sign of the ambiguity leads to a zero point 

 at the boundary of the region of brightness. Accordingly, 



* Communicated by the Author ; for Part I. see Phil. Mag. April 

 1910. 



