172 Bending of Electric Waves round a Large Sphere. 

 and in others, by c. Thus we may write near m=v, 



and accordingly, 



a v = — z*K m (z) /^-..^K m ^) 



bv the use of the differential equation satisfied by the 

 function K. This result is very elegant. To the same order, 

 we may write 



a„ = *»/(*»-»•) = **/*fi .... (98) 



on reduction, and therefore 



y = k-{k< ( ) -i(2>7T sin e)\ 2^8-vi«- '^+^. 



But in non-oscillating terms, we may write v=hi to the 

 order already retained, so that finally 



ry=P(^)-f(27rsin^)i2 v ^-^--W^ - |M+ H (99) 



and only the first term of the summation is really important. 

 For an undisturbed oscillator, the corresponding- formula 

 becomes 



7u = _i/.2(foi)-i cot i6e~ 2ika sin hd+b*, . (100) 



and the ratio of the amplitudes in the two cases is therefore 



(87rsin^(^)^taiU(9.y3-V--^ r/ ^. . . (101) 



and the exponential factor is of the same form as that derived 

 otherwise by M. Poincare, who does not give the other 

 factors nor the value of /3. The impossibility of explaining 

 the experimental results by means of diffraction is now 

 evident. In the next section, a determination of {3 is made, 

 and an examination of the formula numerically is given. 

 Succeeding sections deal with the remaining problems 

 hitherto postponed, viz., the effect at any point in the 

 geometrical shadow, the effect in the neighbourhood of the 

 oscillator, and the determination of a second approximation 

 for points in the region of brightness. 



