366 Dr. Balth. van der Pol on the Propagation of 



was readily obtained * (1903), but the summation of the 

 series presents difficulties, and this summation is to be con- 

 sidered the chief cause of the discrepancy of the final formulae 

 of different investigators. 



This led Nicholson in 1910 to consider the problem under 

 consideration as one in the whole field of mathematical 

 analysis about which most divergent views were held f . 



Up to a short time ago a definite agreement on the 

 numerical side of the problem could not be said to be arrived 

 at, and consequently very divergent opinions were expressed 

 on the possibility of explaining the observed values of wave- 

 amplitude at various orientations from a transmitting station 

 by way of pure diffraction only. 



But recently Watson J has effected a new summation of 

 the said series, and, as will be shown below, agreement can 

 now be obtained with the other solutions within the ranges 

 of their validity. 



When the oscillating dipol is placed outside the sphere at 

 a distance b from the centre with its axis pointing to the 

 centre, a Hertzian potential function IT can be defined such 

 that, using the ordinary notations, the components of the 

 electric and magnetic forces outside the sphere expressed in 

 spherical coordinates are given by 



Er -".*e>/»\ tl ~'* ) ^/' 



E^ = H r =H =O 5 



where 6 is the angular distance and &> is the number of 

 oscillations in 2tt seconds. 



11 has then to satisfy the wave equation 



(V 2 + £ 2 )II = 0, 



ft) 27T 



k being equal to - = — • 



c 



* Macdonald, II. M., Proc. Rov. Soc. vol. lxxi. p. 251 (1903). 

 1 Jahrb. der Drahtl. Telegr. u.'Teleph. iv. p. 20 (1910). 

 t Proc. Roy. Soc. (ser. A) vol. xcv. p. 83 (1918). 



