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

 the final expression for IT(a, 6) is 



^'^-Ja' ^ >--- "■• • • • (3) 



which is the form in which the solution is left by Watson. 

 In order to obtain numerical values for E r and H^ at the 

 surface of the sphere (Ee being zero there) an accurate 

 knowledge of the values of the v's, and therefore of the £'s, 

 is required. Now Macdonald has already calculated the first 

 three fts, viz. the first three roots of J_ 2 (?) — J*(?) = 0, and 



'S 3 



he finds 



ft = 0-6854, 



ft = 3-90, 



ft = 7*05. 



Of these three roots the first one is of dominating import- 

 ance as far as a numerical calculation is concerned. We 

 therefore determined ft independently and obtained 0'6855, 

 in close agreement with the value given above. From these 

 values of f the first three p's follow at once : 



Pl = 0-8083, 

 p 2 = 2'577, 

 p 3 = 3-83 ; 



hen 



ce 



Vl = x + 0-8083 .r*(i-tV3), 

 v 2 = x + 2-577 a% r »V3), 

 v 3 = x + 3-83 **(£-* •S). 



In view of x being a very large quantity, viz. the ratio of 

 the earth's circumference to the wave-length of the sending 

 antenna, the second real part in the vs of low order (these 

 only being of importance; can be neglected in comparison 

 with the rirst, so that these quantities can be written in a 

 more simple way : 



V\ = x — ft tar* 

 v. 2 = x - ft i X*, 

 vz = x - ftia?* 

 where ft = 0'7000, 



ft = 2-232, 



ft = 3-32. 



