374 t)r. Balth. van der Pol on the Propagation of 



these regular interference phenomena will be found in actual 

 practice of Wireless Telegraphy cannot reasonably be ex- 

 pected in view of the irregular distribution of land and sea 

 over the surface of the earth. Moreover, as will be pointed 

 out below, the atmosphere has such an important influence 

 on the amplitude of the waves that it is hardly likely that 

 these regular diffraction zones will actually present them- 

 selves. With regard to the important increase in distance 

 over which signals nowadays are received, it is, however, 

 of some interest to consider to what facts pure diffraction 

 would lead. 



It is now possible to compare these results with the 

 formulae obtained by Nicholson and Macdonald. Nicholson, 

 who determined the magnetic force and thereof only the first 

 term of the series, arrives at a formula which in the present 

 notation can be written 



where /3' = 0-696. 



The formula obtained above for the whole region for 

 which 6 is not near or it was 



1*1-1^1-^."^^, • • (7,8) 

 where & = 07000. 



The difference between Nicholson's fa and Macdonald's fa 

 is very slight indeed, and is due only to a closer approxi- 

 mation by Macdonald to the first root of J$(fy- J_|(?) =0. 



2 



The unimportant factor —^ in (13) does not occur in 

 (7, 8). \/3 



As tlie complete solution is now at hand, it is an easy 

 matter to find the source of the discrepancy between the 



factor \/sin 6 occurring in Nicholson's formula and 



\/sin 6 

 in (7, 8). This discrepancy is found to be due to page 531 



of vol. xix. of the Phil. Mag., where in formula (47) j- 



is written for -=-, an oversight in the very complicated 



analysis by Nicholson, where the factor — sin #, thus intro- 

 duced, has been retained throughout the further analysis. 

 With this correction therefore the above formulse (7, 8) are 

 practically in agreement with Nicholson's result. 



