ELECTRIC WAVES OVER THE SURFACE OF THE EARTH. 



123 



same formula when k/m is taken to be 0'001826. There is some uncertainty about 

 the third figure in the 6 line in each of the last three columns. 



TABLE III. 



Except as regards the uncertain last figures in the G line there is complete 

 agreement between the third and fourth columns of the table ; in other words, my 

 results confirm those of MACDONALD( U ) for the case of perfect conduction. The 

 methods of summation employed by him are so different from those which I have 

 adopted that the results may be accepted with great confidence. The correction for 

 resistance seems to be rather larger than MACDONALD anticipated, but nevertheless 

 not large enough to have the importance expected by SOMMERFKLD, although his 

 expectation that it would be increased by curvature is verified. 



17. Since MACDONALD'S result for the problem of the perfect conductor is confirmed, 

 it appears to be unnecessary to enter into a detailed comparison with the results 

 obtained by PoracARE( 8 ) and NICHOLSON( U ), although it may be stated that the 

 objection raised by MACDONALD( n ) to a step in their analysis seems to the present 

 writer to be well founded. But it is appropriate here to notice a solution of the 

 problem put forward by MARcn( 12 ) and E,YBCZYNSKi( 13 ). MARCH, apparently acting 

 upon a suggestion of SOMMERFELD'S (see " Report " ( 17 )), set out to obtain a solution 

 of the problem in terms of definite integrals, analogous to that obtained by 

 SoMMERFELD( 6 ) for the problem of the plane boundary. He confined his analysis to 

 the case of a perfect conductor ; and his final result was that the amplitude of the 

 waves, received at an angular distance 9 from the originating doublet, should be very 

 approximately proportional to (0 sin 6)~\ An oversight in his work was pointed out 

 by POINCARE,* and its correction was undertaken by E,YBCZYNSKi( 13 ) who also 

 obtained a result differing from that of MACDONALD( U ) ; but MACDONALD( n ) has 



* H. PoiNCARri, 'Paris C.R.,' vol. 154 (1912), p. 795. 

 B 2 



