122 



PEOF. A. E. H. LOVE ON THE TRANSMISSION OF 



TABLE II. 



The amplitude of H may now be taken to be 



2y/2.^ 



v/ '.(TZ sin 0) 



(51) 



and the value of this quantity for any particular value of 6 may be compared with the 

 amplitude of H , the magnetic force at the same point due to the originating doublet 

 alone. Now, when 6 is not nearly equal to 0, R is large of the same order as a, and 

 we have the approximate equation 



H = - Sm a 

 4a sin 3 



so that we may take the ratio of amplitudes to be 



sin 0) /f/g &_ g , 



cosJfe(Cfe-B), (52) 



m 



. . (53) 



The ratio of amplitudes is the quantity tabulated by MACDONALD( U ) in the case of 

 perfect conduction. It has been computed anew by the method described above for 

 the wave-length 5 km. and two values of the ratio k/m, viz., the value zero, answering 

 to the hypothesis of perfect conduction, and the value 0'001826 answering to the 

 conductivity of sea-water (a- = lO' 11 ). In the following table the first column gives 

 the value of 6 in degrees ; the second the corresponding arc-distance D in kilometres ; 

 the third headed A M , the amplitude ratio as computed by MACDONALD( U ) ; the fourth, 

 headed A a , the amplitude ratio computed by means of the formula (53) when k/m is 

 taken to be zero ; the fifth, headed A,, the amplitude ratio computed by means of the 



