Electric Waves round a Large Sphere* 



65 



Application to wireless telegraphy. 



As a typical case, suitable for the tabulation of the 

 formula (101), we may take that of electric waves and the 

 earth, the height of the antennse being about 260 feet, and 

 the corresponding wave-length therefore a quarter of a mile. 

 In this case, ka is 1*01. It) 5 . 



When the orientation of the receiver from the oscillator is 

 not greater than about ten degrees, or seven hundred miles, 

 a convenient practical formula for the ratio of the diffracted 

 amplitude to the amplitude corresponding to an undisturbed 

 oscillator is found to be 



•058 0*0574)0, (108) 



where 6 is in degrees. The value of ka corresponding to 

 average practice has been inserted. A change of the wave- 

 length, say from a quarter to a fifth of a mile, does not 

 change the order of magnitude, or in general, by more than 

 unity, the most significant figure of this formula. The 

 variation of this function is exhibited in the following table. 



Table I. 



e. 



Amp. ratio. 



Terrestrial 

 miles. 



0, 



Amp. ratio. 



Terrestrial 



miles. 



i° 



•033 



69 



6° 



•080 



414 



2° 



•054 



138 



7° 



•022 



483 



3° 



•057 



207 



8° 



•015 



552 



4° 



•050 



276 



9° 



•on 



621 



5° 



•040 



345 



10° 



•007 



690 



Beyond 10°, the amplitude ratio in the same case may be 

 computed from the formula 



50-2 tan \0 ^/linTO (-574)0, . . . (109) 



where 6 is again measured in degrees. 



This is tabulated below for every degree from 0° to 30°, 

 and for every five degrees from 30° to 90°. The values 

 given by the two formulas for 0=10° are in agreement, and 

 between 10° and 30°, an interpolation method may be used 

 for intermediate cases. The convenient notation -0" m has 

 been used for "mlO - ". 



Phil. Mag. S. 6. Vol. 21. No. 121. Jan. 1911. F 



