Electromagnetic Waves round the Earth. 379 



When the value given above is accepted as the limit of 

 measurable energy, an estimate o£ the oscillating electric field 

 near the receiver antenna can be made on the basis of a total 

 antenna resistance of about 25 ohms and an effective receiving 

 antenna height oc 2 h 2 of 146 metres, which are the figures 

 given for the receiving system at Darien (Canal zone), where 

 a part of the measurements were carried out. 



From (14 a) it is seen that the least amplitude of alter- 

 nating potential gradient measurable in this way is of the 

 order of 10~ 11 volt per centimetre, being about 10~ u of the 

 normal static atmospheric potential gradient, and it is there- 

 fore not surprising that proportionally small variations in the 

 latter field occasionally prevent or disturb the measurements 

 of the minute alternating field superposed on it. 



When Austin's observations are accepted as giving the 

 true attenuation of wave-amplitude with distance, it is evident 

 that the pure diffraction theory based on the Maxwellian 

 equations and the assumption of a perfectly insulating- 

 atmosphere yield values for this attenuation which are in 

 flagrant contrast with the experimental data. 



We take as a single instance the measurement at Darien 

 of the waves sent out by the Nauen station. In this case 

 Austin gives 



I 1 = 150amp., X = 9'4 kilometres, a l h l — 120 metres, 

 a 2 A ? =146 metres, R 2 = 29 ohms, ^ = 9400 kilometres. 



This is the biggest distance up to the present over which 

 received antenna currents have been measured. The 

 " audibility " was in this case 200, corresponding to a 

 received antenna current I 2 = 1*3 . 10 -6 amp. ; while the 

 theoretical diffraction formula (15) derived above would 

 yield I 2 = 0-6 10- 12 amp. 



In this case therefore the actual value of the wave- 

 amplitude according to Austin's measurements is about two 

 million times bigger than the value yielded by the pure 

 diffraction theory. Even if the measured quantities are 

 affected by errors of many hundred per cent., agreement be- 

 tween theory and experiment cannot be obtained. As several 

 independent theoretical investigations have undoubtedly 

 proved that the finite conductivity of the earth's crust cannot 

 increase the wave-amplitude to such an enormous extent, and 

 as the conductivity of sea-water has the same value for the 

 frequencies used in wireless telegraphy as for steady cur- 

 rents*, the cause of this discrepancy has to be found higher 

 up — in the atmosphere. The.-e considerations therefore 

 * Phil. Mag-, vol. xxxvi. p. 88 (1918). 



