ELECTRIC WAVES OVER THE SURFACE OF THE EARTH. 127 



can be obtained by taking a = (0'0015)x~' /1 , and introducing suitable values for A, the 

 wave-length X and the distance D being measured in kilometres. Similar curves were 

 drawn by him on the diagrams representing all the series of his observations, and they 

 show that there is a fair agreement between the daylight observations and the formula. 

 HOGAN drew on his diagrams the graphs of expressions of the type (Ae~ aD /D) 3 , with 

 AUSTIN'S values for a in terms of wave-lengths and suitable values for A, and found 

 that the graphs fitted the daylight observations rather well. 



21. When AUSTIN'S formula is expressed in terms of angular distance, so as to 

 become comparable with those written down in 18 above, it takes the form 



a; 



This formula would clearly not show, in a narrow range such as that between 400 

 and 1000 sea miles, very much divergence from those given by RYBCZYNSKl( 13 ) and 

 ZENNECK ( 18 ) ; and both these writers claim that their formulae represent the results 

 of AUSTIN'S experiments better than his own. On the other hand, it would show even 

 in this range a well-marked divergence from MACDONALD'S formula, though not 

 perhaps sufficient to be conclusive. When the comparison is extended to the wider 

 range covered by HOGAN'S experiments, the divergence would appear to be decisive. 

 If the records of the observations could be accepted without criticism, it could be 

 stated that the law of decrease of amplitude of the electro-magnetic waves with 

 increasing distance from the sending station, as expressed by the formula (59), has 

 been tested and found adequate over a wide range of distances and wave-lengths ; 

 and further, since this formula cannot be reconciled even approximately with 

 .MACDONALD'S theory, it could be inferred, as in fact it has been, that diffraction cannot 

 account for the observed facts. 



22. I hesitate to draw this inference for two reasons. First, there is some doubt as 

 to what the observed facts really are. Second, a different interpretation of the 

 available records leads to precisely the opposite conclusion. 



As regards the observations, I wish to make it clear at the outset that I do not 

 undervalue the work of AUSTIN and HOGAN. The investigations which they 

 undertook were of such difficulty that to obtain results, so consistent as theirs, must 

 have required much patient labour and an uncommon degree of skill. Any criticism 

 that I venture to make is prompted solely by the desire to arrive at a more complete 

 comprehension of the matter. 



The method of observation by means of shunted telephone readings appears not to 

 admit of great accuracy. AUSTIN states that the errors of such readings on board 

 ship with good operators in good weather may amount to as much as 20 to 40 per 

 cent. In stormy weather they are increased. There is some obscurity as to the 

 meaning of the numbers and ordinates which represent in AUSTIN'S tables and 

 diagrams the values of the " received current." Many passages convey the impression 



