ELECTRIC WAVES OVER THE SURFACE OF THE EARTH. 



129 



than 29, it seemed to be worth while to see if agreement between MACDONALD'S 

 formula (54) and observation could be attained by supposing the amplitude of the 

 electromagnetic waves at great distances, and therefore the values of the received 

 antenna current, to be proportional to the audibility factor instead of its square root. 

 I therefore compared the formula in the first instance with HOGAN'S long-distance 

 observations. The result of the comparison is shown in figs. 3 and 4, in which the 

 abscissfe of the points marked with crosses represent distances, and the ordinates the 

 values of the audibility factor at those distances, as observed by HOGAN by daylight. 

 Everything in these diagrams, except the curved lines, is taken from HOGAN'S 

 diagrams ; and the curved lines are the graph of H/Hi as given by formula (54) for 

 wave-length 3 '8 km., the scale being adjusted so that the highest point of the curve 

 in fig. 3 answers to angular distance 9 (1000 km.). It will be seen that the graph 



5000 



4000 



3000 



2000 



-5 looo 



3 



\ 



60 

 50 

 40 

 30 



20 

 10 



\ 



75O 1250 I75O 22SO 



D/sbnce in Kilometres 



FIG 3 . 



2500 3000 35OO 400O 



Distance in Kilometres 

 FIG 4. 



fits the observations rather well. I made a similar comparison for HOGAN'S daylight 

 observations on the wave-length 2 km., and again found a good fit. Then I compared 

 the values of the square root of the right-hand member of formula (54) with the values 

 recorded in AUSTIN'S diagrams for wave-lengths 1 km., 1'5 km., and 375 km., and in 

 every case found that the daylight observations for distances exceeding 500 sea miles 

 were in good agreement with the formula thus modified. 



[Note added February 6, 1915. After the paper was read, Prof. C. H. LEES 

 kindly brought to my notice some more recent experiments of L. W. AUSTIN, which 

 are recorded, at present in abstract only, in the ' Journal of the Washington Academy 



Sciences,' of date December 4, 1914. In these experiments the wave-length used 

 km., and observations were taken at various distances ranging from 556 km. 

 to 3705,, km. The method of experiment appears to have been the same as in 



VOL. ccxv. A. s 



