ULTRA-SHORT-WAVE TRANSMISSION PHENOMENA 383 



the earth, we shall have the theoretical curve " A " of Fig. 8. Evi- 

 dently the actual refraction was something of this order. 



The second curve of Fig. 12, was taken spiraling down at Montauk 

 Point on October 3. The third curve was taken at a distance of 90 

 miles from the transmitter while spiraling and gliding down, headed 

 " out," on October 18. Unfortunately this was a day of low humidity 

 and the signals were lost before reaching the 1000-foot level and were 

 not picked up again on the return trip. The reduction in plane noise 

 while idling the engines, after the descent had begun, was pronounced, 

 and permitted following the signal almost to 1000 feet. 



Discussion 



The check with theory for the optical range, though gratifying, was 

 expected from our earlier work. At these low angles of incidence the 

 reflectivity does not vary rapidly with dielectric constant and con- 

 ductivity changes so that the values assumed by us are adequate. 

 The results for the range beyond grazing incidence are rather unex- 

 pected. Diffraction was looked for, and anticipated, but the results 

 themselves seem most readily explicable by a combination of diffraction 

 and refraction, the latter variable with time, and at times predominant. 

 Apparatus variations are ruled out; no effect of ocean roughness has 

 been discernible, and calculations show that the height of the tide is 

 not the explanation. There remain changes in the constants of the 

 air, or in other words, changes in air refraction to consider. Not 

 enough data are available to predict correctly an air refraction effect, 

 but that this is the most plausible explanation is shown by the fol- 

 lowing. 



Because of the change in air density with height, the effect of air 

 refraction is to bend the radio ray into a curved path. This bending 

 is proportional to the gradient of the dielectric constant of the atmos- 

 phere, which in turn is proportional to the sum of the gradients of the 

 dry air and water vapor constituting the atmosphere. The dielectric 

 constant of a gas can be written as, 



€ - 1 = k|- 



In the table below some calculated values of " K " are given. They 

 indicate that water vapor is some 18 times as effective as air, as a 

 refractive medium. They are for wave-lengths greater than 100 

 meters; no measurements at about 5 meters wave-length have been 

 found, so far, in the scientific literature. 



