176 



DIELECTRIC CONSTANT. ABSORPTION AND SCATTERING 



changes in Q. Original difficulties arising from this 

 cause, which were encountered because of variation in 

 the a-c line voltage and the modulator voltage, have 

 been largely eliminated by the use of stabilizing trans- 

 formers and a magnetron load current stabilizing cir- 

 cuit. Furthermore, a method of taking data was de- 

 vised which only required the power output to be 

 maintained constant for a few minutes at a time. 

 The Q of the water vapor, Qy, is given by 



k = ''"' ' (72) 



wliere y is the attenuation in db per nautical mile. A 

 is in centimeters, and A" is a constant. In order to 

 obtain absolute values of the attenuation, it is necessary 

 to introduce into the system a known Q in terms of 

 which the other Q's may be evaluated. For this purpose, 

 the aperture, which acts as a perfect absorber, is used. 

 Lamb has derived a formula for the Q of an a23er- 

 ture, Qa, and this is 





XA 



SttF 



(73) 



where A is the area of the aperture and V is the volume 

 of the box. 



The Q of the whole ensemble may now be written 

 down. 



1 _ J- i_ _L 

 Q~ Qb'^ Qv'^ Qa' 



(74) 



where Qb takes account of all los.ses (including tlie 

 losses in oxygen) other than those in tlie vapor and 

 the aperture. Inserting values, and using I/tj as the 

 proportionality constant connecting the emf, <f^ and 

 Q, one then has 



For constant conditions of humidity, wavelength, and 

 magnetron power output, measurements are now made 

 of the emf f„. with A = 0, and emf £4, with A = A. 

 Using these measured values of emf, equation (75) 

 can be written in the form 



Co — Ca 



\A \Qb J 



F 



(76) 



The humidity is then changed and the measurement 

 repeated until enough fioints have Ijeen obtained to 

 provide a curve of i^ as a function of p, the water vapor 

 density, for constant wavelength. 



Since, ))resuniably, y is the only quantity in this 

 equation which is a function of p, and since y = for 

 p = 0, the plot of F against p extrapolated to zero 

 humidity will yield a value of Qb. Consequently, y is 

 determined as a function of p. 



Examples of the y versus p curves so obtained are 

 shown in Figure 18 for the wavelengths 0.96, 1.16, 

 1.28, and 1.69 cm. Data were also taken at the wave- 



2.2 



2.0 



1.8 



1.6 



_i 

 < 



1.0 ■ 



ae 



0.6 



0.4 



0.2 



10 



50 



20 30 40 



/O IN G PER CU M 



Figure 18. Attonuatii)u in water vapor. 



lengths 1.06, 1.31, 1.37, and 1.1!) cm. These lines are 

 all concave upward with the exception of those at 

 1.28, 1.31, and 1.37 cm. There is some evidence that 

 the line at 1.31 cm is concave downward, while within 

 experimental error the 1.28- and 1.37-em lines are 

 straight. 



The curvature is surprising, since it was believed 

 that y would be proijortional to p. The reason for the 

 curvature is not understood, and it is possible that it 

 arises from some systematic experimental error. How- 

 ever, it is difficult to conceive of a systematic error 

 \\'hich disaj)pears at resonance. 



Because of this curvature, it is not possible to draw 

 a single attenuation curve showing absorption as a 

 function of wavelength for all humidities. Figure 19 

 shows the variation with wavelength of the attenuation 

 coefficient y/p in decibels pier nautical mile per gram 



