A rough value of the mean free path of sodium and chlorine ions 

 in solution may be obtained from the diffusion constant for .2N NaCl 



C Q 



in water which is D = 10~ . The mean free path 1 = 3D/v = 10 cm, 



A 



assuming a velocity of a free ion in vacuum at room temperature(2. 7x10 cm/sec) 

 Thus it can be seen that there will be no absorption from the ions until the 

 region between the infrared and microwaves is reached, and even here, the 

 amount of absorption depends on the amplitude of the electric field. How- 

 ever, in this intermediate region (about 1 cm) there is great absorption 

 from other effects. There is a very broad water absorption line at 1.35 cm, 

 and one due to oxygen (whose concentration in water is about l/lO that in 

 air) at 1/2 cm arising from its electronic magnetic moment. For wavelengths 

 longer than 1 cm, the absorption falls off enough to permit effective use 

 of radar in air at 10 cm. But in water, the skin effect, which arises from 

 the ions, becomes of importance and drastically limits propagation. 



2 r-~ 



For low frequencies (-^-g » D, the absorption factor a = y "o" • 



e CO 

 This term is responsible for the well-known skin effect. At 1 rac/sec, 

 a is about .1 for sea water, giving a mean free path of 10 cm. It is 

 easily seen that propagation of these frequencies is not feasible except 

 perhaps at the lowest ones, and here there are immense problems of efficiency 

 in radiating and receiving equipment. Furthermore, wavelengths in this 

 region are so long that scattering from any object the size of a submarine 

 is apt to be extremely small because of the l/\^ dependence (see above). Low 

 radio frequencies (\ > 30 cm) show little attenuation and have been used in 

 practice. The English station Rugby used 16 kc/sec to transmit to a sub- 

 marine with an antenna 30 feet underwater at ranges up to 3000 miles. 



Experimental Results 



In this section will be presented a brief survey of experimental 

 work measuring absorption in the visible and infrared. 



Clarke and Backus measured a light intensity of 10 watt/cm at 



a depth of 550 meters when there was a surface intensity of .05 watts/cm'^. 



This experiment took place on July 20, 1955, about 200 miles southeast of 



New York City. The measurements correspond to an attenuation of ,0125 or 



a mean free path of about 80 feet. These measurements agreed with those of 



12 

 Hulbert who measured the absorption and scattering of light in distilled 



water, Chesapeake Bay, and coastal waters off Hollywood, Florida. Some of 



his results are reproduced here: 



-10- 



