470 LIEBERMANN [CHAP. 11 



It is noted that sea-water has a conductivity more than 300 times that of dry 

 soil. On the other hand, it can hardly be considered a good conductor compared 

 with copper. The dielectric constant, e, is readily obtained for the insulators ; 

 it is rather difficult to estimate for good conductors such as copper. The perme- 

 ability, fi, is practically identical in all substances except the ferro-magnetic 

 materials. 



The first term under the radical in (2) is often termed the displacement 

 current ; the second term arises from the conduction current. Clearly, in sea- 

 water the conductivity is sufficiently large that the conduction current is 

 dominant except at very high frequencies. When the conduction current is of 

 the same order of magnitude or is comparable to the displacement current, the 

 propagation constant, y, will become small. This phenomenon would appear to 

 occur in sea-water, utilizing the above values in the table, at frequencies in 

 the vicinity of a kilomegacycle (10^ c/s). Actually the frequency at which this 

 transmission "window" occurs is considerably higher because the effective 

 conductivity increases at sufficiently high frequencies ; associated with the 

 rotation of the polar water molecules is an additional contribution which be- 

 comes increasingly important at high frequencies. The electromagnetic "win- 

 dow" actually occurs at much higher frequencies, namely, in the visible light 

 range. Hence the familiar penetration of visible light in the sea is a direct 

 consequence of electromagnetic theory. 



3. Propagation through Sea-Water 



At lower frequencies the displacement current can be neglected and the 

 propagation constant, y, assumes the simpler form 



y = \/(cT/Aaj/2)(l+i). 



The distinction "low frequency" or "high frequency" is purely an academic 

 one, for the low-frequency approximation given immediately above is applicable 

 to sea-water up to frequencies including the microwave range (IQi'^ c/s). As 

 stated above, the real part of y gives the attenuation ; thus the equation often 

 appears, 



S = V(2/a;/xa), 



where S is defined as the "skin depth." The quantity 8 is the distance at which 

 the field intensity is diminished by 8.6 dB. For sea-water, S = 250/'v// meters. 

 For example, at 1 mc/s, 8 is j m ; at 100 c/s the "skin depth" is 25 m. Hence 

 there is little possibility of significant electromagnetic propagation through 

 sea-water except at low audiofrequencies. 



The imaginary part of y is related to the velocity of propagation given by 



V = V(2cu/c7/x). (3) 



It is seen that the velocity of propagation of sea-water, unlike that of electro- 

 magnetic propagation in air, depends on frequency ; as in the case of attenua- 

 tion, velocity increases as oj'/^. Both the variation of velocity with frequency 



