Factors in a Ghyben-Herzberg System— Wentworth 
175 
boundary up and down alternately, any large 
openings which cross the boundary will be 
much more destructive in promoting inter¬ 
penetration of one kind of water by the 
other than small openings. It appears clear 
that heterogeneous permeability will be more 
likely to produce an irregular and disorderly 
boundary than a homogeneous or regular 
permeability. 
A fifth factor of importance is the effec¬ 
tiveness of a cap rock along the coast. Such 
a barrier not only promotes the building of 
higher heads of fresh water but indeed 
creates a condition somewhat akin to a 
U-tube so that at their two upper surfaces 
the fresh- and salt-water bodies are effec¬ 
tively separated. The first and most ad¬ 
vanced intermixing of salt and fresh water 
would normally take place at the coastal 
margin. Here changing head differences 
would be exerted across the shortest dis¬ 
tances between fresh ground water and free 
sea water. Evidently a barrier along the 
coast would have marked protective value. 
In the Honolulu area the thickness and 
width of the cap rock are such as to interpose 
a distance of several thousands of feet in 
most places between the water table and free 
sea water, and this barrier is of tremendous 
importance. 
The factors mentioned above are, in sum¬ 
mary: (1) suitable permeability, (2) ade¬ 
quate infiltration, (3) limited fluctuation, 
(4) regularity of permeability, (5) an ef¬ 
fective cap rock. Some aspects of their inter¬ 
relationships will now be discussed. 
PERMEABILITY 
It would be difficult to over-emphasize 
the importance of time in the inter-relation¬ 
ship of the several factors. The first factor, 
permeability, is of course a rate of discharge 
through a specified cross-section, and infil¬ 
tration is expressed as an amount per unit 
of time and per unit of area. It is the lag in 
the dissipation of infiltrated water through 
permeable rocks which causes the initial ac¬ 
cumulation of ground water and determines 
the ultimate head at which balance between 
gain and loss will be reached. In general, 
on islands of similar geometrical form, infil¬ 
tration proceeds through areas that are pro¬ 
portional to the squares of linear dimensions, 
whereas for the same heads, the areas 
through which discharge to the sea takes 
place are proportional to perimeters, hence to 
the first powers of linear dimensions. Hence 
derives the tendency to build higher water 
tables on larger islands, thus restoring some 
degree of equality with this second dimen¬ 
sion. It is also true that larger islands have 
longer radii and greater likelihood of con¬ 
tinuous discharge even with discontinuous 
rainfall and infiltration. 
Permeability that is too great (relative to 
infiltration and other factors) will result in 
a water table so low that no permanent pres¬ 
sure against salt water will be maintained 
and no permanent Ghyben-Herzberg lens 
will exist. On the other hand, if permeabil¬ 
ity is too low the amount of water infil¬ 
trated will be small, and the exerting of a 
systematic pressure against the sea water is 
less likely to be established. With the higher 
water tables due to less permeable rocks 
there is less likelihood that rocks of reason¬ 
ably uniform permeability will extend to the 
depth below sea level requisite for a func¬ 
tional system. Moreover, even if balance 
exists, the lesser permeability precludes the 
detectable response by which we might recog¬ 
nize it. Thus on various less observable 
grounds the Ghyben-Herzberg condition 
vanishes also with reduced permeability. 
It is possible, too, that in some islands the 
rock near sea level and slightly below at the 
coast is less permeable than the general mass 
below sea level and farther inland. Such 
difference within a favorable range of mag¬ 
nitudes would promote the Ghyben-Herzberg 
condition. 
