Factors in a Ghyben-Herzberg System— Wentworth 
179 
Fig. 3. A numerical model showing growth of the transition zone under the assumption of progressive 
rinsing, analogous to the exponential theory of rinsing. The unmodified fresh and salt waters are 
shown by the respective horizontal and vertical hatching. The transition zone is shown by the growing 
band of figures, the successive values being parts per thousand of salt water. 
Figure 3 is a numerical model showing 
the effect of moving the junction between 
two types of water to and fro in a permeable 
medium having some storage capacity. At 
the beginning of the test period, the junction 
is assumed to be sharp, as shown by the re¬ 
spective patterns (Fig. 3). Each successive 
column of figures represents the composition 
in successive, equal periods of time. The 
fresh water is assumed to move by 10 suc¬ 
cessive units of motion against the salt 
water, thence to retreat by 20 units to a posi¬ 
tion 10 units on the other, or fresh, side of 
the initial line of balance, and finally to 
return by 10 units to that line and thus com¬ 
plete one full cycle. With each unit of 
movement, the water in a given position is 
assumed to be made up of 9 parts of oncom¬ 
ing water and 1 part of residual water. It 
is immaterial for the discussion whether the 
residue be assumed as 10 per cent or some 
other figure. 
The figures represent parts per thousand 
of salt water. Above the transition zone all 
the water is fresh, taken as zero parts. Below 
it, the water is of sea-water composition, 
taken as 1,000 parts. A certain raggedness 
appears at the margins, owing to limiting 
the calculations to the nearest thousandth. 
So far as practicable the accumulation of 
values of the next digit has been anticipated 
in computing the marginal figures. 
It is evident from Figure 3 that changes 
take place both at the advancing margin and 
at the following margin. The composition 
at the advancing margin is changed toward 
that of the water being invaded, and that 
change migrates into the advancing front. 
The same direction of change is reflected 
through the zone, and the compositions in 
the following margin also change toward 
that of the water being invaded. The rates 
of these changes are determined by the exist- 
ing gradient of composition at various points 
in the transition zone. 
After the first reversal, the form of the 
composition diagram becomes nearly sym¬ 
metrical (Fig. 4). With continued fluctua¬ 
tion the transition zone becomes progres¬ 
sively wider and the rate of change of com¬ 
position within it is slower. The fresh water 
is more deeply penetrated by a graded fringe 
of saline composition and the salt water 
more deeply penetrated by a graded fringe 
of freshened water. This effect is indicated 
in the progressive flattening of the transition 
curves of Figure 4, as well as by the march 
of the figures in Figure 3. 
It is possible that with a symmetrical 
series of fluctuations a limit of width would 
in time be reached , in a regularly permeable 
aquifer. However, in any natural aquifer 
and particularly with unsymmetrical fluctua¬ 
tions and with movement under new head 
