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RICE UNIVERSITY STUDIES
the initial and final exponentials will appear as parallel lines ;
the transition corresponds to a curve connecting the two ex-
ponentials which can be irregular. The two exponentials may
actually be parts of one; this is shown in Figure 10, where
the transition is constituted by the rapid decrease in Japanese
population from 1940 to 1945 followed by an even more rapid
increase from 1945 to 1950, bringing the population back up to
the exponential trend line as if World War II had not occurred.
In other cases, the two parallel lines representing exponential
growth do not coincide; usually, the terminal line lies below
the initial one, which means that although the population
growth rate has returned to its initial state, there has been an
unrecovered absolute loss in population. This is well illustrated
by Figure 13 (Basic Oxygen Process Raw Steel Output in the
U. S.) which shows an unrecovered loss which can be inter-
preted as having set the industry back by slightly more than
one year.4
There are other types of departure from exponential growth, but
they are not so easily characterized nor do they seem to play an
important role in the types of populations that are under con-
sideration in this paper.
Fluctuations of Type-III and their connection with unrecover-
able losses are worth some further discussion. An important
example is furnished by population and economic time series for
the United States encompassing the period of the Great Depression,
which is a Type-III fluctuation.
Figure 15 shows the population of the United States during the
1880-1960 period, as given by the decennial census. In connection
with Figure 9, it was pointed out that a Type-II transition occurred
about 1880, corresponding to the closure of the frontiers; the
effect of this transition is visible in the first three data points of
Figure 15; the next three lie on a line (which is not remarkable
since two points determine a line). The remaining three points
lie on another line which is nearly parallel to the first. Therefore,
the data from 1910 to 1960 can be interpreted as indicating a
constant growth rate with a Type-III fluctuation occurring be-
tween 1930 and 1940, the decade of the depression. Pursuing the
implications of this interpretation, shift the 1940-1960 line to the
left so that it coincides with the 1910-1930 line, and measure the
number of years of shift required to obtain this coincidence: it is
approximately 6 years (we will use 5.89 years). Figure 16 shows
the same data used for Figure 15 with a 5.89-year shift to the