56 REPORT UNITED STATES ENTOMOLOGICAL COMMISSION. 
more remarkable invasions were noted. It is also possible, and we are 
inclined to think more than probable, that, in most of the countries 
where locust visitations have long been observed, their invasions have 
become more frequent than formerly, but the records of visitation can 
not be relied upon for the determination of this question. Be this as it 
may, the facts we have presented are sufficient to show conclusively that 
their migrations are not governed by any regular periodicity, and hence 
depend upon some influence which is irregular in its operations, as, for 
example, climatic changes. 
Yet, notwithstanding this conclusion, we cannot pass on without call- 
ing attention to the fact that if we take the years of the great general in- 
vasions of Central Europe, 1333, 1050, 1G93, 1748, and 1825 ; of Spain, 1495, 
1 542, 1G19, and 1082 ; of Algiers and adjoining regions, 1799, 1845, 1866, 
and the recent one of 1878; and the noted locust years in our own west- 
ern country, to wit, 1820, 1855, 1866, and 1874-'76, the interim in each 
case is very nearly a multiple of 11 years. 
II.— PERMANENT BREEDING GROUNDS OR AREAS OF PERMANENT 
DISTRIBUTION. 
That migratory locusts occasionally extend their flights into sections 
where they are not found as permanent residents is too well known to 
require proof, and that they sometimes continue in these extralimital 
areas for two or three years by reproduction has been clearly demon- 
strated. As a proof of this assertion we have only to refer to the paper 
by Koppen already mentioned, and our former report. Therefore, in at- 
tempting to mark the boundaries of the distribution of these erratic in- 
sects, it has been found necessary to draw at least two lines, one to bound 
the inner or permanent area and another to designate the limits of fluc- 
tuation, or, to quote the words of M. Preudhomme de Borre: 152 
In this study, so interesting, there is one point on which we should insist. It is this: 
that the observations of M. Koppen tend to confirm the principle of zoological geo- 
graphy, that the area of a species cannot be limited on the map by a simple curve, 
but between places where the species exist in a constant or normal manner and those 
where its absence is constant there is always a zone, often very broad, of temporary 
visitations, which is to the area properly so called what the penumbra is to the light, 
•within the zone, of which the exterior limit is much more easily traced than the inner; 
this last is subject to continual oscillations with some undulatory movements depend- 
ent on the centrifugal or expansive tendency of the species and from the resistance 
■which opposes it, and external circumstances, and evidently also the tendency of other 
species to spread out, with which it carries on a struggle for existence. 
Koppen, in order to express fully the relation of P. migratorius to the 
regions in which it has been observed, found it necessary to trace upo~ 
the map three concentric lines, one marking the limit of its permanen 
distribution, corresponding to what we in our first report termed " per- 
manent breeding-grounds " ; a second, outside of this, marking the limits 
of its temporary existence in all its stages of development ; and a third or 
162 See former !;>-( ort, p. 475. 
