222 Experimental Zoology 
forms, or mutations mentioned above. This comparison raises 
the question whether the two forms of variation, fluctuating 
and discontinuous, are fundamentally different, or whether they 
are only extremes of the same process. Let us examine this 
question more closely. 
Lang gives the following imaginary case that bears on our 
problem. Suppose there existed a species having three varieties, 
differing according to size, being 4, 6, and 8 centimeters in 
length. On crossing they Mendelize and do not give intermedi- 
ate types. Differences in nourishment, however, may cause the 
size of any one of the three types to be a little larger or smaller, 
2 millimeters being the extreme in either direction, but this 
will cause no overlapping. Suppose, however, that the fluctua- 
tions, due to differences in food, for example, are so great that 
the largest individual of the 4-centimeter variety is as large or 
larger than the smallest individual of the 6-centimeter variety. 
In other words, the individuals éransgress the limits of each 
variety, z.e. the breadth of the fluctuation of the variety is so 
great that it overlaps the limits of the nearest related variety. 
Then we should have a population in which a continuous series 
could be traced from one extreme to the other. Apparently we 
should be dealing with a continuous variation, but in reality 
with three pure lines that overlap. Breeding experiments alone 
could determine that these three types actually exist. Such 
experiments would be comparatively simple where self-fertiliza- 
tion is possible; but where cross-fertilization is necessary, the 
separation of the population into its three true races becomes 
more difficult. 
Lang has found in Helix hortensis somewhat similar conditions 
to those given in this imaginary case. It has been pointed out 
that while in some colonies only two sharply separated types 
appear, in other colonies numerous variations are found whose 
extremes run into each other. Within the species there exist the 
possibilities of eighty-nine variations in the banding, and the color 
may be white, yellow, orange and brown, or ash-gray. There 
are size varieties also, and the bands themselves may be continu- 
