STUDIES OF VARIATION IN INSECTS 32 1 



tory as regards insects of complete metamorphosis, and has been 

 ah-eady explained in the introduction. 



Continuous and Discontinttous Variation. — By continuous 

 variations we mean to refer to those variations variously called 

 fluctuating, individual, etc., which are present in any series of 

 individuals of a species, and which cluster about the modal 

 or most abundantly represented form of the species as would be 

 expected from the law of error (law of probabilities). Although 

 the extremes (at either end of the range) among these varia- 

 tions may differ considerably, they are so connected with the 

 mode, by such a nearly perfect series of gradatory or intermedi- 

 ate steps, that a curve or polygon graphically expressing their 

 frequency and range will usually (where the number of indi- 

 viduals in the series examined is large enough to exhibit the 

 actual conditions of variation in the species) correspond closely 

 to the theoretical curve which may be plotted for the species on 

 the basis of the law of error. Although Morgan (Evolution 

 and Adaptation) objects to the use of ''continuous" as a de- 

 scriptive name for these variations, on the ground that the word 

 suggests persistence or continuity through successive genera- 

 tions, it seems to us that the name is apt if " continuous" be 

 taken to mean that the occurring variations in any (sufficiently 

 large) set of individuals form a continuous series, the extremes 

 being connected or immediately merging into each other by a 

 series of small gradatory steps. By discontinuous variations we 

 would mean, in contrast to continuous, such considerable and 

 radical variations as have been variously called single varia- 

 ions, sports, mutations, etc., that is, variations, which are not 

 members of a gradatory series, do not group themselves in 

 orderly manner about the modal species form according to the 

 law of error, and although often not large are yet rarely so 

 minute as those differences which distinguish the adjacent mem- 

 bers in any series of individuals arranged on a basis of con- 

 tinuous or fluctuating variation. Mutations, according to the 

 usage of De Vries, our discontinuous variations may or may 

 not be. Thus, all mutations might be called discontinuous 

 variations, although not all discontinuous variations are neces- 

 sarily De Vriesian mutations, that is, certain to breed true under 

 varying conditions of environment. 



