3 22 KELLOGG AND BELL 



As a matter of fact not all continuous variation follows the 

 law of error ; the curve or polygon of frequency is not infre- 

 quently an asymmetrical one; " skewness " prevails, or the 

 curve may even be bi-modal. But nevertheless the " continuity " 

 of the variations is unmistakable. In a sufficiently large series 

 the extremes of the range are perfectly connected with the mode 

 or modes and hence with each other by gradatory steps very 

 small in size. Whatever the largeness of the difference be- 

 tween the extremes, any two adjacent members of the series are 

 hardly distinguishable. This gradual, insensible but yet effec- 

 tive (as regards widely separated members of the series) kind of 

 variation is most typically illustrated in cases of what Bateson 

 calls " substantive" variation, that is, where the varying char- 

 acteristic is one of pattern, of length, width, or bulk, of the 

 curving of a vein or leg or spine. Excellent examples of this 

 continuous substantive variation are presented by the abdominal 

 and face patterns of Vespa (see p. 284), the elytral pattern of 

 Diabrotica (see p. 274), the prothoracic pattern of Corisa (seep. 

 293) and others. According to Bateson, variations in number 

 of antennal and tarsal segments, number of spines, hairs or 

 other processes, and often such numerical or, as called by him, 

 meristic variations, must be looked on as different in kind from 

 the substantive variations, those capable of perfect mergence 

 from one condition to another, in other words, practically incap- 

 able of quantitative measurement. These meristic variations 

 are called discontinuous by Bateson. Numerous typical ex- 

 amples are included in our data. (See the accounts of the 

 variation of the number of the costal wing-hooks in bees and 

 ants, the number of tibial spines in the locust and the cicada, 

 the number of metathoracic tactile hairs in biting bird-lice, etc.) 

 But when one stops to consider the fact that in all these cases 

 variation could hardly occur by any less steps than those of one 

 hook or one spine or one hair, that a half hook or half antennal 

 segment is inconceivable, some serious doubts as to the validity 

 of Bateson's classification of variations as continuous and dis- 

 continuous will certainly result. The doubt is strengthened by 

 the difficulty of a clean classification presented by such cases as 

 that of Hippodamta convergens. Here we have a substantive 



