VARIATION AND MUTATION 141 



by the influence of extrinsic factors. Or variations may be di- 

 vided into determinate and indeterminate; that is, those (if there 

 really are such) which are apparently controlled by some, to us 

 unknown, influences and are by these influences confined to cer- 

 tain definite lines or directions of change; and, on the other hand, 

 those which are* apparently wholly accidental, or rather which 

 may represent any conceivably possible line or kind of change. 

 Finally, variations may be distinguished as to their general 

 character as discontinuous and continuous; tliat is, variations oc- 

 curring irregularly, mostly large and comparatively rarely, and 

 small, abundant variations occurring in graded series. Among 

 the former are to be ranked the occasional sports and monsters 

 familiar to all breeders; while in the latter, Darwin believed him- 

 self to have at hand the necessary ever-present materials to 

 serve natural selection as a basis for species transformation. 

 Hence the shght but abundant and ever-present fluctuating 

 continuous variations are often called "Darwinian variations." 



Now the law of Quetelet ap})lies solely to the Darwinian 

 variations. The law is, that these variations occur according 

 to the law of probabilities (or law of error): that is, that the 

 shghtest variations away from the modal or average type will 

 be the most abundant, and that the number of varying individ- 

 uals will be progressively less the farther away from the modal 

 type the variations of these individuals are. That is, if the vari- 

 ations in some characteristic of a species be determined for, say, 

 10,000 individuals of the species, and tabulated, and a curve 

 erected to express graphically tlie facts of this variability, this 

 curve will practically coincide with that one which would simi- 

 larly express the variation, if the variation actually occurred 

 according to the mathematical law of the frequency of error; 

 this theoretical curve being obtained by the formula deduced 

 originally by Gauss at the beginning of the last century. Fig. 

 83 show^s graphically how certain studied cases of continuous 

 variation reveal the condition expressed by Quetelet 's law. 



As compared with discontinuous and sport variati(Mi, con- 

 tinuous variation is by great odds the more common. Hateson, 

 an English student of variations, has attemi)ted to show that 

 discontinuous variations are more conunon than is generally 

 believed, and has filled a large volume with accounts and illus- 

 trations of such alleged variations. Hut it has been proved 

 that manv of these arc cases of teratogenic regeneration, or ab- 



