May 26, 1911] 



SCIENCE 



827 



tain regions. It has recently been found that 

 tiie ancestral titanotheres are doliclioceplialic, 

 of the type known as proopic-doliciiocephaly 

 because the chief elongation is in front of the 

 orbital region. Their descendants are also 

 dolichocephalic, but the type is opisthopic 

 dolichocephaly, that is, the chief elongation 

 is behind the orbital region. 



Similar allometric indices are also found in 

 the limbs. For example, the ratio of the 

 length of the tibia to that of the femur is very 

 significant and is constantly changing in 

 adaptation to weight and to speed. 



Considering the transformation of the 

 titanotheres in comparison with that of the 

 horses and many other lines of mammals, 

 where successive series have been obtained, we 

 observe again exactly similar phenomena. It 

 appears that the law of continuity, of orderly 

 and in a sense of predetermined transforma- 

 tion can now he estailished beyond refutation. 



The question then arises whether these laws 

 of " continuity " can be harmonized with the 

 potent demonstration that certain new char- 

 acters and certain new proportions arise as 

 saltations or discontinuously. The hypoth- 

 esis which is here advanced is that continuity 

 is the normal mode of development under nat- 

 ural conditions, that there are certain definite 

 trends or tendencies, that there is in continu- 

 ous series a " Mutationsrichtung ," that by 

 this continuous development the greater num- 

 ber of so-caUed " unit characters " have arisen, 

 that occasionally, however, new unit charac- 

 ters may and do arise suddenly. The hy- 

 pothesis may be expressed as follows: that the 

 normal development of unit characters is a 

 continuous progress, that under certain ab- 

 normal conditions, as of sudden change of 

 environment, certain new unit characters may 

 appear suddenly, that the cross-breeding of 

 pure natural races in which unit characters 

 have been built up by continuous processes 

 breaks up these unit characters into a mosaic 

 and gives rise to the larger part of the appar- 

 ently saltatory or discontinuous phenomena 

 which are being observed by the modern ex- 

 perimentalists. 



As illustrations of this hypothesis, take as 



a very simple one the transformation of the 

 head form in various human races; the de- 

 velopment of dolichocephaly and of brachy- 

 cephaly has in all probability been by con- 

 tinuous transformation in one direction or 

 the other. In support of continuity is the 

 evidence adduced among the titanotheres. 

 When dolichocephalic and brachycephalic races 

 intermingle, the fact that dolichocephaly or 

 brachycephaly is a unit character appears at 

 once in the non-blending of head form subject 

 to the law of alternate inheritance. Another 

 illustration is afEorded by the results of the 

 interbreeding of pure stocks of the horse, 

 namely, according to the observations of 

 Ewart, the Arab, or plateau type, the Prze- 

 walsky, or steppe type, and the draught, or 

 forest type. Each of these pure original 

 stocks apparently acquired by gradual trans- 

 formation a very large number of distinctive 

 characters displayed in the head, in the teeth, 

 in the backbone, in the limbs, and last but not 

 least in the psychic activities of these three 

 great strains which have been bred for ages 

 among very diverse environmental conditions. 

 As soon as these three pure stocks are inter- 

 mingled the fact that each is a mosaic of an 

 enormous number of single, or unit characters 

 becomes apparent in the mosaic type of horse 

 which is produced, a horse showing singly or 

 in groups various unit characters of the 

 plateau, steppe or forest types. The trans- 

 formation which, for example, has built up 

 respectively the slender cannon bones of the 

 desert and heavy cannon bones of the forest 

 type has been, we have every reason to believe, 

 a continuous, or progressive, or allometric 

 change. On interbreeding, these slender or 

 massive proportions may partly blend or may 

 be detached as " units " from the progressively 

 slender or massive head types to which they 

 belong. 



By far the greater number of the experi- 

 ments carried on in support of the theory 

 of discontinuity have been among hybrids, 

 crossed strains, artificial strains, or strains 

 subjected to unnatural changes of environ- 

 ment. It is important, therefore, for experi- 

 mentalists to extend their work among abso- 



