278 ANIMAL MORPHOLOGY 



ancestors, they are in internal fluctuation and it is this that we do not 

 see. 1 



If modifications should be produced in the veins of an insect's wing, 

 for example, it is impossible that these modifications should express 

 themselves otherwise than by a new mechanical disposition constitut- 

 ing in relation to the preceding a sudden variation in the disposition of 

 the cells and of the veins. In the same way, the appearance of a new 

 vertebra or of a new metamere in an animal whose metamerism was 

 fixed could occur only in discontinuous fashion and not by infinitesi- 

 mal fractions of a vertebra or of a metamere. The fact that mutations 

 always appear in limited number (seven in the case of CEnothera 

 Lamarckiana) shows clearly that a certain number of positions of 

 equilibrium are in question, among which there are no realizable 

 morphological transitions, and of which some seem difficult to obtain. 

 Of the seven species of CEnothera, a single one, CEnothera gigas, has 

 proved robust. The others are for the most part very weak, and de- 

 mand much care in order to flower and to mature their seed. Often, 

 indeed, there are only two possible equilibriums; this is true in the 

 case of dimorphism or ditaxies of colors, to use the language of Cou- 

 tagne, so common in plants, in mollusks, in the lepidoptera, etc. 



In reality, as I wrote a dozen years ago, while fluctuations may be 

 compared to gradual oscillations from one side to another of a mean 

 position, mutations represent so many states of stable equilibrium 

 among which continuous passage cannot be established. The inter- 

 mediate forms of these states of equilibrium are not explicitly real- 

 ized because they do not correspond to sufficiently stable states. The 

 following trivial comparison will serve to render my thought easier 

 of apprehension: we cannot rise a half or any fraction of a step of a 

 stair. In such cases progress is necessarily discontinuous, or, what 

 amounts to the same, is manifested only in a discontinuous manner. 

 But we cannot adduce from these facts any argument against the 

 formation of species by natural selections; there is all the more reason 

 why it is not necessary to seek the unique and complete solution 

 of the very complex problems of transformation. 2 



1 A botanist whose original researches concerning variation in plants have not 

 attracted sufficient attention, A. T. Carriere, made an ingenious comparison in thi. 

 connection : 



"Nous pouvons," he says, "afin de nous repre"senter le double effet, 1'effet lent 

 et 1'effet brusque sous lequel se montre le dimorphisme (ce que nous appelle"rions 

 aujourd'hui une mutation ditaxique) supposer une horloge a secondes dont on ne 

 verrait que le cadran. Dans ce cas, 1'effet continu mais lent, nous serait repre- 

 sente" par le balancier, qui, bien que nous ne le voyions pas, ne s'arrete cependant 

 jamais, et 1'effet brusque ou intermittent par chaque saut que feraient les ai- 

 guilles, saut qui est la rdsultante d'une action incessante tellement lente qu'ellc 

 n'est point appreciable a nos sens et qui ne se manifesto d'une maniere sensible 

 que lorsqu'il y a une certaine quantite" de force accumule'e." A. Carriere, Produc- 

 tion et fixation des varictcs dans les vfqctaux, Revue horticole. note 42, p. 71. Paris, 

 1868. 



2 A. Giard, Sur un exemplaire de Pterodela pedicularia L. a nervation doublcmcnt 

 anormale, Actes de la Socie'te' Scientifique du Chili, iv, p. 21, 1895. 



