April 21, 1916] 



SCIENCE 



555 



tions and who tries to analyze the prop- 

 erties and the function about a point with- 

 out being able as in the ease of an ele- 

 mentary function to study it in itself, di- 

 rectly, in all its aspects. The properties 

 ascertained about one point are not neces- 

 sarily applicable to all space. 



As far as the organisms are concerned, 

 the conditions of their variability have not 

 certainly been the same in all periods. The 

 idea of a progressive diminution of their 

 variability has been often expressed, nota- 

 bly by D. Rosa. Le Dantec, according to 

 his favorite theoretical method in which he 

 considers only the fundamental principles 

 of the problem, has tried to reconcile these 

 facts with the Lamarckian doctrine in his 

 book on La Stabilite de la Vie.^ In the 

 transformation of organisms as well as in 

 that of inert matter, he regards every 

 change as the passage from a less stable to 

 a more stable state. The many organisms, 

 after having varied much and rapidly, 

 might then, perhaps, be for the present in a 

 state of very constant stability, at least the 

 greater part of them. But for the time 

 being, I must omit further consideration of 

 this suggestion. 



We shall have then in the third part of 

 the course to examine, while bearing in 

 mind the preceding opinions, the general 

 results of recent researches in variation and 

 heredity. I shall now sum up the prin- 

 cipal lines of investigation preparatory to 

 tracing the plan of these lectures. 



The methodical study of variations in 

 animals and in plants has led us to recog- 

 nize that the greater part of these varia- 

 tions are not inherited. If we apply to 

 them the methods of the Belgian statistician 

 Quetelet, we shall perceive that for each 

 property numerically stated the different 

 individuals of a species range themselves 



3 ' ' BibliotMque seientifiqiie Internationale, ' ' 

 Paris, Alcan. 



according to the curve of the probability of 

 error, the greatest number of individuals 

 corresponding to a certain measure which 

 represents what is called the mean. The 

 term fluctuation is given to those variations 

 that are on either side of the mean and the 

 study of these fluctuations, begun in Eng- 

 land by G-alton, has been developed and 

 systematized by H. de Vries and Johannsen. 

 In short, it is the whole of the curve of 

 fluctuations which is characteristic of 

 heredity in a given organism, and not such 

 and such a particular measure correspond- 

 ing to a point in the curve. In cross-bred 

 organisms there is, in each generation, an 

 intermixture of two very complex inher- 

 itances, since these organisms result from 

 an infinite number of these intermixtures 

 in former generations. On the contrary, 

 the problem is very simplified, if one con- 

 siders the organisms regularly reproducing 

 themselves by self-fertilization as is the ease 

 in certain plants. Here there is no longer 

 in each generation a combination of new 

 lines, but a continuation of one and the same 

 line. It is the same hereditary substance 

 which perpetuates itself. The Danish 

 physiologist and botanist Johannsen at- 

 tacked, as you know, the problem in this 

 way, by studying variation along a series 

 of generations in lines of beans, and the 

 conclusion of his researches, which have had 

 in recent years a very great influence is 

 that each pure line gives a curve of special 

 fluctuations under special conditions. The 

 variations that we observe in the action of 

 external agents explain the different re- 

 actions of the hereditary substance to the 

 conditions of the environment, but this sub- 

 stance itself remains unaltered. The conse- 

 quence is that, in what since the time of 

 Linne we have considered a species, and 

 have admitted to be a more or less real 

 entity, there is an infinity of lines, more or 

 less different among themselves in their 



