The Various Forms of Variability. 



49 



from this mean are inversely proportional to their mag- 

 nitude. The variation may be exhibited in size or number 

 and the results of observation can be treated by mathe- 

 matical signs and formulae. 



Galton, Weldon, Bateson^ Ludwig, Duncker, 

 and many other investigators have raised this line of 

 inquiry to a special branch of science. But, unfortunately, 

 a recognized term for the phenomena with which they 

 deal does not exist. It has been called fluctuating, grad- 

 ual, continuous, reversible, limited, statistical and indi- 

 vidual variability. The latter seems to be the most widely 

 distributed in zoological and anthropological literature, 



Fig. II. The Ogive-form of the curve of individual variation, 

 made of the leaves of Pvumis Lauro-Cerasus.^ 



while tlie name fluctuating, which was often used by 

 Darwin^ seems to be the best.^ On the botanical side 

 individual is opposed to partial variability, the former 



^ Individual variability can be very simply demonstrated by past- 

 ing the leaves of a tree in a row side by side. They are arranged 

 according to their size and are placed at equal distances along a 

 horizontal base line in such a way that their midribs are parallel ; 

 then their tips are joined by a line. In the above figure this line is 

 placed at a little distance from the tips of the leaves for the sake of 

 clearness. This line (the Ogive of Galton, who has made most use 

 of it) at first mounts quickly, then in the middle only slightly and 

 at the end rapidly ascends again, following Qi'Etelet's law. The 

 points Q, M, Q divide it into 4 quarters (Q = Quartile). 



^ See KoLLMANN in Correspondenz-Blatt d. d. Gesellsch. f. An- 

 thropologic, Bd. 31. No. I, Jan. 1900. 



