412 H, M. KYLE [December 



character, or the variation in a character, as being " good for the 

 species," as having a " selective valne," when nothing definite is 

 known. 



On the one side, therefore, we have " organs," on the other side 

 " species " ; and when we consider things as they naturally are, over 

 all is the environment. Is it not possible, then, to find a method of 

 grasping the mean ? Between the organs and the species lies the 

 most real of all, the individual — the unity of biology. If we conld 

 but understand the single life in its entirety through concentrating and 

 testing on it all the conceptions of biology, we should know better 

 the meaning of " change " — how it arises, and thence also the 

 meaning of " evolution." 



This is the background of the task which Professor Heincke 1 set 

 himself. After various trials at combining variations, and the making 

 of formulas to represent groups and species, he advanced towards a 

 method of determining, and a conception of the individual — not as an 

 abstraction, but as something real and composed of organs, and forming 

 one of many exactly equal under equal conditions. 



The method consists, not in the correlation of the variations of two 

 or three characters, but in the correlation of the averages of as many 

 characters as possible. If the variations of many characters are 

 obtained, those of each character may be arranged about the centre 0, 

 as in the ordinary mode of dealing with variations. Hence a system 

 of groups of variations is obtained, each group representing the most 

 probable distribution of the variations for that character, and the 

 common centre representing the average of each group. If the varia- 

 tions are then arranged in parallel columns they may be summed up 

 and treated as if they were deviations from the common average at 0. 



In other words, the sum represents the distribution of the variations 

 just as the ordinary arrangement of deviations about an average repre- 

 sents their chance distribution. 



The assumption underlying this method 2 is that each group of 

 variations conforms to the same "type" of probability, that of the 

 " probability integral." This assumption has already been challenged 

 as if it invalidated the whole principle, but although it is not easy to 

 say what correction should be made, a summation is certainly possible, 

 and the warrant of its being near the truth is shown in the results. 



The law which arises from this summation holds good over all the 

 individuals of a group under the same conditions. It gives the second 

 proposition. 



2. The standard deviation of all the variations of the individuals 

 when grouped about the common centre is T18, and the probable 



1 " Naturgeschichte des Herings," Abliandl. des Dculsch. Seefi'sch.-Vereins, R. ii. H. 1, 



1898. 



2 A further assumption is that each character presents an independent series of 



variations. 



