VARIATION IN THE GENUS EREBIA. 307 



lines were drawn between the various individuals of a species 

 according as they had 0, 1, 2, 3, &c., spots. In order to give 

 any idea of this variability, the relative sizes, distribution, &c., 

 of those spots would have to be described. Now, this is done 

 roughly by means of the scheme ; when the statement that ten 

 individuals have 4 spots apiece is transcribed into the scheme, 

 all that is said about these individuals is that each one of them 

 has a "spot-power" somewhere above 3 and up to 4 — e.g. 3'1, 

 3*5, 3"7, &c. In this way the variations in size, &c., of the spots 

 is taken into account, without actually measuring the individuals 

 separately, except in so far as they have 0, 1, 2, 3, &c., spots of 

 some kind. 



How far it is possible to treat wing patterns in this manner 

 can only be decided when actual data are considered ; but it is 

 obvious that in other characters, such as length of wing, weight, 

 &c., the method is invaluable. For, instead of having to 

 measure or weigh each individual accurately, convenient ordinal 

 numbers are chosen, and the individuals are grouped according 

 as they exceed or fall short of those numbers with regard to the 

 character to be considered. 



By means of this scheme, then, we are able to determine the 

 M or mid-value of a group of individuals with regard to some 

 character or other. The properties of this M are, besides its 

 relation to the arithmetical mean — (1) the chance is an equal 

 one of any previously unknown measure in the group exceeding 

 or falling short of M ; (2) the most probable value of any un- 

 known measure in the group is M. 



From these properties we gather that if individuals are 

 selected at random from a group, the M of the smaller group 

 so formed tends to remain the same as the original M of the 

 whole group. In nature a chance selection must always be 

 made, apart from natural or sexual selection, to determine which 

 individuals shall breed : since these individuals in each genera- 

 tion will be selected according to the laws of chance, we may 

 treat every generation as breeding in terms of its M. 



In this way we bring our numbers under the light of the laws 

 of chance, and it is under this light especially that it is intended 

 here to bring the phenomena to be considered. 



It is now time to answer an objection that will probably have 

 occurred to the reader with regard to the discussion of fig. 1 on 

 p. 279. It was there stated that if there were only a very few 

 females, these would receive mates hy chance, and so the equili- 

 brium would be thrown out of order. But we have just seen that 

 a selection of mates is always made hy chance, and on this is 

 based our system of dealing with the numbers ; so that it would 

 seem that in the case of the females being in a minority, there 

 would be an equal chance of an equilibrium being established. 

 But the word chance is used here in two different senses. In 



