EVOLUTION 389 



in units of some kind even if they be millionths of an inch 

 {^footnote, p. 199), and our final measures are discrete. 

 Even where we think to measure to a considerable degree 

 of exactness, we group our data to rougher units, for the 

 " real " length is an impossible conception ; it changes 

 with position, humidity, temperature, etc. What is the 

 " real " stature of a man at a given age ? His height 

 when he gets up in the morning, or when he goes to bed 

 at night? When he is standing or lying? After a forty 

 mile walk, or when he returns from his summer vacation ? 

 What is the length of a bone ? Even if we agree to 

 an identical mode of measuring, still time of preserva- 

 tion, degree of moisture, temperature, etc., all affect its 

 length, and it is idle to hope for more than a certain 

 degree of exactness. Accordingly even in the case of 

 characters, which vary continuously, we form discrete 

 groups ; we take inches of stature, 2 mm. of bone, etc, 

 and group all individuals falling within this inch or these 

 2 mm. together as having sensibly the same value of the 

 character, much as we speak of men of 50 or of 70, 

 meaning men in their 51st or 71st year of life. Then 

 we proceed, just as with discrete quantities like stigmatic 

 bands in poppies, to find the type and the variability.^ 



Thus for both the discrete and continuous variations 

 of characters we obtain frequency polygons, like those 

 figured in the diagram on p. 385. From such a diagram 

 we can calculate the probability that any given variation 

 will occur ; for example, that the capsule of a wild poppy 

 picked at random will have a given number of stigmatic 

 bands. Thus, what is the chance that a capsule picked 

 at random will have less than 9 bands? There are 399 

 such capsules per 2268 poppies, or about 18 per cent, or 

 the odds are about 9 to 2 against the randomly selected 

 poppy having so few bands. The problem thus resembles 

 in character that of the odds to be determined when a die 

 is cast or a teetotum spun. The whole theory of variation 



1 A slight modification is made in determining the variability of the con- 

 tinuous distribution, but this correction is not of importance when we are 

 dealing with the general features of the subject. 



