NORMAL CURVE OF VARIATION 153 



whole numbers of inches. It is clear that a zig-zag line formed 

 by joining the dots in the diagram would approximate fairly 

 closely to the curve actually drawn. 



Such a normal curve of variation agrees very closely with what 

 mathematicians term the curve of frequency of error, which is 

 the graphic representation of the mode of occurrence of chance 

 deviations from a mean or average and may be derived from the 

 theory of probability. 



Such a curve may be experimentally produced by drawing a 

 vertical line on a target and firing a large number of shots at it. 

 There will be a more or less strongly marked tendency for the 

 shots to hit the line, depending upon the skill or otherwise of the 

 marksman. Most of them will probably strike to the right or 

 left of the line and fairly near it, but a few will probably be 

 very wide of the mark on either side. If the distances of the 

 striking places from the vertical line be measured and tabulated 

 the result may be expressed in the form of a curve which, if the 

 number of shots be large enough, will probably closely resemble 

 the curves described above. 



The fact that the normal curve of fluctuating variation for any 

 kind of organism is practically identical with the mathematical 

 curve of frequency of error suggests very forcibly that the 

 variation in question is due to chance or accident causing each 

 individual in the course of its development to depart more or 

 less from the mean or average condition of the species to which 

 it belongs. These deviations must depend upon numerous factors. 

 They are to some extent, no doubt, due to the direct influence of 

 the environment, such as the effect of nutrition upon the size of 

 the organism, but they may also depend largely upon the vary- 

 ing characters of the germ cells from which the organism 

 develops, and especially upon the permutations and combinations 

 of characters which happen to take place in the maturation of 

 the germ cells and in their sexual union or amphimixis. 



In short, the general tendency is doubtless for each individual 

 to conform to the type of the species to which it belongs, but 

 many accidental circumstances combine to prevent the realization 

 of this tendency and deviations from the type (or mean) take 

 place in accordance with the laws of chance. 



Mutations. The term mutation, or discontinuous variation, is 

 applied to the process whereby new and more or less conspicuous 

 characters appear suddenly and spontaneously, without any 



