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. 



The 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 an4 tabulated the result may be expressed in the form 

 of a curve which, if the number of shots be large enough, will 

 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 typical 

 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 varying 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. 



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 take place in 

 accordance with the laws of chance. It should be noted, however, j 

 that the curve of variation is by no means always symmetrical. 



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 



