Pedigree Moth-breeding. 25 



When we represent the wing-length of every specimen in a large 

 brood by a corresponding vertical line, and arrange these lines in 

 an orderly manner according to their lengths, and at equal 

 distances apart upon an horizontal base, we shall obtain a figure 

 like that shown in fig. 1. Here, however, only some twenty 

 vertical lines have been drawn, sufficient to indicate what is meant. 

 It is not necessary to make a larger or more minute drawing for the 

 sake of mere explanation. The variability of wing-length, as indi- 

 cated by the difference between the lengths of the longer and shorter 

 lines, has been purposely exaggerated to make the meaning of the 

 figures more clear. 



In fig. 2 these upright lines had been enclosed within a dotted 

 boundary whose vertical sides should lie at an interval of one-half 

 space before the first and beyond the last of the lines respectively, 

 and whose upper portion is a smooth curve drawn with a free 

 hand, touching the tops of the vertical lines ; then the vertical 

 lines are supposed to have been rubbed out, and only the contour 

 or " scheme " to remain. This scheme contains, in a most com- 

 pact form, the measurement of every individual in a brood, or in 

 a population however large. A dotted vertical line, or ordinate, M, 

 is drawn to the curve from a point that bisects the base, and a 

 horizontal line is drawn through the point O in the curve where 

 this ordinate, which is the "median " of the curve, meets it. The 

 median is practically the same as the average, and it is clear from 

 the construction that its value is quite independent both of the 

 width of the scheme and of the number of individuals to which the 

 scheme refers, so long as they are fairly numerous. The hori- 

 zontal line AOB is the "axis" of the curve; it divides it into 

 symmetrical halves. In fig. 3 the nearer half of the axis A O is 

 itself bisected, and an ordinate Q is drawn to the curve from 

 the point of bisection. Q is what I call the " Quartile " of the 

 curve. 



In fig. 4, M and Q are all that remain, and they are all that we 

 are mathematically concerned with. When they and the interval 

 between them are given the whole of the scheme can be calcu- 

 lated ; but the interval between them is unimportant for the 

 objects in view. It does not in the least matter on what horizontal 

 scale the scheme is drawn, as the values of Q M and other 

 ordinates at different fractional divisions of the axis are inde- 

 pendent of the horizontal extension. Q and M are the only values 

 in which we are interested, and it is with these that I work. 



It has been abundantly shown by many, from Quetelet onwards, 

 and all my own many statistical inquiries confirm the view, that 



