REGRESSION IX A PURE LINE OF PLANT LICE. 167 



each side of it other parallel lines are laid off at equal distances. 

 Each of these represents a difference of 0.025 in the index ratio 

 for the antennal segments considered. 



On this diagram small round circles have been placed repre- 

 senting the position of each of the eighteen parents according to 

 their antennal index-ratio. These naturally form a straight line 

 which is indicated. Now the mean index of the offspring of each 

 parent is represented by an arrow-head, placed immediately 

 above or below, as the case may be, the circle indicating the 

 index of the parent. A line connecting these two points forms 

 the arrow which indicates the actual amount of regression in 

 each instance. In three instances we have more than one stem 

 parent with the same index-ratio, hence in these cases the arrows 

 showing regression are superimposed. 



It is observed that in some instances the regression is not to 

 the mean of the strain, and in other instances it is much beyond 

 the mean of the strain; while in two instances there is no regres- 

 sion at all, but a deviation from the mean of the strain even 

 greater than that that existed before in the parent. 



In order to compute the average amount of regression we may 

 arrange in parallel series the deviations as shown in the indices 

 of the various parents from that of the mean of the strain, and 

 the deviation shown by the average for the indices of their 

 progenies. This is here done, the mean of the strain being given 

 as zero and the deviation found in the various antennal ratios 

 from this mean being given in hundredths, plus or minus, as the 

 case may be. 



Deviations in indices of parents 14 13131310- 3- 3- 2 - i 

 Average deviation found in off- 

 spring. . +8-3+3-11+1-3-9+4+15 



Deviations in indices of parents o+ 5+ 6+ 6+ 8 + 9+18+28+31 

 Average deviation found in off- 

 spring +21 o- 3+5 0+13+5-14+9 



This relation of the regression can be expressed in the form 

 of fractions by taking in each instance the difference in the devia- 

 tion of the offspring from that of the parent, for the numerator; 

 and the deviations of the parent itself in each instance as the 

 denominator. These will then be : 



