MULTIPLE FACTORS IN MENDELIAN INHERITANCE 185 



would have far greater significance than an equal deviation in a 

 long measurement, and so in any average the large deviations 

 in the long measurements would entirely overbalance the equally 

 important small deviations in the short measurements. The fol- 

 lowing method was used to obtain a number for each animal, 

 which may be called the coefficient of size (C. S.), a number 

 based on relative deviations. The average of a character for one 

 fraternity was used as a dividend into which were divided the 

 individual measurements of the animals in the same fraternity. 

 The quotients so formed gave a series of ratios expressing the 

 relative sizes of the various sibs above or below their mean. By 

 this method the ratios of the other characters of one animal to 

 the corresponding fraternal means were obtained. The average 

 of these ratios gave the coefficient of size (C. S.) for that animal. 

 These coefficients range from 0.930 for the largest animals to 

 1.070 for the smallest ones. In classifying them, classes 0.005 

 in extent were used. From these distributions, standard devia- 

 tions were calculated. Since the means of all fraternities lie 

 always in the column whose value is 1, it will be realized that the 

 sums of all the individuals in each column will give a correct de- 

 scription of the variability of one generation of a whole family; 

 in other words, different fraternities from the same family may 

 be classified together. The standard deviations of these family 

 distributions will be based on deviations from the various fra- 

 ternal means. This will give a more accurate result than if the 

 actual deviations had been calculated from the means of all the 

 individuals averaged together, as would be done in applying the 

 formula for standard deviation to the values themselves. It must 

 be supposed that the means of all the fraternities do not coincide. 

 The mean of all the values would give the extreme variates even 

 greater deviations and the standard deviations would be higher 

 than those obtained by this method. It will be seen now that 

 the coefficients of size of all the animals in one generation may 

 also be classified together. 



In the tabulation of these coefficients of size it is at once ob- 

 served that all the most extreme coefficients belong to individuals 



