1906.] 



FEMALE LINE IN POLAND SOWS. 249 



terms and the method used in the determination, the reader is re- 

 ferred to the above-mentioned book by Dr. Davenport. 



For the general reader, who may not be famihar with the ap- 

 proved methods of such work, it may be stated that the standard 

 deviation (a) is a relative measure, expressed in terms of the mean, 

 of the concentration about the mean or average, and therefore is an 

 excellent measure of the amount of variation. If the standard 

 deviation (a) is divided by the average (A), the result is the coeffi- 

 cient of variation (C) which expresses in percents the amount of 

 variation of any group of individuals for the character under con- 

 sideration. A large coefficient of variation indicates therefore that 

 the individuals are not closely grouped about the average in the 

 character measured, and consequently that the character is highly 

 variable one and vice versa. The use of an assumed integral mean 

 and then the correction of that mean by the subtraction of the 

 product of the two differences between the assumed and real means 

 ( — z''v" in formula) is merely for the sake of avoiding long frac- 

 tions and has no effect on the general result. The formula 



na or 



represents the true formula for calculating correlations, but by the 

 use of the first formula given, we get an identical result with very 

 much less labor. In this formula, of course, x' and y are the 

 deviations from the true mean of the subject and relative classes 

 respectively. 



The probable error (E) describes the probable limits above and 

 below the calculated value within which the true value lies, — the 

 absolute value being capable of determination only by an examina- 

 tion of an infinite number of cases. Thus r == .0601 ± .0086 

 indicates that the coefficient of correlation probably lies between 

 .0687 and .0515. The probable error for r is found from the formula 



0.6745 (I— r-) 

 Er = -j= 



for cr from the formula 



Ed = 0.6745 — = 

 V2n 



