MODERN THEORIES OF HEREDITY. 



377 



to the nearest inch, we shall find the largest number are 69 

 inches high, and that the next largest numbers are 68 and 66 

 inches, and so on, the total range of variation being from about 

 62 inches to about 76 inches or a little more. The curve is 

 shown in Fig. 4 by a continuous line with the mode (M) and 

 the quartiles (O and Q'). 



M' Q 



Q'M" 



1-ig- 4- 



Now, since a greater degree of variability will obviously 

 cause a flatter cnvvc, it will increase the quartile, hence the 

 quartile is a measure of the variability of a character. It is also 

 equal to what is known as the " probable error." P)y this is 

 meant that distance from the mode at which it is an even chance 

 whether any individual shows a character value inside or out- 

 side this distance; i.e., in Fig. 4, it is an even chance whether 

 any one man's height lies between about 67 and about 70^ inches 

 or outside of those values. The chances against the character 

 value lying outside tzcicc these limits is a little more than 4 to 

 I n.e., it is about 5^ : i that a man's height will lie between 

 65 and 72 inches). The chances against 3 times the probable 

 error are more than 20 : i, against 4 times, nearly 150 : i. and 

 for more than 4 times they are negligible. 



Such curves, therefore, provide a very valuable means of 

 dealing with statistics. Now, if the 1,000 men whose heights 

 were measured each had one son, i: will be easy to see whether 

 height is an inherited character, and if so. to what extent. To 

 show this we take all the sons of the fathers who were 62 

 inches high, and construct an exactly similar curve for their 



