XII] 



lxx\i\ 



Let the- figure represent a Gaussian curve of total area N, and standard di*via- 

 linn <r. Let AH bu the onliimtc at which it is truncated and let OB= It, -//. 



Then N, h', and o- fully define the required normal curve; they must be found from 

 constants of the shaded portion BADGE. Let G be the centroid at abscissa OH of 

 this portion, and suppose EH = d,n = area of shaded portion and 2 = standard devia- 

 tion of this portion about GH, the centroid vertical. Then n, d, 2 are known or 

 can be found from the observed data. We have three "Gaussian tail functions," 

 ^i = 2 2 /^ 2 , ^2 = o-jd, and i/r 3 = N/n. 2 and d being known from the data, we know 

 I/T!. Table XII then gives us h' t which enables us to find -^ 2 and ^ 3 ; the former 

 gives us <r and the latter N. A knowledge of h' and a- gives us h or OB, which 

 determines the mean of the required normal curve. Thus the problem is completely 

 solved. 



Illustration. The following frequency distribution f consists of the measure- 

 ments of the diameter of the head of the femur in 279 bones, without regard 



to sex : 



Now DwightJ terms any femur with head less than 45 mm., female, and any 

 femur with head greater than 47 mm., male. Measurements on the head of the 

 femur for a single sex distribute themselves very nearly normally. Dwight and 



* h and h' arc actually of opposite sign to those in Part i. 



t Journal of Anatomy and Physiology, Vol. XLVIII. pp. 238 267. 



American Journal of Anatomy, Vol. iv. p. 19. 



B. II. 





