XII XIV] Introduction \<-i 



It is clear that the present process gives means and standard 1 

 both sexes exceedingly close to the results that may be deduced from Parsons' 

 anatomical MKUIg. l'ut the total number of femora is 8-5 short, i.<-. 103-9 -- 166'6 

 = 270-5 instead of 279. This is sufficient to indicate that taking all fi-mnni with 

 cliainrtiT of head under 44'5 as female and all with diameter over 47'5 as mal.-, is 

 nnt very satisfactory. 



If we treat the total frequency of 279 femora by the method of Phil. Trans. 

 Vol. 185, A, p. 64, and break it up into two normal curves, we find the following 

 results : 



Male Female 



Mean 49'83 mm. 4372 mm. 



Standard Deviation 2'23l 2-662 



Frequency 13325 145?:. 



This suggests that the female distribution extends much further into the 

 region beyond 47'5 than Dwight's rule permits, thus raising both the male and 

 female means, and increasing the female standard deviation while lessening that of 

 the male. 



The chief weakness of the method represented by Table XII beyond the 

 often quite legitimate assumption of a normal distribution lies in the absence, 

 as yet, of the values of the probable errors, which values, especially in the case of N, 

 must be very considerable for slender data such as those used in our illustration. 



TABLE XIII. 



The, llth and I2th Incomplete Normal Moment Functions. (E. M. Elderton and 

 J. Wishart.) 



This table carries to the llth and 12th orders the table of Incomplete Normal 

 Moment Functions to be found in Part I of this work (Table IX, pp. 22 23). The 

 normal moment functions are useful for a variety of purposes. Chief among these 

 may be noted the determination of the area of the curves 



I/ -JJ &%/& I ft _,, /yV? QTlfl Ql I/ "7*P (\ t* rl 



(f "/O V ^^ J C*llv4 U WQ *c I JL w I 



for ranges round the mode not exceeding a distance from the mode of 1 to 1'5 

 times the standard deviation. 



Illustration of the use for m-& will be found in the section of this Introduction 

 dealing with the evaluation of the Incomplete B-Function for high powers. 



TABLE XIV. 



Values of {3 3 , $ 4 , /3 5 and y3 6 in terms of @i and # 2 > on the assumption that the 

 Frequency falls into one or other of Pearsons Types. (Kazutaro Yasukawa, Biometrika, 

 Vol. xvin. pp. 268275.) 



This table is a much extended form of that provided by Rhind and reissued as 

 Table XLII of Part I of this work. For more exact work it .should be used in 

 preference to that table. The purpose of both tables is to obtain approximate values 



