XXXV— XLVI] Introduction Ixix 



start at zero*, but the vagueness of what is meant by ' percentage of black ' as a 

 factor, when the entire pigmentation of tlie skin probably arises from a single 

 melanin pigment, only varying in concentration in the pigment granules and in 

 the density of granules themselves. We have therefore contented ourselves by 

 fitting a Type I curve, as further illustration of the use of the tables in the 

 present work. The theory of fitting is given in the paper cited below f. Following 

 the usual notation we find : 



r = 6 (;8, - /3. - l)/(3/3, - 2,8, + 6) = 21-7755, 



e = rV{4 + i/3, {r + 2)V(r + 1)1 = 57-764,468, 



h"- =/i,r-(y+l)/6 = (36-9391)1 



Hence: m, = 2-0917, mo= 176838, 



a, =3-9071, rt, =33-0320, 

 and : 



^"^"1^ + 3^9071) V ' 33032oJ 

 To find 2/o since iiu is large, we use the approximation to the formula: 



r (j/(,i + Hi, + 1 ) 



N {rih + m.,+ \) ]e-(""+"'--:)(7Hi + ?».,)" , 



Vo = T „ . , ,, X =77 7-^^ (IXXVIU), 



{' 



e~ '"'^ ?*i»"'2 



1/1 i\ 



namely, 'A = 7- t^ , ' ,/ 1 \/ —^ — e ...(xxix) 



•^ -^ h r (m, + l)/(e-"'. wi,'"') V ,„, "^ ^ '' 



the evaluation of the two T-functious for m^ + du + 1 and wi, + 1 following easily 

 by Stirling's Theorem. If we write Z= r(3-0917)/(e-'-»»i" (2-0917)-^-"'"'} we have 



logZ= log 2-0917 -2-0917 log 2 0917, 

 + log 1-0917, 

 + log r (1-0917), 

 + 2-0917 log e. 



From Table XXXI (p. 58) we find log F (10917) = T-979,8897 and loge is 

 given by Table LV (p. 143). Hence we determine, log Z= -576,5176. Evaluating 

 the rest of the expression for log y, we have : 



log 2/0 = 2-233,3986, ' 



2/0=171-157. 

 Thus our curve is 



/ ^ \ 2-0(117 / ^ \ 17.6838 



2/ = 171-157 (l + 3,g^^-j) (1-33.0320) 



* For method, see Phil. Trans. Vol. 186, A, pp. 370, 371. 



t Phil. Tram. Vol. 186, A, pp. 367—370. See also Palin Elderton: Frequency Curves and Corre- 

 lation, Layton Brothers. 



