XXXV — XLVI] Introduction lxix 



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

 factor, when the entire pigmentation of the 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 (& - /?, - l)/(3ft - 2ft + 6) = 21-7755, 

 e = r 2 /{4 + J/3, (r + 2) 2 /(r + 1)} = 57-764,468, 

 & 2 = A M- 2 (r+l)/e = (36-9391) 2 . 



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



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



an 



(1 



(g. \ 2-0917 / g. \17.683S 



1 + 3^9071/ I 1 " 3¥032()J ' 



To find y since m* is large, we use the approximation to the formula: 



f r(» tl +w 2 +l ) | 



N(rn 1 + m i + 1) 1e _ < Ml+m °->(mi + inS m ^ lll *\ 



ro»._+i). (lxxvm >' 



V* = 7, r, m , iu x 



6 



r (m, + i)i 



1 to," 



...(lxxix) 



1/ 1 l\ 



namelv -^ (m 1 +m 2 + 1) /to, + to 2 12 \m, + m 2 raj 



" y ° 6 T (to, + I )/(«-"' m,"') V ^ ~ e 



the evaluation of the two T-functious for to 2 + in* + I and to 2 + 1 following easily 

 by Stirling's Theorem. If we write Z = r(3-0917)/{e- M917 (20917) 20917 } we have 



\ogZ= log2-0917 -2-0917 log 2 0917, 

 + log 1-0917, 

 + log T (1-0917), 

 + 2-0917 loge. 



From Table XXXI (p. 58) we find log T (1-0917) = T'979,8897 and log e 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/ = 2-233,3936, 

 2/„=171157. 



Thus 



our curve is 



(m \ 20917 / <r \ 17-6838 



1 + 3-90-71 i l ~ 33^320 



* 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. 



