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 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 08, - ft - l)/(3& - 2& + 6) = 21-7755, 

 = r/{4 + JA (r + 2)V(r + 1)) = 57-764,468, 

 b- = /*,?- (> + l)/e = (36-9391)'. 



Hence: m, = 2-0917, m. 2 =17'6838, 



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



and : 



x 



l- 



V \ 33-03207 

 To find j/ since m, is large, we use the approximation to the formula : 



N (i, + m. + 1) <r ( "" + 1 , 



...... (lxxvm)) 



i l i\ 



namely w-- (*, + i 1 +l) /OT, +m a I9\mi+mt m,) 



~ b r ( mi + 1)/(.-, ,,") v-~^- 



the evaluation of the two P-functious for m, + wi, + 1 and m a + 1 following easily 

 by Stirling's Theorem. If we write Z= r(3-0917)/{e- 8 ' 0917 (2-0917) 2 - 0917 } we have 



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

 + log 1-091 7, 

 + log T( 1-0917), 

 + 2-0917 loge. 



From Table XXXI (p. 58) we find log F (1-0917) = 1-979,8897 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 a we have : 



log y = 2-233,3936, . 



2/ =171-157. 

 Thus our curve is 



( 

 1 



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



t Phil. Traru. Vol. 186, A, pp. 367370. See also Palin Elderton : Frequency Curves and Corre- 

 lation, Lay ton Brothers. 



