MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 2 1 J1 



it gives 30 per mille instead of 10 per mille with no glands. These difficulties are 

 entirely met by the skew curve, which gives no frequency whatever of negative 

 glands (see figure). 



Taking the number of glands in the right fore-leg of female swine, we have the 

 frequency series : 



We have worked with the frequency per mille for convenience of reduction, 

 although the actual number of observed cases, 2,000, is used, of course, in the 

 determination of the probable errors. 



Using the method of the paper in the ' Phil. Trans.,' A, vol. 186, p. 367, we found 



mean = 3'501 glands. 

 Hz = 2-824,999 

 /*,= 2-417,278 

 j* 4 = 24-826,297 



6-f 



0-= 1-680,774 

 /8, = 0-259,1825 

 &= 3-110,8211 

 ?, 2/3 2 = 0-555,905 



Thus the criterion is greater than zero, or the frequency distribution is of Type I., 

 or has a limited range. 

 Proceeding we found 



r= 19-985119 

 m l = 3783718 

 a, = 3-79623 

 I = 18-0446 

 d = 0-522996 

 Mode = 2-978 



e= 72-71918 

 m, = 14-201402 

 a, = 14-24837 

 y = 237-263 

 Sk. = 0-311164 

 Start of curve = 0*818 gland. 



Thus it would appear that both the distance (d) from mean to mode and the 

 skewness are very sensible, and that, unless their probable errors be very large, it is 

 quite impossible to represent the results by a normal curve. 



We may note that the range starts from - 0'818 gland and runs to 17'227 glands, 

 so since it gives zero at 1 gland, we see that it sensibly confines the possible 

 number of glands between and 17, but we should have to examine considerably 

 more than 2,000 swine to have a probability of more than 10 glands occurring. The 



2p2 



