274 



Prof. K. Pearson. On a Criterion which may [Mar. 4, 



or, since x does not exceed 2 to 3 oy we have for the part of the 

 parabola involved very nearly the straight line 



tyri* >/f(l+A|) (xviii).. 



This, substituting the values of <r c and oy, is a straight line of slope 

 0*021. Now the best fitting line to the observations, A' A', has a 

 slope of 0'022, or we conclude that the Mendelian parabola is when the 

 number of couplets is as large as in the present case sensibly parallel 

 to the line which best represents the variability of the arrays plotted 

 to the parents' character. The Mendelian line B'B' of Diagram I 

 is not as good a fit as the line AA, because the theory constrains it 

 to pass through the point given by <r 8 = >J '(8/ '9) o- c , and not through 

 the actual mean point <r c J (I -rf c 2 ). This is owing to the fact that 

 the Mendelian theory gives iy c constant and equal to 1/3. Hence, we 

 see that the Mendelian theory will not, as a rule, give as good a fit 

 to the observations as the best fitting line, when the number of 

 couplets is large as in this case and the correlation differs from 1 /3. 

 The parabola thus sensibly coincides in direction with the best fitting 

 straight line, but is raised above it in position. 



I give the best fitting straight lines for the three characters we have 

 been considering 



For Span — 



y-T-762 = 0-011 (a;-67"-396). 

 Probable error of the slope 0*011, equals 0*013. 



For Stature — 



y-rSU = 0-022 (a?-67'"-686). 

 Probable error of the slope 0-022, equals 0*0 13. 



For Forearm — 



y-r-773 = - 0-003 (£-18"-279). 

 Probable error of the slope - 0*003, equals 0*009. 



Thus, of the three slopes all differ by less than twice and two of 

 them by less than once their probable error from zero. We may 

 accordingly conclude that neither in the best fitting straight lines, 

 nor consequently in the Mendelian parabolas for the measurable range, 

 is there any sensible deviation from horizontality. In fact we have 

 48 couplets in the case of stature, and roundly 150 for span* and 

 2000 for forearm. With such numbers the Mendelian theory cannot 

 on the problem of variability of arrays give any other sensible answer 

 for the range available for investigation than the constant variability 



* If the Mendelian theory discussed were correct, it would, be difficult to grasp 

 how the forearm-inheritance could be determined by far more couplets than the 

 span is, or why one slope should be negative and the other positive. 



