44 NATURAL INHERITANCE. [chap. 



The Shape of Schemes is Independent of the Number 

 of Observations. — When Schemes are drawn from dif- 

 ferent samples of the same large group of measurements, 

 though the number in the several samples may differ 

 greatly, we can always so adjust the horizontal scales 

 that the breadth of the several Schemes shall be uniform. 

 Then the shapes of the Schemes drawn from different 

 samples will be little affected by the number of observa- 

 tions used in each, supposing of course that the numbers 

 are never too small for ordinary statistical purposes. 

 The only recognisable differences between the Schemes 

 will be, that, if the number of observations in the 

 sample is very large, the upper margin of the Scheme 

 will fall into a more regular curve, especially towards 

 either of its limits. Some irregularity will be found in 

 the above curve of the Strength of Pull ; but if the 

 observations had been ten times more numerous, it is 

 probable, judging from much experience of such curves, 

 that the irregularity would have been less conspicuous, 

 and perhaps would have disappeared altogether. 



However numerous the observations may be, the 

 curve will always be uncertain and incomplete at its 

 extreme ends, because the next value may happen to be 

 greater or less than any one of those that preceded it. 

 Again, the position of the first and the last observation, 

 supposing each observation to have been laid down sepa- 

 rately, can never coincide with the adjacent limit. The 

 more numerous the observations, and therefore the closer 

 the perpendiculars by which they are represented, the 

 nearer will the two extreme perpendiculars approach the 



