59 



the actuaJly-observed result, when the number of trials is 

 fairly large. Even when the chance results are due to the 

 operation of a number of small causes, some of which can be 

 controlled (say the " loading " of the dice, or the cutting away 

 of the metal from some of the sides of a " put and take " top), 

 the theory does not fail us. When the causes of variation are 

 quite beyond our control we obtain a symmetrical curve of a 

 certain mathematical form, and most biological variation 

 curves approach more or less closely to this form (the normal 

 curve of error). Human biological inequalities (say variability 

 in stature, or in the ability to pass an examination) come very 

 close to this symmetrical form. On the other hand, social 

 inequalities (say the annual value of the house a man inhabits ; 

 the income on which he pays tax, etc.) are entirely dii^^erent, 

 for the curve of variability in such cases is an asymmetrical, 

 " J-shaped," exponential one. The meaning is that the causes 

 of wealth and poverty have come under our control, and that 

 the control endeavours to bring about the observed form of 

 inequality. 



In many of its applications (insurance and actuarial 

 calculations) the theory is sound. When it is applied to the 

 results of the study of organic variability it must also be 

 regarded as sound. Obviously, when we apply it to finding 

 out how much we are to qualify the results of taking a sample 

 of something we are also on the right lines. Now these observa- 

 tions which we study here are samples. There are some 

 millions of plaice on a certain fishing ground and we want to 

 know their average length as well as the numbers that differ 

 from the average by definite gradings above or below the 

 average. We take a sample of, say, 1,000 plaice from this 

 population and measure them and find the average and the 

 variations from the average. But we cannot be certain that 

 our sampling has been representative : some of the size-groups 

 are always over-sampled and others are under-sampled. 



