Ill] THE CURVE OF ERROR 131 



that correlation tends to be closest, or a norm to be most nearly 

 approached*. 



The whole subject of variabiHty, both of magnitude and rate of 

 increment, is highly suggestive and instructive: inasmuch as it 

 helps further to impress upon us that growth and specific rate of 

 growth are the main physiological factors, of which specific mag- 

 nitude, dimensions and form are the concrete and visible resultant. 

 Nor may we forget for a moment that growth-rate, and growth 

 itself, are both of them very complex things. The increase of the 

 active tissues, the building of the skeleton and the laying up 

 of fat and other stores, all these and more enter into the complex 

 phenomenon of growth. In the first instance we may treat these 

 many factors as though they were all one. But the breeder and 

 the geneticist will soon want to deal with them apart; and the 

 mathematician will scarce look for a simple expression where 

 so many factors are involved. But the problems of variability, 

 though they are intimately related to the general problem of 

 growth, carry us very soon beyond our hmitations. 



The curve of error 



To return to the curve of error. 



The normal curve is a symmetrical one. Its middle point, or 

 median ordinate, marks the arithmetic mean of all the measurements ; 

 it is also the mode, or class to which the largest number of individual 

 instances belong. Mean, median and mode are three diiferent sorts 

 of average; but they are one and the same in the normal curve. 



It is easy to produce a related curve which is not symmetrical, 

 and in which mean, median and mode are no longer the same. 

 The heap of corn will be lop-sided or "skew" if the wind be blowing 

 while the grain is falling: in other words, if some prevailing cause 

 disturb the quasi-equihbrium of fortuity ; and there are other ways, 

 some simple, some more subtle, by^ which asymmetry may be 

 impressed upon our curve. 



The Gaussian curve is only one of many similar bell-shaped curves ; 

 and the binomial coefficients, the numerical coefficients of (a + by, 

 yield a curve so Hke it that we may treat them as the same. The 



* Cf. Joseph Bergson, Growth -changes in physical correlation, Human Biology, 

 I, p. 4, 1930. 



