146 THE QUANTITATIVE METHOD IN BIOLOGY 



the central ordinate m ^ is, indeed, the highest one : it corre- 

 sponds to the so-called summit or hump of the curve. The 

 successive ordinates become shorter in proportion as they are 

 farther from the centre. In other words, the positive as weU 

 as the negative errors (deviations from the mean value) become 

 less numerous in proportion as they are greater. The curve 

 is symmetrical : the positive and negative errors are equally 

 numerous. 



Each error, considered in isolation, depends on chance, and 

 may be looked upon as being accidental. When we consider. 



4-84 



VI 



Fig. 1 8.— Curve of errors (a + 6) i<^ 



5-16 



however, all the errors at the same time as a whole, we see that 

 their distribution (among the eleven groups) is governed by a 

 definite rule. According to experience, the length of the succes- 

 sive ordinates is approximately proportionate to the^^numerical 

 values of the terms obtained by expanding {a + h^, in which 

 a = h = \. If we suppose n=io, we obtain ii terms — viz. 



a 



1^ + loa^b + 45^^62 ^ i2oa'^¥ + 2io^^Z>* + 2^2a^h^ + 

 2ioa^b^ + 120^^6^ + 45^2^8 + loab^ + b^^ 



The numerical value of each term is given by its coefficient 

 divided by 21^ = 1024, thus ^^^, yifj, etc. 



^ The length of the central ordinate represents the number of measurements 

 from 4*99 to 5'oi. The mean is 5*00. 



