54Q 



SCIENCE PROGRESS 



This is the hypergeometrical series and we have to deduce a 

 series of curves from it in the same way that the curves men- 

 tioned above were deduced from the symmetrical and skew 

 binomial series. 



Fig. 2. 



Let the graph of the symmetrical binomial expansion 



( — I — J be as above. The slope (or rate of variation of y 



with respect to x) is given (for the mean ordinate ed) by 

 the ratio bc/ab. The non-mathematical reader may then be 

 able to puzzle out for himself (he will have to do so anyway, 

 since the mathematicians omit the steps as obvious) that 



slope 2 x mean abscissa 



mean ordinate 2 (standard deviation) 3 



and this relationship may be reduced to 



I^= _ * (1) 



y Bx Co' 



Co being a constant. 



In the same way it can be shown that we have for the 

 series of skew binomials 



yhx 



x 



Co + Cix' 



(2) 







