MR. K. PEARSON ON THE MATHEMATICAL THEORY OF EVOLUTION. 365 
“prevalence of extremes” may appear not only in meteorological phenomena but in 
competitive examinations, where the mediocre have occasionally sufficient wisdom to 
refrain from entering. The typeis that of Mr. F. Gatron’s curve of “consumptivity.””* 
The curve contains an interesting number of less fundamental subtypes. 
(iv.) Make a, = o in (i.), 
y= Y)(1 + w/a) e~™. 
wh 
=e >0 oo = 
This is the limit to the asymmetrical binomial, which has been already referred to 
in § 8. 
(v.) Make a, = ay, 
y = Yo (1 — */a*)™. 
<—4a4 0 2 x 
This is the symmetrical frequency curve of limited range. 
(vi.) Make v negative in (v.), 
Pata Yo i 
I= a= # ay" 
y 
———_ 7, ————> 0<-——- ———> xz 
This is a symmetrical frequency curve, with limited range, and minimum of 
mediocrity. 
(vii.) Put v = pa, in (v.) and make a, = o, 
y=yer. 
This is the normal curve. 
* ‘Natural Inheritance,’ 1889, p. 174, 
