272 
Proceedings of the Royal Society of Edinburgh. [Sess. 
fessor Pearson, but it is much simpler in the case of plant life. We have to 
deal with the integral 
y = a 
/. 
oo - 2(a H-Q 
h 
dt 
y= 
, mm 
Ka —cr 
Application of this will be given. 
(5) Secondly, the form 
y = a 
fx+c f c 
dx 
Jx-c Jo 
, X 2 
~ — ~y <r 
cr n e <r " da 
may be considered. In this the distribution of frequency of a is taken as 
cr n+2 e~y <r . The moments are easily calculated, and are given by 
A — 2c /- T ( n + 2 ) 
1 n + 2 
Vl y 
u - c2 4- ('* + 3)(” + 3 ) 
3 2y 2 
_ c 4 c 2 (?z + 3)(?z. + 2) 3(w + o)(w + 4)(w + 3)(w + 2) 
^4 ~ e 2 + 4 
5 y 2 / 
These equations are solved most easily if c and n be eliminated. This 
gives, if 2 Jirv 1 is denoted by f, 
1444+ 
2 y 6 0 y- 
1 2 t 3 + + ( -ir ^ 2 + ttM 2 - _ ^4 ) = °- 
The rest of the solution is easy. I have not been able to arrive at the 
curve without mechanical quadrature. In the instance in which it has 
been fitted (Diagram III.) it proves exceedingly unsuitable, and it is there- 
fore evident that the form discussed cannot represent the distribution of 
a even approximately. 
Asymmetry. 
(6) Asymmetry in the epidemic curve deserves some notice. As we 
found before, 12ILP must in general be equal to a constant, as the epidemic 
is symmetrical. If, however, |°g P_ [ s a function of a it majq on account of 
the near symmetry of the epidemic, be assumed that it can be expanded in 
terms of a of a rapidly convergent nature so that all the terms in the 
expansion except that of or may be neglected. 
