244 Prof. K. Pearson on certain Properties 



Thus the mean is : 



2-498,5484; 



and transferring moments to this mean, we have 



^2 = 1-564,0839, 

 ya 3 = -530,4806, 

 ^=7*074,6464, 

 ^ = 7-903,2620; 

 and 



/3 X = -073,5460, 

 &= 2-891,9091, 

 /3 3 = 9'525,2597. 



Substituting in (32) we find 



n = 65-203,378. 

 Hence by (33) 



^ = 451,811-067, 

 and (34) 



^ = 2839-1404. 

 Thus 



S 2 - 2839-1404?+ 451,811-067 = 0. 



This leads to 



m 2 = 169-2229, 



6 = 2669-9175. 

 Whence by (36) 



mj=— 26-85115. 

 Thus (37) is now 



? 2 + 26-85115f+169-2229, 

 and 



a= -10-10546, 



/3= -16-74569. 

 Then from (40) we find 



c=-972077, 

 and from (41) 



d=2'5229. 



Thus we conclude that the frequency may be represented 

 by a hypergeometrical series of which the start is *0244 before 

 zero occurrence, the base unit is '9721, and the mean is at 

 2-4985. Further, from (39) 



r= 10-1055, 

 jt> = -7432, £ = -2568; 



or 



j9tt=48-4577, ^=16-7457. 



Further, we conclude that the range .of frequency cannot be 



