VARIABILITY OF SUCCESSIVELY FORMED WHORLS. 



99 



(Pearson, :02) , using the corrective terms for the moments of trapezia. 

 The equations are as follows: 



Straight line, y = 0.5845 1 1 — 0.5103 (y) 



Parabola, y = 0.5845 ] 1.1084 — 0.5103 (^)- 0.3249 (q)' 



where y is the ordinate (i. e. , the probable value of (^nj^^y) and I, the 

 half range, equals 7 units. In these and all the curves which follow in 

 this section of the paper the origin of x is taken at the central ordinate 

 of the group. Both line and parabola give very reasonable graduations, 

 and until we have much larger numbers than at present it is impossible 

 to say which one gives the truer representation of the scedastic curve for 

 Ceratophyllum. What I wish to bring out now is that when we smooth 

 the observations by a graduation formula there can be no doubt that 

 the general trend of the variability is to decrease as the position of the 

 whorl on the branch, or in other words, the order of its formation, 

 increases. 



1.0 



0.9 



0.8 



0.7 



o 



+-" 



0.6 



0.5 



a3 



0.2 



0.1 



^_- 



\\ 



V 



\ 

 \ 



:: X 



\ 

 \ 



a 



l+Z 3+4 5+6 7+8 9+10 M+12 13+14 15+16 17+18 19+20 El+ZZ 23+24 



Whorls 

 Fig. 18.— Scedastic curves for primary-branch whorls of Serle.s IV. 

 Significance of lines as in fig. 17. 



Do the other series show the same relation? Treating the data given 

 in table 49 for primary-branch whorls of Series IV in exactly the same 



