Sept, x, 1921 
Rate of Culm Formation in Bromus inermis 
807 
DEVELOPMENT OF EQUATIONS 
In order to give this series of observations a symbolical expression it 
will be necessary to develop an equation which, when plotted, will show 
a reasonable accordance with the observations. Such an equation was 
developed according to the method of moments developed by Pearson. 1 
In the problem at hand there were 17, counting dates, and this gives us 
at once the odd number of classes required when this method is used. 
In working out the problem the first time the various counting dates 
were considered as natural numbers up to 17. The range would there¬ 
fore be 1 to 17, or, in terms of the solution, 
2/= 16, or 1 =8. 
By this method of working the problem it is seen that the dates of 
counting are spaced at equal distances, when as a matter of fact occa¬ 
sionally 6 days (one instance each of 4 and 7 days) elapsed between 
two consecutive counting dates. To attempt a correction of this error 
the range was made coextensive with the entire counting period. The 
origin of x was taken at the middle counting date and extended 42 days 
both plus and minus. The table of corrective terms for moments of 
trapezia given by Pearson 1 had to be extended for values of L t and 
L 2 , as l equaled 42 in this instance. This was easily done. Working 
the problem according to the first or non-weighted method, the follow¬ 
ing equation of a parabola of the second order was developed: 
(I) 
^=40.313 1 0.749029 4 “ 1*405701 
+ 0.752914 
The equation of a similar parabola developed according to weighted 
method was 
(II) 
^=40.313 jo.749786+1.395915 
+ 0.750641 
An attempt was made to fit parabolas of the third and fourth order 
by the non-weighted method, but with poor results. No attempts were 
made to fit parabolas of higher orders than the fourth. 
Equations I and II are seen to be very similar, and both seem to give 
quite satisfactory fittings, equation II being perhaps appreciably better. 
There was a doubtful possibility that a better fit could be secured if a 
parabola of the third order, for instance, had been obtained by the 
method of weighting, but to secure this was not possible with the calcu¬ 
lating machine at hand. 
Equation II is fitted in figure 1 to the observations as shown by the 
curve with circles. Except for the two lower and four higher values of 
1 Pearson, Karl, on the systematic fitting of curves to observations and measurements. 
In Biometrika, v. i, pt. 3, p. 265-303; v. 2, pt. 1, p. 1-23,10 fig. 1902. 
