370 Quantitative Analysis of Plant Growth 



Date of harvest Mass IV V II 



June 1st -268 gm. 



108 70-4 73-5 



„ 8th -559 



91 62-7 64-8 



„ 15th 1069 



Column IV shows the values given by Briggs, Kidd and West, 

 column V the values obtained from the approximate formula V, which 

 would be appropriate for the assumption of linear increase 1 , column II 

 gives the true values of formula II; for comparison all are written as 

 percentages. It will be observed that in the first instance IV is 34-5 in 

 excess of the true value, while V is 3-1 in defect, in the second instance 

 IV is 26-2 in excess, and V is 2-1 in defect. The greater part of the error 

 in IV is due to reckoning the increase upon the initial mass. 



The errors produced in this way are very irregular; for positive values 

 the rates of increase are exaggerated, for negative values they are made 

 unduly small; so that if in one week the mass is diminished, and in the 

 second it is increased to its former value, the rate of decrease calculated 

 by formula IV will be smaller than the rate of increase which has exactly 

 counterbalanced it. For very small values the formula is approximately 

 accurate. Applied to such data as those presented its irregularities 

 render it most unsuitable for statistical treatment. 



But another irregularity is introduced by Briggs, Kidd and West. 



In the words of a footnote ((4), p. 105), "Where results are not given 



for a week, we have calculated the increase per 100 gms. for the period, 



and divided the result by the number of weeks in the period." Such a 



procedure would indeed be accurate, if the true measure of relative rate 



of increase had been chosen. Its effect upon the growth rate as estimated 



by formula IV may best be shown by recalculating the growth rate in 



the above example, ignoring the value of June 8th. Then for the whole 



fortnight : 



Relative rate of increase per week 



. A 



Date of harvest Mass IV V II 



June 1st -268 gm. 



149-4 59-9 69-2 



„ 15th 1-069 



The average weekly rate of increase for the fortnight as calculated 

 by the principles of Simple Interest is thus much greater than that of 

 either of the weeks composing it. The value given by formula V, though 



1 In the case of linear increase, the relative growth rate necessarily diminishes, having 

 its highest value at the beginning and its lowest at the end of the period. Column IV 

 then shows the value at the beginning, V the value at the centre of the period, and II, 

 in this as in other cases shows the mean value over the whole period. 



