R. A. Fisher 369 



to measure, should we be reduced to measuring it by a "purely con- 

 ventional method " which " does not pretend to mathematical accuracy ? " 

 The reasons given for this falling away are quite inadequate. It is true 

 that "to achieve mathematical accuracy," in determining the rate of 

 growth at any instant, "the increase should be measured over an in- 

 finitely short period"; it should also be measured with infinite accuracy, 

 and on an infinite sample of plants. But the discussion being devoted to 

 the quantitative analysis of such data as Kreusler supplies, it is not 

 clear what would be gained if we could determine the relative growth 

 rate with mathematical accuracy at any one instant. The environmental 

 data quoted by Briggs, Kidd and West are the Mean Temperatures for 

 the week, and in some cases the total hours of sunshine. Both of these 

 may be regarded as mean values of quantities which vary in an unknown 

 manner during the week. The corresponding quantity which we require 

 for comparison with them is the mean value of the relative growth rate, 

 which is given with mathematical accuracy by formula II. The difficulty 

 of obtaining the relative rate of increase with high accuracy at any 

 instant thus hardly justifies the complaint that "nothing more accurate 

 can be obtained" than a "purely conventional method," which in fact 

 introduces errors up to 100 per cent, or more ! 

 For the Simple Interest formula employed 



ioox m *~ m f \ (iv) 



is extremely inaccurate in relation to the data to which it is applied. 

 The principal cause of this inaccuracy is that the dry mass of the active 

 plant is assumed to have throughout the week that value that is assigned 

 to it at the beginning of the week. It often happens that during the 

 week the mass has more than doubled; in such cases the relative rate 

 of increase is much exaggerated by reckoning the increase on the initial 

 mass. This error has nothing to do with the assumption of linear in- 

 crease, for if the rate of increase during the week be assumed to be 

 linear, the mean value of the mass for this period will be 



\ (m x + m 2 ) 

 and the rate of increase reckoned on this mean mass, gives a much 

 better approximation. The formula obtained in this way 



100 x 2 («i ~ %) (V ) 



(m 1 + m 2 ) (t 2 - t x ) v 



is compared with that of Briggs, Kidd and West in the following 

 example ((4), p. 107). 



