R A. Fisher 371 



not so ridiculously discordant, shows that the error of this formula 

 increases rapidly as the time interval is increased, that of formula III 

 alone gives a concordant result, being the mean of the values of the two 

 component weeks. 



This example brings out a point in the utility of II which is worth 

 noting. It illustrates the fact that growth rates calculated by II may 

 be expressed at once in any unit of time, irrespective of the intervals 

 employed experimentally. In general it is most suitable to use the day 

 as the unit, and for this purpose the values in column II need only be 

 divided bv 7. For the values of IV a dilemma arises; according to the 

 method of correction quoted above, they also should be divided by 7, 

 although this would lead to values inconsistent with any possible daily 

 increases in weight; the only self-consistent method would be to reckon 

 the interest payable daily on the principles of compound interest, and 

 this if performed by the use of logarithms amounts to calculating the 

 value of column II from that of IV, dividing by 7, and then finding the 

 corresponding value of column IV. This process should be in itself of 

 considerable educative value in the study of these different methods of 

 measurement. 



These being the facts, it remains to enquire how it was that with 

 Blackman's work before them, and knowing that the efficiency index 

 had been successfully applied (2), the authors of (4) chose to employ so 

 inaccurate a method of calculation. The point is dealt with in the 

 following passage ((4), p. 106). 



"It might be suggested that allowance could easily be made for the continuous 

 increase in dry weight during the week by assuming that this takes place at a uniform 

 rate, and consequently that by means of the following logarithmic formula the rate 

 could be determined: 



log W - log W„ = r, 

 where W is the dry weight at the end of the week, and W the dry weight at the 

 beginning of the week. 



In curve A, Fig. 1, this allowance has been made. In curve B, the ordinates are 

 relative growth rates calculated by our method, that is, without making allowance 

 for the continuous increase during the week. The curves show similar variations of 

 growth rate from week to week. The more complicated method, however, does not 

 achieve accuracy, as it rests on the assumption that the rate remains constant during 

 the week, an assumption manifestly incorrect since the rate varies from week to 

 week. Both methods are purely conventional and only approximate to accuracy, and 

 nothing definite is to be gained by adopting the more complicated procedure." 



At first sight one might judge from this paragraph that the two 

 methods of calculation had been judged to be practically equivalent by 

 an inspection of the diagram referred to, but a glance at that diagram 

 is sufficient to show that this cannot be so, for while the disagreement is 



