312 



THE AMEBIC AX XATU EALlsT [Vol. XLITI 



examine some of the tables given. Table I of the first paper 

 (pp. 581-591) deals with Donaldson's 6 data on the growth of the 

 male white rat in respect to body weight. In this table are given 

 the observed body weights for rats of different ages and the 

 calculated body weights according to the autocatalytic growth 

 curve. In addition there is given a column showing the differ- 

 ences in grams between the observed and the calculated body 

 weights. Now it is a first principle of scientific curve fitting 

 (and on this point science and common sense are as usual in 

 agreement) that a curve which gives a good graduation of 

 observational data will fairly and equably distribute the errors. 

 That is to say, a theoretical curve if it is to be regarded as 

 fitting the data should strike through the observations in such 

 way that there will be on the average as many and as great 

 differences where theory is in excess of observation as there are 

 where it is in defect of observation. If a great majority of the 

 differences between theory and observation are in one direction 

 there is clearly a bias and the theoretical curve can not fairly 

 be said to be an adequate representation of the observations. 

 Now, let us examine the actual facts for Robertson 's Table I. In 

 this table are included 63 separate observations or ordinate*. In 

 one case out of the 63 the theoretical and the observed ordinate 

 exactly agree. Of the remaining 62 cases where theory and 

 observation can be compared the calculated ordinate is greater 

 than the observed in only 14. The observed ordinate is greater 



than the calculated : 



; of the 62. Furthermore, the 



total deviation between observation and theory when theorv 

 greater than observation is 19.6, whereas when observation is 

 greater than theory the total deviation is 706.0! This certainly 

 does not look like a fair distribution of the errors when in 77 

 per cent, of the ordinates the theoretical curve lies always on 

 the same side of the observational line. 



Let us turn to Table II. This table is exactly like Table I 

 except that it deals with Donaldson's data for the growth of 

 female white rats in body weight, whereas Table I deals with 

 the males. In this table there are in all 50 ordinates. Of these 

 one again shows an exact agreement between observation and 

 theory. In 43 or 88 per cent, of the remaining 49 ordinates the 

 calculated value is less than the observed. Only in 6 cases is 

 the calculated value greater than the observed ! Practically the 



9 Boas Memorial Volume, New York, 190G. 



