Robertson, Explanatory Remarks concerning the Normal Rate of Growth etc. 319 



appearance of precision 5 ). One instance to which Pearl points 

 with emphasis is not chosen fairly. The instance in question is 

 one (Table I in my first paper, cited above) in which the total deviation 

 from theory is very large (642) when the observed ordinate is 

 greater than the calculated ordinate. and only small (19.6) when 

 the observed ordinate is less than the calculated ordinate. Pearl 

 omits to mention, however, that 578 of these units of total deviation, 

 when the observed ordinate is greater than the calculated, occur 

 in a portion of the particular curve of growth under consideration 

 to which, as is expressly stated in my paper, my equation does not 

 apply. Possible reasons for this lack of agreement are adduced in 

 the text accompanying my table; from Pearl's statement one would 

 gather the impression that I regarded this part of the experimental 

 curve as lending confirmation to the theory. 



The remarks put forward above in relation to Enriques' 

 criticisms also apply, it is needless to say. to the criticisms formu- 

 lated by Pearl. 



Towards the conclusion of his remarks concerning my publi- 

 cations Pearl states that ,,it would appear to be impossible to 

 form any just and significant estimate, on the basis of the only 

 kind of evidence which Robertson presents, namely the com- 

 parison of curves, as to the value of his theory as a general theory 

 of growth . . . Can not evidence of another and more convincing 

 kind than that adduced in the present papers be brought forward 

 in its support?" Pearl has evidently overlooked Ostwald's paper 



5) It may be mentioned, in passing, that Pearl cites, in his criticism, only 

 those comparisons in my paper which utilise, as experimental data, the observations 

 of Donaldson upon white rats and upon the growth of the brain in the frog. 

 Pearl says ,,The tables which have been chosen as illustrations of the point under 

 discussion have been taken in preference to others for two reasons; one that they 

 were long tables, involving a fairly large number of ordinates, the other that the 

 observational data in these tables were obtained by most careful and painstaking 

 measuring and are absolutely trustworthy. On such data, if anywhere, a theoretical 

 curve may fairly be expected to give good results." Without for a moment calling 

 in question the accuracy of the measurements I nevertheless cannot agree with Pearl 

 that ,,on such data, if anywhere, a theoretical curve may fairly be expected to give 

 good results." We are dealing with living, that is to say with excesyively variable 

 material in other words, for example, the constants A, K und t, in the curve of 

 growth differ widely in different individuals. Xo matter how precise our measure- 

 ments may be, trustworthy results possessed of physico-chemical meaning can only 

 be obtained if the determinations are performed upon a very large number of indi- 

 viduals so that the mean group of individuals can be accurately ascertained and the 

 growth of the mean individual accurately followed. Now Donaldson's deter- 

 minations were carried out upon only 19 individuals and the individual departures 

 from the average weight frequently amounted to from 30 to 50/ of the average! 

 T consider that the determinations of the curve of growth in human beings, cited 

 in my first paper, probably come most near to satisfying the requirements enumerated 

 above, and in these, although the conditions are exceptionally complex, since there 



