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



the relation thus predicted is only one among t an infinite number 

 of relations which might be written down haphazard. Among an 

 enormous number of chance relations or formulae which might be 

 written down, only one or two would be found to represent, even 

 approximately, the experimental relations observed. If, therefore, 

 a relation which is deduced from theoretical considerations repre- 

 sents even approximately the experimental relation, the probabilities 

 are enormously in favour of the theoretical considerations being 

 correct, since it is excessively unlikely that a formula chosen by 

 chance will represent, even approximately, the given relation between 

 the variables. 



The degree of approximation to the experimental relations 

 which we demand as evidence of the probability that our theo- 

 retical assumptions are valid depends upon the nature of the variables 

 under consideration and upon the simplicity or complexity of the 

 relations subsisting between them. Thus we demand a much 

 greater precision of agreement between theory and experiment in 

 an astronomical problem, where the variables are few and can be 

 measured with the utmost precision, than in a biological problem, 

 where the variables are many and diverse and can be measured 

 only with approximate accuracy owing to the non-homogeneous 

 character of our experimental material. 



In a recent paper Pearl 4 ) has raised the objection that in 

 many of my comparisons between the theoretical and experimental 

 curves of growth the experimentally determined curve lies to a 

 greater extent on one than on the other side of the theoretical 

 curve. This objection of Pearl's would be a perfectly valid one 

 provided (I) that there were no systematic errors in the experi- 

 mental determinations (II), that there were no disturbing factors 

 such as deposition of fat, senile decay etc. and (III) that the con- 

 stants of the theoretical curve were computed from the experi- 

 mental determinations by the method of least squares. Not one 

 of these conditions is, however, fulfilled in the present investigation, 

 and Pearl's criticism is therefore deprived of its value. It is a 

 complex and excessively tedious matter to compute constants in 

 a transcendental equation by a least squares method and the com- 

 putation, unless the experimental determinations attain the greatest 

 precision, is a very uncertain one. Having regard to the innac- 

 curacy which necessarily attaches to quantitative determinations 

 upon living material, when these are not carried out in a strictly 

 statistical manner upon an enormous number of individuals all 

 under like conditions, it did not appear to me worth while to 

 expend the amount of labour necessary to secure a probably fictitious 



4) Raymond Pearl ,,Biometrics", The American Naturalist, 43 (1909), p. 302. 



