414 ON INCREASE IN SIZE [pt. iii 



rate has in the earliest stages, e.g. five hundred and forty bilHon per 

 cent. But, as Meyer seems to have completely failed to understand 

 that Robertson and Minot were using different methods in calcu- 

 lating the "growth-rate", his criticism of Robertson was not of 

 any importance. On the other hand, he did draw attention to the 

 fact that growth-curves can be very misleading if it is not remembered 

 that, though in the early stages the absolute growth is minute, the 

 relative growth is enormous. "The weight of the impregnated human 

 ovum", said Meyer, "is approximately 0-005 ^§"^-5 ^.nd yet in- 

 vestigators in all seriousness indicate its weight on a short ordinate 

 reading in grams or even hundreds of grams. Little wonder, then, 

 perhaps, that Robertson, Ostwald, and Read have unwittingly as- 

 sumed that the curve of growth in man and mammals hugs the 

 abscissa for several months as the curve of autocatalysis does." This 

 was a good tilt at a common fallacy, but Meyer did not point out 

 that it could be remedied by using log. paper, and he left it quite 

 open to Robertson to reply that, even when strictly comparable 

 quantities were taken, the S-shaped curve or a succession of S-shaped 

 curves still resulted. 



More serious criticisms than these have, however, been brought 

 against the Robertson method of treating embryonic growth. Luyet 

 has pointed out that it may suffer more than the other methods 

 from illusory difTerences in material. Again, Murray has written 

 as follows: "(i) The formula demands the introduction of three 

 separate constants which must be separately determined for every 

 set of figures collected. (2) The equation does not give the weight 

 as a function of age throughout life but only during an arbitrarily 

 selected part of the growth-cycle. For these two reasons the 

 equation as a practical simplification is not of great value. If 

 the equation were in such a form that knowing the species, the 

 age, the T°, and other environmental variables, one might calculate 

 the weight and growth-rate, it might be of use. But as it stands now, 

 it is necessary in each case to collect complete statistics and then find 

 a mathematical expression of the figures obtained. For instance, all 

 three constants in the equation for the growth of South Australian 

 males differ from the constants used in the equation for the South 

 Australian females. As one cannot extrapolate, the formula, like the 

 man with one talent, returns what it receives. In fact as it covers 

 only a section of the growth-curve, it yields less information than the 



