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THE AMEBIC AX XA TV 11 A 1.1 > T 



VOL.XLIII 



agreement between theory and observation be obtained. Until 

 this is tried it would appear to be impossible to form any just 

 and significant estimation, on the basis of the only kind of evi- 

 dence which Robertson presents, namely, the comparison of 

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

 growth. On many general grounds the theory is particularly 

 suggestive. Can not evidence of another and more convincing 

 kind than that adduced in the present papers be brought for- 

 ward in its support ? 



The kind of evidence under discussion, when used for a pur- 

 pose like the present one. can at best have but inferential sig- 

 nificance; it can never be of demonstrative worth. It is based 

 on a process of reasoning which assumes a fundamental or 

 necessary relationship to exist between two sets of phenomena 

 because the same curve describes the quantitative relations of 

 both sets. A little consideration indicates that this method of 

 reasoning certainly can not be of general application, even though 

 we assume it to be correct in particular cases. The difficulty 

 arises from the fact that the mathematical functions commonly 

 used with adequate results in physical, chemical, biological and 

 mathematical investigations are comparatively few in number. 

 The literature of science shows nothing clearer than that the 

 same type of curve frequently serves to describe with complete 

 accuracy the quantitative relations of widely different natural 

 phenomena. As a consequence any proposition to conclude that 

 two sets of phenomena are causally or in any oilier wav funda- 

 mentally related solely because they are described bv the same 

 type of curve is of very doubtful validity. A few examples will 

 make clear the point here under discussion. 



In a recent paper Armsby 8 shows that the rate of gain of 

 protein per thousand pounds live weight in -tow in-' animals 

 follows extremely closely the following curve : g L 135/% + 20) , 

 where g is gam m protein per day per 1,000 lbs. live weight 

 and ,/ is age in days. This curve, as his Fm. 1 clearlv shows. 



