202 



SCIENCE 



[N. S. Vol. XLVI. No. 1183 



classes are plotted against the number of 

 individuals in each class, the resulting 

 curve approaches the normal curve of error, 

 if a sufficiently large number of individ- 

 uals are used. Exceptional instances of 

 curves with more than one maximum, or 

 only parts of curves, are easily accounted 

 for and for convenience will be left out of 

 consideration. Since the empirical data 

 bear out the conclusions arrived at by the 

 above procedure, the explanation may be 

 considered valid. 



However, the explanation involves the 

 addition of the values of the various fac- 

 tors, which is in reality averaging them, 

 since their value is measured in terms of 

 net gain or loss. Although this process of 

 averaging the various factors involved is 

 borne out by comparing the results with em- 

 pirical data, it is done, nevertheless, in con- 

 tradiction to the Law of the Minimum. Ac- 

 cording to this law n/Z2 should be + 1 aii<i 

 31n/32 should be — 1, because all the fac- 

 tors are -|- 1 in only one permutation, and 

 : — 1 occurs in all the others and would be 

 a limiting factor. The curve that would 

 result if the Law of Minimum held would 

 start from one at the upper end of the 

 scale of sizes, weights or what not and 

 would rise with great rapidity toward the 

 lower end, where it would reach its maxi- 

 mum. This kind of curve is not the rule. 



Every case where Galton's Law holds is 

 a case where the Law of the Minimum does 

 not hold. The resultant size or weight of 

 an organism, which is a measure of its 

 growth, shows that this is not determined 

 by the limiting factor of its environment, 

 but represents some sort of average between 

 all the factors involved. In other words, a 

 process of compensation or integration has 

 taken place, the factors giving the largest 

 values being utilized to some extent at 

 least to alleviate the influence of the limit- 

 ing factor — a utilization of surplus to cover 

 deficit. Individual pi'ocesses obey the Law 



of the Minimum; but the grand total is 

 governed by what may be termed a prin- 

 ciple of integration. 



The means by which this integration is 

 brought about are not hard to find. At 

 least four important processes are at work 

 in living organisms to this effect, namely — 



1. Eesponses to stimuli, 



2. Development, 



3. Evolution, 



4. Biotie succession. 



A few examples will illustrate the way in 

 which integration is effected by each of 

 these. A seedling placed upside down is in 

 the wrong position with respect to the cen- 

 ter of the earth, its source of light, and mois- 

 ture. Position with respect to gravity may 

 be considered to be the limiting factor 

 here; but the germinating rootlet is posi- 

 tively geotropic and bends toward the 

 earth; the young shoot is negatively geo- 

 tropic and bends away from the earth. In 

 this way these responses to the geotropic 

 stimulus counteract the influence of the 

 limiting factor. Roots behave similarly in 

 response to moisture content of the soil; 

 stems and leaves in response to light. 



In plants it is hard to draw a line be- 

 tween simple responses to stimuli and 

 morphogenic responses which involve per- 

 manent changes of form and structure. 

 The difference between sun leaves and 

 shade leaves is a familiar example of a 

 morphogenic response. The shape, size and 

 structure of the leaf here counteract the 

 limiting factor light. Again, plants which 

 are shaded by others so that they receive 

 insufficient light usually become etiolated, 

 that is, the stems and leaf -petioles in many 

 cases increase in length until some por1;ion 

 of the plant is brought to a position where 

 it receives adequate illumination. Here 

 again the limiting factor is light, and the 

 result of etiolation is to overcome its effect. 



Evolution is likewise an integrating 

 process. Its results are not accomplished 



