174 THE QUANTITATIVE METHOD IN BIOLOGY 



mined specific constant. Suppose the panicles of a number of 

 specimens, collected from various places, have been measured, 

 and that the longest one has a length of 119 mm.^ This value 

 is the measure of the greatest possible length which the hving 

 mixture of Poa annua is able to produce when the combination 

 of aU the external factors is as favourable as possible ; in other 

 words, when the resultant of the combined factors is optimal. 

 Since the maximal effect of each factor (considered separately) 

 does not coincide with its maximal value, but with its optimum, 

 the effect of any combination whatever cannot exceed a certain 

 determined maximum. 



This conclusion is confirmed by daily observation. 



We know from experience that a given property of a given species never 

 exceeds a certain value. The length of a leaf of Qiiercus pedunculata, the 

 number of marginal teeth of a leaf of Castanea vesca, the number of cells of a 

 hair on the leaves of Primula sinensis, the length of the tibia of a horse or the 

 tail of a cow, the weight of a potato, the breadth of a petal of Ranunculus acris 

 never exceed a certain figure, however favourable the conditions of existence 

 may be, whatever may be the efforts of the gardener or the breeder. 



When a vegetable species is brought under CULTIVATION 

 it often happens that the new combination of external factors 

 is, on the whole, nearer the optimum (with regard to a given 

 property) ^ than the combination which is the most frequent in 

 the state of nature. The mean value may therefore be aug- 

 mented, and it is also possible that the highest observed value 

 becomes greater. I think, however, that if numerous wild 

 specimens collected from a wide area and developed under 

 various conditions had been measured, the obtained maximum 

 would be hardly or not inferior to the maximum which might 

 be obtained from cultivated specimens. In this question, any 

 conclusion drawn from a mere impression must be distrusted : 

 it is only by measuring each primordium separately that exact 

 information can be obtained. (Compare § 23.) 



When the maximum of a primordium has been determined 

 by the measurement of numerous (wild and eventually culti- 

 vated) specimens, it is possible that a higher maximum is found 

 by more observations. In this occurrence the specific constant 

 is to be corrected, and this may be repeated several times. 

 Many physical and chemical constants have also been corrected 

 step by step. After each correction of a biological constant 

 we are brought nearer exactitude, and the probability of a new 

 correction and its probable importance become smaller.^ At 



1 This is the figure I have found. According to J. D. HOOKER, the maxi- 

 mum is 3 in. =76 mm. 



2 It is possible, of course, that the reverse happens if the conditions of 

 existence are less favourable under cultivation than in the state of nature. 



^ Because we are approaching more and more the extremity of the curve 

 of frequency (Fig. 24) . 



