MEASUREMENT OF VARIABLE PROPERTIES 175 



the end the error will be as small as the unavoidable errors of 

 measurement. 



In order to discover the extreme values (maximum and 

 minimum) of a primordium it is not always necessary to 

 measure very numerous specimens. The value of many pri- 

 mordia may be roughly estimated without any instrument. In 

 all such cases we may content ourselves with collecting and 

 measuring, among a large number of individuals (in each 

 locality or spot), the specimens which approach the limits. 



§ 120a.— MINIMAL VALUES.— The minimal value of a 

 primordium may be looked upon, with certain restrictions, as 

 being a constant of the species. The lowest value of a pri- 

 mordium p coincides with the most unfavourable (pessimal) 

 combination of external factors under which its existence is 

 possible. The resultant of the pessimal combination is, of 

 course, a critical value, just as the limits of each factor con- 

 sidered separately. (See p. i68.) On the other hand, the 

 value of p at the beginning of its development is ordinarily 

 very small, practically not different from zero. If the prevail- 

 ing combination of factors is only a httle better than the pessi- 

 mum, the growth of p is stopped in a very early state, when its 

 value harcfly exceeds o. If the combination of factors is more 

 vmfavourable than the pessimum, p does not come into exist- 

 ence, which is expressed by the value o. In both cases the 

 value of p is practically o. This value being the same for very 

 numerous primordia of innumerable species, the minimal 

 value of a primordium is, in general (no restrictions being 

 made), deprived of any specific significance. 



This conclusion is confirmed by the observation of facts. 

 I take as FIRST EXAMPLE the length of the limb of the 

 leaf in Castanea vesca, Fagus silvatica and Betula alba. The 

 maximal values are distinctly different and characteristic of 

 each species. In the three mentioned species the limb of the 

 smallest leaves is very short, and since the three minimal values 

 converge towards the same limit (which is o), these values are 

 not characteristic.! 



I take the height h of the stem of the rye as SECOND 

 EXAMPLE. In the ripe seed h is, as it were, infinitely small 

 (compared with its maximal value, which is 2 metres or there- 

 about). In the course of the germination and later on h in- 

 creases, passing through a series of successive values h-^, h^, h^. 

 ... Its growth may be stopped in any state whatever of its 

 development, when the value h^, or h^, or A3 ... is reached. 

 Since many (practically all) other Gramineoe (for instance, Poa 



' The smallest leaves are to be looked for a short time after the buds have 

 expanded because they often disappear later on. 



