172 THE QUANTITATIVE METHOD IN BIOLOGY 



discovered as often as the conditions under which the measure- 

 ments are made are various enough to include 0°. It is a 

 constant of the race. 



I have taken temperature as example. The same rule holds, 

 in general/ for the various factors mentioned in the list, p. 167. 

 For each factor there are two limits and an optimum. We 

 know from experience, for instance, for the substances nitrogen, 

 phosphorus, potassium, etc., that the development of an 

 organism is impossible when they are not available in sufficient 

 quantity and that, on the other hand, too high a dose becomes 

 detrimental and even poisonous. Every gardener knows that 

 the development of many species (for instance, a number of 

 ferns) is impossible in a sunny place or in a place which is too 

 dry, and also when the intensity of light is too weak or the 

 watering too abundant ; etc., etc. 



The absolute values of the minimum, optimum and maxi- 

 mum (values m-o-M) of each factor (with reference to each 

 primordium and to the individual considered as a whole) are the 

 expression of properties of each living species. They are, how- 

 ever, variable within the limits of one species. The chief 

 cause of this variability is the fact that the values m-o-M of 

 each factor are more or less modified by the variation of other 

 factors. 



We know, for instance, that the optimal value of the tension 

 of carbon dioxide in the atmosphere depends on the intensity of 

 light. The m-o-M of temperature are modified (in an intricate 

 way) by the available quantity of water. Potassium, calcium, 

 phosphorus, etc., are absorbed by each species in certain pro- 

 portions : if the available quantity of one substance a (for 

 instance, potassium) is modified, the absorption of the others 

 b, c . . . is modified in its turn, and one would therefore expect 

 that any variation of a would result in a variation of the m-o-M 

 oi b, c. . . . Although our knowledge of the relations alluded to 

 is still incomplete, we may assume that they are very numerous 

 and intricate. Therefore the exact experimental determination 

 of the values m-o-M of a given cause (factor) with regard to a 

 given primordium of a given species is an exceedingly com- 

 plicated problem.^ 



In each specimen the numerous factors enumerated (p. 167) 

 are combined in a certain way. The diversity of the combina- 

 tions brings about variation of the primordia, each primordium 

 being variable according to its specific energy. 



' Perhaps with certain restrictions, which are unimportant for our subject. 



^ Physicists and astronomers are faced with questions which are almost 

 as involved as the biological problems alluded to. I recall the numerous 

 corrections which have to be made in order to deduce from the height of the 

 mercury in a barometer the exact pressure of the atmosphere. This is a 

 comparatively simple example. 



