112 



How hâve we to picture to oursclves the way in which 

 just this distribution and no other has originated? 



Let us begin by imagining that on a certain date (say 

 1 May), shortly after the time of blossoming, we isolate 

 a great number p of unripe berries of equal diameter. On 

 that date there will fall a certain quantity of rain which 

 causes some growth of the berries. The gain in diameter 

 will not be the same, however, for ail the berries. Some 

 of the shrubs will be much exposed to the rain, others 

 will be more or less screened. The différence of the soil 

 will be cause that some plants will dérive a greater benifit 

 from the same quantity of water than others. Varions 

 causes in the plants themselves will favour some of the 

 fruits more than others etc. etc. 



Most probably, ail the fruits will gain in diameter. For 

 the présent we will neglect the mean growth of the p 

 berries, however, and confine our attention to the déviations 

 from this mean growth. 



Part of thèse déviations must necessarily be positive 

 while another part must be négative. If we suppose, as 

 the simplest, though certainly by no means probable case, 

 thath half of the berries grow in diameter: mean growth 

 + A, while for the other half this quantity is: mean 

 growth — A, then, owing to the rain on 1 May, and to 

 this cause alone, we would hâve at the end of that date: 



a. l-p berries whose diameters deviate — A from the mean, 



b. \p „ „ „ „ + A 



Now consider a second cause of déviation in opération 



at the same or at some other time. 



For the sake of clearness let us take the sunshine of 

 the 2"*^ of May. This sunshine will be profitable to the 

 berries, but not for ail in the same degree. We will 

 suppose that its effect will be the same as that of the 

 rain of the preceding day, that is to say, that it will 

 cause half of the fruits to grow in diameter A more, half 



