164 THE QUANTITATIVE METHOD IN BIOLOGY 



(52 cards, 4 suits) the following facial values (without dis- 

 tinguishing the suits) : — whole numbers i to 10 ; Knave = 11 ; 

 Queen = 12 ; King = 13. 



Drawing from a complete pack 4 cards simultaneously at 

 random, I ascertain the sum of their facial values (example : 

 ace + 7 + 9 + queen = 29). This experiment is repeated a 

 number of times. (After each drawing the 4 cards are put 

 back into the pack and this is shuffled before the next 

 drawing.) 



If we take only the compound facial values into account 

 (the suits being overlooked), all the possible compound events 

 (combinations of 4 cards) are reduced to 49 events, measured 

 by the whole numbers from 4 (4 aces) to 52 (4 kings). Each 

 of both extreme values may be realized only in one way. 



The 49 different values may be looked upon as representing 

 49 kinds of specimens of a certain species, variable in a certain 

 property, which is measured in each specimen (4 cards) by 

 the facial value. The variation curve is S5anmetrical : its 

 hump (most frequent value) coincides with 28, which is also 

 the arithmetical mean. 



In this example the range of variation is very wide and the 

 probability of discovering the extremes by a series of measure- 

 ments (drawings) is small. Therefore the experimental dis- 

 covery of the extremes is more difficult, I think, than in the 

 majority of the living subspecies or monotypic species. I 

 have carried out 1200 drawings of 4 cards divided into three 

 series of 400 successive drawings each. Result (facial values) : 



Second Experiment : Similar to the first, the cards i, 2, 12 and 

 13 of each suit being suppressed. The cards are drawn simul- 

 taneously 4 by 4. The extreme facial values (4 cards) are 12 

 (4 X 3) and 44 (4 knaves) . Curve symmetrical. Arithmetical 

 mean, 28. Result : 



