MEASUREMENT OF VARIABLE PROPERTIES 165 



4th Series 5th Series 6th Series 



Drawings 

 Minimum 

 Mean 

 Maximum 



1601-2000 



14 



28-83 

 42 



2001-2400 



14 



27-69 



42 



1201-1600 



15 



28-16 



43 

 4th + 5th + 6th series (1200 drawings) : 



Minimum : Observed 14 Calculated 12 



Mean: ,, 28-23 .. 28 



Maximum : „ 43 „ 44 



Third Experiment : Similar to the first, with 13 cards of one 

 suit. Cards drawn simultaneously 4 by 4. The extreme facial 

 values are 10 ( = 1 + 2 + 3 + 4) ^^^ 4^ (10 + 11 + 12 + 13) . Curve 

 symmetrical. Arithmetical mean, 28. Result (facial values) : 



7th Series 



8th Series 



9th Series 



Drawings . . . 2401-2800 2801-3200 3201-3600 



Minimum ... 11 10 10 



Mean . . . 27-62 27-42 28-04 



Maximum ... 46 44 44 



7th + 8th + 9th series (1200 drawings) : 



Minimum : Observed 10 Calculated 10 

 Mean : „ 27-69 ,, 28 



Maximum : ,, 46 ,,46 



REMARKS : In each series of 1200 drawings and even in 

 almost all the series of 400 drawings the mean value has been 

 discovered in a satisfactory way. 



With regard to the extreme values, the result is misatisfactory 

 in the first experiment (this was expected, the frequency of the 

 extremes being very small) ; the approximation is closer in the 

 second experiment. In the third experiment both extremes 

 have been found exactly. The exceptional wide range of 

 variation in the first experiment being taken into account, we 

 may conclude from the above result that the discovery of the 

 extreme values, with a sufficient degree of approximation, is 

 practically within the reach of observation. 



§ 118.— NINETEENTH EXAMPLE. VARIATION 

 CURVE OF A PROPERTY OF A LIVING SPECIES (BIO- 

 LOGICAL VARIATION CURVE).— Starting from a very 

 simple example (sphere, § 91) in which all the possible effects 

 of chance are reduced to one event, we have been brought step 



