MEASUREMENT OF VARIABLE PROPERTIES 161 



body.) From this similitude QUETELET has deduced that 

 variation in the living beings is governed by chance (law of 

 errors). (See §§ 32 and 118.) 



From a mathematical standpoint, a curve of errors obtained 

 by measuring a density (§ 108) and a typical variation curve 

 (height of the prisms, § 115 ) are similar. From the standpoint 

 of the naturalist, however, two fundamental differences exist 

 between them. 



A first difference exists with regard to the significance of the 

 mean value. When the density of a solid a is determined by 

 means of a series of measurements, two groups of causes 



■m. 



Fig. 24. — Symmetrical variation curve (a+b)'" 



(forces) are at play : (i) a definite simple cause, the density of 

 a; (2) a variable combined cause (chance). The mean value 

 represents a definite something : it is the measure of a property 

 of a — i.e. a physical constant (§ 108) ; the errors (deviations 

 from the mean) are produced by chance.^ In the example of 

 the prisms it is possible to calculate a mean (its value is 25 cm.), 

 but this does not represent a definite constant, a property of 

 the objects (compound prisms) under consideration. Here the 

 mean is produced by the variable combined cause (chance). 

 Its value depends (i) on the simple causes which have been 

 combined (0 = 2 cm. ; 6 = 3 cm. ; see § 115) ; (2) on the fre- 

 quency of those causes {a = \; b = \) ; (3) on the number of 

 causes (simple events) which have been combined {n ; in the 



1 In other words, each observed value consists of the constant + an enof. 



