148 THE QUANTITATIVE METHOD IN BIOLOGY 



§109. — THIRTEENTH EXAMPLE: THE MEASURE 

 MENT OF A GIVEN WEIGHT OF A CERTAIN SUBSTANCE 

 —1 want a certain number of portions of sand, each weighing 

 200 gr. A first operator A, inexperienced and disposing 

 of a mediocre balance, is trusted with the necessary work 

 A weight of 200 gr. being placed in one of the scales of his 

 balance, he weighs successively a ist, a 2nd ... a ^th portion 

 of sand, each portion being kept separately. A second skilled 

 operator B, disposing of a good balance, is trusted with the veri- 

 fication of the work of A. Let us suppose that B does not 

 commit any error. He will find that almost all or aU the portions 

 of sand weigh more or less than 200 gr. The figures observed 

 by B are comparable to those observed in the preceding 

 example (density, § 108). If we construct the curve of the 

 errors (variation curve of the portions of sand) committed by A 

 and discovered by B, we see that they are distributed accord- 

 ing to the rule expressed by {a + 6)», just as in the preceding 

 example, the mean value being (approximately) 200 gr. (and 

 the extreme errors being indefinite). 



Here again we discern : 



(i) One simple cause/which is measured by the mean (200 gr.). 



(2) Chance, which is variable and brings about errors 

 (deviations). 



From a mathematical standpoint both examples (§§ 108 and 

 109) are identical. For the naturalist, however, they are dis- 

 similar because the mean value does not represent the same thing 

 in both. 



In the first example we have discovered a certain property 

 (density) of a measured by the mean value. In the second 

 example the mean value represents something quite distinct 

 from any property of the sand. It represents, indeed, a cause 

 or force (the weight of 200 gr. in one scale of the balance) external 

 with regard to the substance sand and acting continually and 

 uniformly through the whole time during which the successive 

 portions {individuals) of sand were taking birth. 



Using biological language, we might say that the mean 

 value (200 gr.) and the variation curve discovered by the verifier 

 B express the conditions of existence which prevailed while 

 the individuals (portions) of the species sand were developing.^ 

 These conditions are : (i) one simple cause ; (2) chance (variable 

 combined cause). 



§ 110.— FOURTEENTH EXAMPLE: A MIXTURE OF 

 TWO VOLUMES OF WATER.— We dispose of two pipettes 

 A and B. The pipette A is narrow, exactly graduated, each 



1 More strictly, while the primordium weight of the individuals was reach- 

 ing its state of final equilibrium (adult state). (See § 45.) 



