MEASUREMENT OF VARIABLE PROPERTIES 149 



division being ooi c.c. The pipette B is wider, graduated in 

 such a way that each division is o-i c.c. It is supposed that 

 it is possible to measure exactly a certain volume of water by 

 means of A , whereas errors are unavoidable when B is used. 



By means of A we measure exactly a volume of water of 

 10 c.c, and an equal volume is measured rather inexactly by 

 means of B. Both volumes are united into one portion. The 

 same operation is repeated a number of times, each portion 

 being kept separately. 



Thereafter all the portions are measured exactly. From the 

 collected figures we may calculate the mean volume (approxi- 

 mately 20 c.c). We may construct the curve of errors (varia- 

 tion curve of the individuals) ; the limits of error are indefinite. 



On the whole, this example recalls the preceding one (sand, 

 § 109). There is, however, a difference between both with 

 regard to the significance of the mean value. In the case of 

 the sand, the mean value represents one simple invariable cause 

 (200 gr.) ; in the case of the water the mean (20 c.c) represents 

 the resultant ^ of two simple causes, which have acted in each 

 of the successive operations. One of these causes (pipette A) 

 is invariable ; the other cause (pipette B) is also invariable, but 

 its effects have been continually augmented or diminished by 

 chance. 



Looking upon the portions of water as being specimens of 

 the species water of which we have measured one variable 

 property (volume), we may say that the observed values re- 

 present the conditions of existence under which the specimens 

 have been developed. The mean value and the variation curve 

 are independent of any property whatever of the water. 



In the previously discussed examples, in which there is 

 question of a sphere, coins, halls in an urn, dice, and in the example 

 of the typical Mendelian hybrids, chance produces a limited 

 number of simple events (heads or tails, seeds round or wrinkled, 

 etc.). Chance is acting through a machinery which may be 

 brought into a limited number of states of equilibrium. The 

 observed effects depend on certain properties (specific energy) 

 of the objects under consideration. In the two last examples, 

 in which the machinery consists of sand or water, the observed 

 and measured facts are independent of the machinery through 

 which chance is acting. Each figure is a direct effect of external 

 causes. The variation is unlimited, because it depends merely 

 on the variation of chance, which has no limits. 



§ 111.— FIFTEENTH EXAMPLE : A MIXTURE OF AN 

 ACID AND AN ALKALINE LIQUID.— We dispose of two 



1 In this example, the resultant is simply the axithmetical sum of both causes 

 under consideration (10 + 10). 



