PART VI 



THE, MEASUREMENT OF VARIABLE PROPERTIES OF 

 ANIMALS AND PLANTS. SIMPLE NOTIONS OF 

 PROBABILITY (FREQUENCY). 



§ 90. — The application of the quantitative method to the 

 study of animals and plants is almost entirely based upon the 

 theory of probabiUty (theory of chance) . This theory has been 

 applied to biological problems along two different lines : by 

 QUETELET (1846) and his followers (see § 32) to the measure- 

 ment of variable properties and by MENDEL (1866) to the 

 study of heredity (see § 33). 



The knowledge of the principles of this part of mathematical 

 science is indispensable to any biologist who wants to investi- 

 gate quantitatively the properties of hving beings. In the 

 works in which the theory of probability is expounded we find 

 a large amoxmt of mathematical knowledge, whereas facts and 

 realities are mentioned in a few words only and looked upon as 

 being of secondary importance. Such works do not answer 

 the needs of the biologist ; they are beyond his reach. This is a 

 fact ... a reality by which the progress of biology is seriously 

 hampered. 



The path followed by the theory of probability is slippery 

 ground. From a biological standpoint the theory of chance 

 (frequency) ought to be built up by continual association 

 of observation, measurement, comparison, experiment and 

 mathematical deduction. A conclusion, drawn from exact 

 figures by means of an irreproachable mathematical argu- 

 ment may be delusive ! Therefore any conclusion ought to be 

 VERIFIED by the quantitative observation of more facts. 



Many biologists seem to beUeve that the quantitative method 

 is in relation with certain theoretical views about heredity, 

 variation, selection, origin of species, etc. ; that the object of 

 the method is to DEMONSTRATE the reahty of certain 

 principles. This conception of the question is erroneous.^ I 

 want to emphasize once more that the object of the quantita- 

 tive method is not to demonstrate something, but to DIS- 

 COVER facts and reaUties which it is impossible to discover in 



iThe same mathematical principles have been applied by MENDEL to 

 the study of the hybrids and by QUETELET to the measurement of the 

 stature of man. 



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