32 THE QUANTITATIVE METHOD IN BIOLOGY 



calculation. There is often a complicated relation between a 

 given mean value and the thing which it is regarded to express.^ 

 This relation is very diverse, according to the case under con- 

 sideration, and it is sometimes very difficult or even impossible 

 to make it clear. When the significance of a mean value is 

 vague, any figure deduced from it is still more vague (this 

 question is expounded in Part VI., especially in §§ 109, no, 116). 

 In biometrical literature some examples of a SECOND weak 

 point are found. When we have collected a series of figures 

 by measuring a property in a number of specimens, we are 

 tempted to believe that the observed differences depend on 

 chance (according to the principle laid down by QUETELET) and 

 our calculations are based upon this belief. This is, however, not 

 always the case. There are sometimes between the collected 

 figures certain relations which are not governed by the laws of 

 chance (probability), but by the laws of gradation. If chance 

 and gradation are not distinguished, confusion is inevitable. 

 This difficulty has not always been avoided. (See Part VIII. 

 See also variation steps, § 127.) 



§ 33. — APPLICATION OF THE QUANTITATIVE 

 METHOD ON THE STUDY OF HYBRIDIZATION. 

 MENDELISM. — The use of the quantitative method in bio- 

 logical science has been initiated along a third line by 

 GREGORIUS MENDEL in 1865-1866.2 This author chose 

 Pisum sativum for his subject. Varieties (subspecies) in culti- 

 vation are distinguished by striking characters recognizable 

 without trouble. The plants are habitually self-fertihzed. 

 Following his idea that the heredity of each character (property) 

 must be separately investigated, he chose a number of pairs 

 of properties, and made crosses between subspecies differing 

 markedly in respect of one pair of properties. MENDEL took, 

 for instance, two subspecies of which one was tall, being 6-7 

 feet high, and the other was dwarf, f to i| feet (the pair of 

 properties is here tallness-dwarfness). 



These two were crossed together. The cross-bred seeds 

 thus produced grew into plants which were always tall, having 

 a height not sensibly different from that of the pure tall sub- 

 species. I call these plants F^ (first fiUal generation). The 



1 In other words, a mean value is often an indirect expression, not the direct 

 expression of a reality. 



2 See W. BATESON, MendeVs Principles 0/ Heredity (Cambridge University 

 Press, 1909 ) ; xiv. + 396 pp., with three portraits of MENDEL, 6 coloured plates 

 and 33 figures. This book contains a very instructive and complete account 

 of the subject, a biography of MENDEL and a translation of his memoir, 

 which was published in Verhandl. NaturJ. Ver. in Briinn {Abhandlungen, vi. 

 1865) and appeared in 1866. 



The short and simplified account given in the present paragraph is borrowed 

 from BATESON (pp. 8-1 1) and MENDEL (BATESON, loc. cit., pp. 332-335). 



