10 



Galton's Law of averages. In the current 

 text-books on genetics and plant physiol- 

 ogy^^ the following ingenious explanation 

 of Galton's Law is given. Assume that the 

 size of a bean is determined by only five 

 variables, each of which must occur in one 

 of two categories ; in one case the size of the 

 bean will be increased by one unit of size, 

 in the other it will be decreased by the same 

 amount. Considering all the possible per- 

 mutations of these five variables, we get the 

 following arrangement: 



The beans will be of six sizes, +5, -j- 3, 

 -|- 1, — 1, — 3, — 5, and out of a very large 

 number (n), n/32 will be +5, 5n/32 will 

 be + 3, lOn/32 will be + 1, 10^/32 will be 



— 1, 5?i/32 will be — 3, and n/S2 will be 



— 5. The six sizes are in the ratio 

 1:5:10:10:5:1. If we plot the sizes of 

 the various classes of beans against the fre- 



12 E. Baur, ' ' Einf iihrung in die experimentelle 

 Vererbungslehre, " 2*« Auflage, 1914. L. Jost, 

 "Vorlesungen iiber Pflanzenphysiologie, " 3'* Au- 

 1913. 



