EVOLUTION 401 



mean value of its array) is w., = M., +j', where/ = ,rx ra^^jcr^. 

 Thus the value of ;«., is given by — 



w, = M., + r ^' (w, - AL). 



Such an equation is termed a regression equation, and 

 ra-^jcT^ is termed the coefficient of regression. In words : 

 the probable deviation of a second organ from its mean is 

 the product of the coefficient of regression into the 

 observed deviation of the first or^an from its mean. 

 When the regression is perfect, i.e. vi.y = Mo, the co- 

 efficient of regression, or the correlation r, must vanish. 

 When the correlation is perfect, or r= i, then the 

 regression is least, or in.^ differs most from M2 (see p. 



396). 



Correlation enables us to reconstruct from one organ 

 the probable value of a second, or in the case of the full 

 mathematical theorythevalueof one organ from any number 

 of known organs. Thus if we pick up the femur, tibia, 

 humerus, radius of a prehistoric man, or one or more such 

 bones, we can reconstruct his probable stature, or from a 

 single bone alone we can reconstruct other parts of the 

 skeleton. Nowadays the numerical value of the correla- 

 tion is known for a considerable number of characters in 

 man : skeleton — long bones, skull, hand, — stature, weight, 

 physique, etc., for some organs in Crustacea and fishes, 

 and for the parts of a few plants. But all work in 

 this direction is the work of the last few years, and the 

 boastful statement of Cuvier that " commencing our 

 investigation by a careful survey of any one bone by 

 itself, a person who is sufficiently master of the laws of 

 organic structure may, as it were, reconstruct the whole 

 animal to which that bone belonged," was idle in 18 12, 

 and is only a very partial truth to-day. 



I close this section with a table of a few coefficients of 

 correlation in man, so that the reader may have some 

 idea of the extent to which characters and organs in one 

 type of life are correlated. 



26 



